Low-dose cryo electron ptychography via non-convex Bayesian optimization
Electron ptychography has seen a recent surge of interest for phase sensitive imaging at atomic or near-atomic resolution. However, applications are so far mainly limited to radiation-hard samples because the required doses are too high for imaging biological samples at high resolution. We propose the use of non-convex, Bayesian optimization to overcome this problem and reduce the dose required for successful reconstruction by two orders of magnitude compared to previous experiments. We suggest to use this method for imaging single biological macromolecules at cryogenic temperatures and demonstrate 2D single-particle reconstructions from simulated data with a resolution of \SI{7.9{\angstrom at a dose of \SI{20{\elementarycharge^-\per\angstrom^2. When averaging over only 15 low-dose datasets, a resolution of \SI{4{\angstrom is possible for large macromolecular complexes. With its independence from microscope transfer function, direct recovery of phase contrast and better scaling of signal-to-noise ratio, cryo-electron ptychography may become a promising alternative to Zernike phase-contrast microscopy.
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@article{li_ptychographic_2014,
  title = {Ptychographic Inversion via {{Wigner}} Distribution Deconvolution: {{Noise}} Suppression and Probe Design},
  volume = {147},
  issn = {0304-3991},
  shorttitle = {Ptychographic Inversion via {{Wigner}} Distribution Deconvolution},
  doi = {10.1016/j.ultramic.2014.07.004},
  abstract = {We reconsider the closed form solution of the ptychographic phase problem called the Wigner Distribution Deconvolution Method (WDDM), which has remained discarded for twenty years. Ptychographic reconstruction is nowadays always undertaken by iterative algorithms. WDDM gives rise to a 4 dimensional data cube of all the relative phases between points in the diffraction plane. Here we demonstrate a novel method to use all this information, instead of just the small subset used in the original `stepping out' procedure developed in the 1990s, thus greatly suppressing noise. We further develop a method for designing an improved probe (illumination function) to further decrease noise effects during the deconvolution division. Combining these two with an iterative procedure for the deconvolution, which avoids the usual difficulty of a divide by a small number, we show in model calculations that WDDM competes well with the modern conventional iterative methods like ePIE (the extended Ptychographical Iterative Engine).},
  timestamp = {2017-01-13T09:31:31Z},
  urldate = {2015-09-08},
  journal = {Ultramicroscopy},
  author = {Li, Peng and Edo, Tega B. and Rodenburg, John M.},
  month = dec,
  year = {2014},
  note = {00007},
  keywords = {cdi,imaging,lensless imaging,lowdose,ptychography},
  pages = {106--113}
}

@article{Hue2010,
  title = {Wave-Front Phase Retrieval in Transmission Electron Microscopy via Ptychography},
  volume = {82},
  issn = {1098-0121},
  doi = {10.1103/PhysRevB.82.121415},
  timestamp = {2017-01-01T14:38:23Z},
  number = {12},
  journal = {Phys. Rev. B},
  author = {H{\"u}e, F. and Rodenburg, J. M. and Maiden, a. M. and Sweeney, F. and {\noopsort{midgley}}a. Midgley, P.},
  month = sep,
  year = {2010},
  note = {00044},
  keywords = {cdi,Electron,electron microscopy,imaging,lensless imaging,lowdose,particle,ptychography},
  pages = {121415},
  file = {Hüe et al_2010_Wave-front phase retrieval in transmission electron microscopy via ptychography.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Hüe et al_2010_Wave-front phase retrieval in transmission electron microscopy via ptychography.pdf:application/pdf;Hüe et al_2010_Wave-front phase retrieval in transmission electron microscopy via ptychography.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Hüe et al_2010_Wave-front phase retrieval in transmission electron microscopy via ptychography2.pdf:application/pdf},
  mendeley-tags = {cdi,electron microscopy,ptychography}
}

@article{Enders2014,
  title = {Ptychography with Broad-Bandwidth Radiation},
  volume = {104},
  issn = {0003-6951},
  doi = {10.1063/1.4874304},
  timestamp = {2017-01-10T11:29:56Z},
  number = {17},
  journal = {Appl. Phys. Lett.},
  author = {Enders, B and Dierolf, M and Cloetens, P and Stockmar, M and Pfeiffer, F and Thibault, P},
  month = apr,
  year = {2014},
  note = {00019},
  keywords = {cdi,imaging,lensless imaging,lowdose,partial coh.,particle,photon,ptychography,x-ray},
  pages = {171104},
  file = {Enders et al_2014_Ptychography with broad-bandwidth radiation.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Enders et al_2014_Ptychography with broad-bandwidth radiation.pdf:application/pdf}
}

@article{lubk_phase-space_2015,
  title = {Phase-Space Foundations of Electron Holography},
  volume = {92},
  doi = {10.1103/PhysRevA.92.033844},
  abstract = {We present a unified formalism for describing various forms of electron holography in quantum mechanical phase space including their extensions to quantum-state reconstructions. The phase-space perspective allows for taking into account partial coherence as well as the quantum mechanical detection process typically hampering the unique reconstruction of a wave function. We elaborate on the limitations imposed by the electron optical elements of the transmission electron microscope as well as the scattering at the target. The results provide the basis for vastly extending the scope of electron holographic techniques towards analyzing partially coherent signals such as inelastically scattered electrons or electron pulses used in ultrafast transmission electron microscopy.},
  timestamp = {2017-01-13T09:31:31Z},
  number = {3},
  urldate = {2015-09-29},
  journal = {Phys. Rev. A},
  author = {Lubk, A. and R{\"o}der, F.},
  month = sep,
  year = {2015},
  note = {00000},
  keywords = {holography,imaging,lensless imaging,lowdose,phase space,theory},
  pages = {033844},
  file = {Lubk_Röder_2015_Phase-space foundations of electron holography.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Lubk_Röder_2015_Phase-space foundations of electron holography.pdf:application/pdf}
}

@article{Thibault2013b,
  title = {Reconstructing State Mixtures from Diffraction Measurements},
  volume = {494},
  issn = {1476-4687},
  doi = {10.1038/nature11806},
  abstract = {Progress in imaging and metrology depends on exquisite control over and comprehensive characterization of wave fields. As reflected in its name, coherent diffractive imaging relies on high coherence when reconstructing highly resolved images from diffraction intensities alone without the need for image-forming lenses. Fully coherent light can be described adequately by a single pure state. Yet partial coherence and imperfect detection often need to be accounted for, requiring statistical optics or the superposition of states. Furthermore, the dynamics of samples are increasingly the very objectives of experiments. Here we provide a general analytic approach to the characterization of diffractive imaging systems that can be described as low-rank mixed states. We use experimental data and simulations to show how the reconstruction technique compensates for and characterizes various sources of decoherence quantitatively. Based on ptychography, the procedure is closely related to quantum state tomography and is equally applicable to high-resolution microscopy, wave sensing and fluctuation measurements. As a result, some of the most stringent experimental conditions in ptychography can be relaxed, and susceptibility to imaging artefacts is reduced. Furthermore, the method yields high-resolution images of mixed states within the sample, which may include quantum mixtures or fast stationary stochastic processes such as vibrations, switching or steady flows.},
  timestamp = {2017-01-10T11:29:57Z},
  number = {7435},
  journal = {Nature},
  author = {Thibault, Pierre and Menzel, Andreas},
  month = feb,
  year = {2013},
  note = {00135},
  keywords = {cdi,imaging,lensless imaging,phase space,theory,tomography},
  pages = {68--71},
  file = {nature11806-s1.pdf:/media/philipp/My Book/Dropbox/mpapers/nature11806-s1.pdf:application/pdf;Thibault_Menzel_2013_Reconstructing state mixtures from diffraction measurements.pdf:/media/philipp/My Book/Dropbox/mpapers/Thibault_Menzel_2013_Reconstructing state mixtures from diffraction measurements.pdf:application/pdf},
  pmid = {23389541}
}

@article{Ix1942,
  title = {Phase Contrast, a New Method for the Microscopic Observation of Transparent Objects Part {{II}}},
  doi = {10.1016/S0031-8914(42)80079-8},
  timestamp = {2017-01-11T10:01:22Z},
  number = {7},
  journal = {Physica},
  author = {Ix, Physica and Zernike, F and Ii, Part and Contrast, Phase and Rayleigh, The},
  year = {1942},
  note = {00000},
  keywords = {Electron,imaging,lens imaging,lowdose,methods,particle,phase contrast,tem},
  pages = {686--698}
}

@article{Humphry2012,
  title = {Ptychographic Electron Microscopy Using High-Angle Dark-Field Scattering for Sub-Nanometre Resolution Imaging},
  volume = {3},
  doi = {10.1038/ncomms1733},
  timestamp = {2017-01-10T11:29:58Z},
  journal = {Nat. ldots},
  author = {Humphry, MJ and Kraus, B and Hurst, AC},
  year = {2012},
  note = {00123},
  keywords = {algorithms,Electron,electron microscopy,imaging,lensless imaging,Low-dose ptychography,particle,phase retrieval,ptychography,shift variance},
  pages = {730--737},
  file = {Humphry et al_2012_Ptychographic electron microscopy using high-angle dark-field scattering for.pdf:/media/philipp/My Book/Dropbox/mpapers/Humphry et al_2012_Ptychographic electron microscopy using high-angle dark-field scattering for.pdf:application/pdf},
  mendeley-tags = {cdi,electron microscopy,ptychography}
}

@article{maiden_quantitative_2015,
  title = {Quantitative Electron Phase Imaging with High Sensitivity and an Unlimited Field of View},
  volume = {5},
  issn = {2045-2322},
  doi = {10.1038/srep14690},
  abstract = {Scientific Reports is an online, open access journal from the publishers of Nature. The 2014 Impact Factor for Scientific Reports is 5.578.},
  language = {en},
  timestamp = {2017-01-10T11:29:59Z},
  urldate = {2015-10-12},
  journal = {Scientific Reports},
  author = {Maiden, A. M. and Sarahan, M. C. and Stagg, M. D. and Schramm, S. M. and Humphry, M. J.},
  month = oct,
  year = {2015},
  note = {00005},
  keywords = {cdi,Electron,imaging,lensless imaging,Low-dose ptychography,microscope,particle,ptychography,setups},
  pages = {14690},
  file = {Maiden et al_2015_Quantitative electron phase imaging with high sensitivity and an unlimited.pdf:/media/philipp/My Book/Dropbox/mpapers/Maiden et al_2015_Quantitative electron phase imaging with high sensitivity and an unlimited.pdf:application/pdf;Maiden et al_2015_Quantitative electron phase imaging with high sensitivity and an unlimited2.pdf:/media/philipp/My Book/Dropbox/mpapers/Maiden et al_2015_Quantitative electron phase imaging with high sensitivity and an unlimited2.pdf:application/pdf}
}

@article{maiden_annealing_2012,
  title = {An Annealing Algorithm to Correct Positioning Errors in Ptychography},
  volume = {120},
  issn = {0304-3991},
  doi = {10.1016/j.ultramic.2012.06.001},
  abstract = {Ptychography offers the possibility of improving the resolution of atomic-scale (electron and X-ray) transmission microscopy without any of the demands of high quality lenses: its resolution is in theory only limited by the effective synthetic numerical aperture determined by the angular size of the detector. However, it has been realised experimentally that a major weakness of the approach is that the obtainable resolution is only as good as the accuracy to which the illuminating beam can be moved relative to the specimen. This can be catastrophic in the electron case because of thermal drift and hysteresis in the probe scan coils. We present here a computationally efficient extension of the `ePIE' ptychographic reconstruction algorithm for correcting these errors retrospectively. We demonstrate its effectiveness using simulations and results from visible light and electron beam experiments that show it can correct positioning errors tens of times larger than the pixel size in the resulting image.},
  timestamp = {2017-01-10T11:30:00Z},
  urldate = {2015-02-26},
  journal = {Ultramicroscopy},
  author = {Maiden, A. M. and Humphry, M. J. and Sarahan, M. C. and Kraus, B. and Rodenburg, J. M.},
  month = sep,
  year = {2012},
  note = {00068},
  keywords = {cdi,coherent diffractive imaging,imaging,lensless imaging,lowdose,my papers,Phase retrieval,Ptychography,ptychography},
  pages = {64--72}
}

@article{Zernike1942,
  title = {Phase Contrast, a New Method for the Microscopic Observation of Transparent Objects},
  timestamp = {2017-01-11T10:01:23Z},
  number = {7},
  url = {http://scholar.google.com/scholar?hl=en\&btnG=Search\&q=intitle:PHASE+CONTRAST+,+A+NEW+METHOD+FOR+THE+MICROSCOPIC+OBSERVATION+TRANSPARENT\#0},
  journal = {Physica},
  author = {Zernike, F},
  year = {1942},
  keywords = {imaging,lens imaging,lowdose,methods,phase contrast,tem},
  pages = {686--698}
}

@article{Putkunz2012,
  title = {Atom-{{Scale Ptychographic Electron Diffractive Imaging}} of {{Boron Nitride Cones}}},
  volume = {108},
  issn = {0031-9007},
  doi = {10.1103/PhysRevLett.108.073901},
  timestamp = {2017-01-10T11:30:01Z},
  number = {7},
  journal = {Phys. Rev. Lett.},
  author = {Putkunz, Corey T. and D'Alfonso, Adrian J. and Morgan, Andrew J. and Weyland, Matthew and Dwyer, Christian and Bourgeois, Laure and Etheridge, Joanne and Roberts, Ann and Scholten, Robert E. and {\noopsort{nugent}}a. Nugent, Keith and Allen, Leslie J.},
  month = feb,
  year = {2012},
  note = {00027},
  keywords = {Electron,imaging,lensless imaging,Low-dose ptychography,particle,ptychography},
  pages = {073901},
  file = {Putkunz et al_2012_Atom-Scale Ptychographic Electron Diffractive Imaging of Boron Nitride Cones.pdf:/media/philipp/My Book/Dropbox/mpapers/Putkunz et al_2012_Atom-Scale Ptychographic Electron Diffractive Imaging of Boron Nitride Cones.pdf:application/pdf}
}

@article{Thibault2008,
  title = {High-Resolution Scanning x-Ray Diffraction Microscopy.},
  volume = {321},
  issn = {1095-9203},
  doi = {10.1126/science.1158573},
  abstract = {Coherent diffractive imaging (CDI) and scanning transmission x-ray microscopy (STXM) are two popular microscopy techniques that have evolved quite independently. CDI promises to reach resolutions below 10 nanometers, but the reconstruction procedures put stringent requirements on data quality and sample preparation. In contrast, STXM features straightforward data analysis, but its resolution is limited by the spot size on the specimen. We demonstrate a ptychographic imaging method that bridges the gap between CDI and STXM by measuring complete diffraction patterns at each point of a STXM scan. The high penetration power of x-rays in combination with the high spatial resolution will allow investigation of a wide range of complex mesoscopic life and material science specimens, such as embedded semiconductor devices or cellular networks.},
  timestamp = {2017-01-10T11:30:02Z},
  number = {5887},
  journal = {Science},
  author = {Thibault, Pierre and Dierolf, Martin and Menzel, Andreas and Bunk, Oliver and David, Christian and Pfeiffer, Franz},
  month = jul,
  year = {2008},
  note = {00619},
  keywords = {cdi,Computer-Assisted,fourier analysis,hard x-ray,image processing,imaging,lensless imaging,lowdose,Microscopy,Microscopy: instrumentation,Microscopy: methods,Nanostructures,Nanostructures: ultrastructure,particle,photon,scattering,Small Angle,x-ray},
  pages = {379--82},
  file = {Thibault et al_2008_High-Resolution Scanning X-ray Diffraction Microscopy.pdf:/media/philipp/My Book/Dropbox/mpapers/Thibault et al_2008_High-Resolution Scanning X-ray Diffraction Microscopy.pdf:application/pdf;Thibault_et_al_2008_High-Resolution_Scanning_X-ray_Diffraction_Microscopy.pdf:/media/philipp/My Book/Dropbox/mpapers/Thibault_et_al_2008_High-Resolution_Scanning_X-ray_Diffraction_Microscopy.pdf:application/pdf},
  pmid = {18635796}
}

@article{Heel2005,
  title = {Fourier Shell Correlation Threshold Criteria Q},
  volume = {151},
  doi = {10.1016/j.jsb.2005.05.009},
  timestamp = {2014-12-27T19:33:37Z},
  journal = {J. Struct. Biol.},
  author = {Heel, Marin Van and Schatz, Michael},
  year = {2005},
  note = {00000},
  keywords = {cryo-em,fourier shell correlation,information,lowdose,resolution,resolution criteria,single particles,theory},
  pages = {250--262}
}

@article{kuhlbrandt_cryo-em_2014,
  title = {Cryo-{{EM}} Enters a New Era},
  volume = {3},
  copyright = {\textcopyright{} 2014, K{\"u}hlbrandt. This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.},
  issn = {2050-084X},
  doi = {10.7554/eLife.03678},
  abstract = {Advances in detector hardware and image-processing software have led to a revolution in the use of electron cryo-microscopy to determine complex molecular structures at high resolution.View Full Text
Advances in detector hardware and image-processing software have led to a revolution in the use of electron cryo-microscopy to determine complex molecular structures at high resolution.},
  language = {en},
  timestamp = {2017-01-10T11:30:03Z},
  urldate = {2015-03-18},
  journal = {eLife Sciences},
  author = {K{\"u}hlbrandt, Werner},
  month = aug,
  year = {2014},
  note = {00064},
  keywords = {<italic>E. coli</italic>,<italic>S. cerevisiae</italic>,cryo-em,cryo-EM,Human,image analysis,imaging,lens imaging,lowdose,methods,micoscopy,Single-particle analysis,tem},
  pages = {e03678},
  file = {Kühlbrandt_2014_Cryo-EM enters a new era.pdf:/media/philipp/My Book/Dropbox/mpapers/Kühlbrandt_2014_Cryo-EM enters a new era.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/357UWQN4/e03678.html:text/html}
}

@article{rodenburg_phase_1989,
  title = {The Phase Problem, Microdiffraction and Wavelength-Limited Resolution \textemdash{} a Discussion},
  volume = {27},
  issn = {0304-3991},
  doi = {10.1016/0304-3991(89)90009-0},
  abstract = {If it were possible to assign phase to the microdiffraction plane available in a scanning transmission electron microscope (STEM) extremely high spatial resolution would be possible, limited only by the electron wavelength as opposed to the poor electron optics of the objective lens. This paper reviews the phase problem with respect to the microdiffraction plane.},
  timestamp = {2017-01-10T11:30:04Z},
  number = {4},
  urldate = {2015-10-13},
  journal = {Ultramicroscopy},
  author = {Rodenburg, J. M.},
  month = may,
  year = {1989},
  note = {00018},
  keywords = {algorithms,Electron,imaging,lensless imaging,lowdose,Low-dose ptychography,particle,phase retrieval,ptychography},
  pages = {413--422},
  file = {Rodenburg_1989_The phase problem, microdiffraction and wavelength-limited resolution — a.pdf:/media/philipp/My Book/Dropbox/mpapers/Rodenburg_1989_The phase problem, microdiffraction and wavelength-limited resolution — a.pdf:application/pdf;Rodenburg_1989_The phase problem, microdiffraction and wavelength-limited resolution — a.pdf:/media/philipp/My Book/Dropbox/mpapers/Rodenburg_1989_The phase problem, microdiffraction and wavelength-limited resolution — a.pdf:application/pdf;Rodenburg_1989_The phase problem, microdiffraction and wavelength-limited resolution — a2.pdf:/media/philipp/My Book/Dropbox/mpapers/Rodenburg_1989_The phase problem, microdiffraction and wavelength-limited resolution — a2.pdf:application/pdf;ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/2FGAMXVM/0304399189900090.html:text/html}
}

@article{Ruskin2013,
  title = {Quantitative Characterization of Electron Detectors for Transmission Electron Microscopy},
  volume = {184},
  issn = {1047-8477},
  doi = {10.1016/j.jsb.2013.10.016},
  timestamp = {2017-01-10T11:30:05Z},
  number = {3},
  journal = {J. Struct. Biol.},
  author = {Ruskin, Rachel S and Yu, Zhiheng and Grigorieff, Nikolaus},
  year = {2013},
  note = {00071},
  keywords = {Direct electron detector,DQE,Electron,Low-dose ptychography,MTF,noise,particle,theory,Transmission electron microscopy},
  pages = {385--393},
  file = {Ruskin et al_2013_Quantitative characterization of electron detectors for transmission electron.pdf:/media/philipp/My Book/Dropbox/mpapers/Ruskin et al_2013_Quantitative characterization of electron detectors for transmission electron.pdf:application/pdf;Ruskin et al_2013_Quantitative characterization of electron detectors for transmission electron.pdf:/media/philipp/My Book/Dropbox/mpapers/Ruskin et al_2013_Quantitative characterization of electron detectors for transmission electron2.pdf:application/pdf}
}

@article{Clark2011,
  title = {Dynamic Sample Imaging in Coherent Diffractive Imaging.},
  volume = {36},
  issn = {1539-4794},
  shorttitle = {Opt. {{Lett}}.},
  doi = {10.1364/OL.36.001954},
  abstract = {As the resolution in coherent diffractive imaging improves, interexposure and intraexposure sample dynamics, such as motion, degrade the quality of the reconstructed image. Selecting data sets that include only exposures where tolerably little motion has occurred is an inefficient use of time and flux, especially when detector readout time is significant. We provide an experimental demonstration of an approach in which all images of a data set exhibiting sample motion are combined to improve the quality of a reconstruction. This approach is applicable to more general sample dynamics (including sample damage) that occur during measurement.},
  timestamp = {2017-01-10T11:30:06Z},
  number = {11},
  journal = {Opt. Lett.},
  author = {Clark, Jesse N. and Putkunz, Corey T. and Curwood, Evan K. and Vine, David J. and Scholten, Robert and McNulty, Ian and Nugent, Keith A. and Peele, Andrew G.},
  month = jun,
  year = {2011},
  note = {00016},
  keywords = {cdi,Image reconstruction techniques,imaging,lensless imaging,lowdose,partial coh.,particle,photon,x-ray,X-ray imaging,x-ray microscopy},
  pages = {1954--6},
  pmid = {21633413}
}

@article{Maiden2009,
  title = {An Improved Ptychographical Phase Retrieval Algorithm for Diffractive Imaging.},
  volume = {109},
  issn = {1879-2723},
  doi = {10.1016/j.ultramic.2009.05.012},
  abstract = {The ptychographical iterative engine (or PIE) is a recently developed phase retrieval algorithm that employs a series of diffraction patterns recorded as a known illumination function is translated to a set of overlapping positions relative to a target sample. The technique has been demonstrated successfully at optical and X-ray wavelengths and has been shown to be robust to detector noise and to converge considerably faster than support-based phase retrieval methods. In this paper, the PIE is extended so that the requirement for an accurate model of the illumination function is removed.},
  timestamp = {2015-06-22T18:20:56Z},
  number = {10},
  journal = {Ultramicroscopy},
  author = {Maiden, Andrew M and Rodenburg, John M},
  month = sep,
  year = {2009},
  keywords = {algorithms,Diffractive imaging,lowdose,phase retrieval,ptychography,shift variance},
  pages = {1256--62},
  file = {Maiden_Rodenburg_2009_An improved ptychographical phase retrieval algorithm for diffractive imaging.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Maiden_Rodenburg_2009_An improved ptychographical phase retrieval algorithm for diffractive imaging.pdf:application/pdf},
  mendeley-tags = {CDI,phase retrieval,ptychography},
  pmid = {19541420}
}

@article{Clark2014,
  title = {Dynamic {{Imaging Using Ptychography}}},
  volume = {112},
  issn = {0031-9007},
  doi = {10.1103/PhysRevLett.112.113901},
  timestamp = {2017-01-11T10:01:27Z},
  number = {11},
  journal = {Phys. Rev. Lett.},
  author = {Clark, Jesse N. and Huang, Xiaojing and Harder, Ross J. and Robinson, Ian K.},
  month = mar,
  year = {2014},
  note = {00004},
  keywords = {cdi,imaging,lensless imaging,lowdose,partial coh.,particle,photon,ptychography,x-ray},
  pages = {113901},
  file = {APS Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/97JJU68F/PhysRevLett.112.html:text/html}
}

@article{hoppe_trace_1982,
  title = {Trace Structure Analysis, Ptychography, Phase Tomography},
  volume = {10},
  issn = {0304-3991},
  doi = {10.1016/0304-3991(82)90038-9},
  abstract = {Three papers dedicated to the author elicit further comment stemming from his own engagement with the three topics- trace structure analysis, ptychography and phase tomography.},
  timestamp = {2017-01-10T11:30:07Z},
  number = {3},
  urldate = {2015-10-13},
  journal = {Ultramicroscopy},
  author = {Hoppe, W.},
  year = {1982},
  note = {00043},
  keywords = {Electron,imaging,lensless imaging,lowdose,Low-dose ptychography,particle,ptychography},
  pages = {187--198},
  file = {Hoppe_1982_Trace structure analysis, ptychography, phase tomography.pdf:/media/philipp/My Book/Dropbox/mpapers/Hoppe_1982_Trace structure analysis, ptychography, phase tomography.pdf:application/pdf;ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/A9BXJ3NC/0304399182900389.html:text/html}
}

@article{Thibault2009,
  title = {Probe Retrieval in Ptychographic Coherent Diffractive Imaging.},
  volume = {109},
  issn = {0304-3991},
  doi = {10.1016/j.ultramic.2008.12.011},
  abstract = {Ptychography is a coherent diffractive imaging method that uses multiple diffraction patterns obtained through the scan of a localized illumination on the specimen. Until recently, reconstruction algorithms for ptychographic datasets needed the a priori knowledge of the incident illumination. A new reconstruction procedure that retrieves both the specimen's image and the illumination profile was recently demonstrated with hard X-ray data. We present here the algorithm in greater details and illustrate its practical applicability with a visible light dataset. Improvements in the quality of the reconstruction are shown and compared to previous reconstruction techniques. Implications for future applications with other types of radiation are discussed.},
  timestamp = {2015-09-30T20:36:16Z},
  number = {4},
  journal = {Ultramicroscopy},
  author = {Thibault, Pierre and Dierolf, Martin and Bunk, Oliver and Menzel, Andreas and Pfeiffer, Franz},
  month = mar,
  year = {2009},
  keywords = {cdi,imaging,lensless imaging,lowdose,Phase retrieval,Ptychography},
  pages = {338--43},
  file = {Thibault et al_2009_Probe retrieval in ptychographic coherent diffractive imaging.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Thibault et al_2009_Probe retrieval in ptychographic coherent diffractive imaging.pdf:application/pdf},
  pmid = {19201540}
}

@article{Katkovnik2013a,
  title = {Sparse Ptychographical Coherent Diffractive Imaging from Noisy Measurements.},
  volume = {30},
  issn = {1520-8532},
  doi = {10.1364/JOSAA.30.000367},
  abstract = {Ptychography is a lensless coherent diffractive imaging that uses intensity measurements of multiple diffraction patterns collected with a localized illumination probe from overlapping regions of an object. An iterative algorithm is proposed that is targeted on optimal processing noisy measurements. The noise suppression is enabled by two instruments: first, the maximum-likelihood technique formulated for Poissonian (photon-counting) measurements, and, second, sparse approximation of the phase and magnitude of the object and probe. It is shown that the maximum-likelihood estimate of the wavefield at the sensor plane for noisy measurements is essentially different from the famous Gerchberg-Saxton-Fienup solution, where the magnitude of the estimate is replaced by the square root of the intensity measurement. The simulation experiments demonstrate the state-of-the-art performance of the proposed algorithm both numerically and visually.},
  timestamp = {2017-01-10T11:30:09Z},
  number = {3},
  journal = {J. Opt. Soc. Am. A. Opt. Image Sci. Vis.},
  author = {Katkovnik, Vladimir and Astola, Jaakko},
  year = {2013},
  note = {00004},
  keywords = {algorithms,cdi,imaging,lensless imaging,lowdose,phase retrieval,ptychography,shift variance},
  pages = {367--79},
  file = {josaa-30-3-367.pdf:/media/philipp/My Book/Dropbox/mpapers/josaa-30-3-367.pdf:application/pdf;Katkovnik_Astola_2013_Sparse ptychographical coherent diffractive imaging from noisy measurements.pdf:/media/philipp/My Book/Dropbox/mpapers/Katkovnik_Astola_2013_Sparse ptychographical coherent diffractive imaging from noisy measurements.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/3NGGCT75/abstract.html:text/html},
  pmid = {23456112}
}

@article{bian_fourier_2016,
  title = {Fourier Ptychographic Reconstruction Using {{Poisson}} Maximum Likelihood and Truncated {{Wirtinger}} Gradient},
  abstract = {Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample's high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for error removal. Results on both simulated data and real data captured using our laser FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use.},
  timestamp = {2017-01-10T11:30:20Z},
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1603.04746},
  primaryClass = {physics},
  urldate = {2016-03-19},
  url = {http://arxiv.org/abs/1603.04746},
  journal = {arXiv:1603.04746 [physics]},
  author = {Bian, Liheng and Suo, Jinli and Chung, Jaebum and Ou, Xiaoze and Yang, Changhuei and Chen, Feng and Dai, Qionghai},
  month = mar,
  year = {2016},
  note = {00003 arXiv: 1603.04746},
  keywords = {Computer Science - Computer Vision and Pattern Recognition,Low-dose ptychography,Physics - Optics},
  file = {Bian et al_2016_Fourier ptychographic reconstruction using Poisson maximum likelihood and.pdf:/media/philipp/My Book/Dropbox/mpapers/Bian et al_2016_Fourier ptychographic reconstruction using Poisson maximum likelihood and.pdf:application/pdf;Bian et al_2016_Fourier ptychographic reconstruction using Poisson maximum likelihood and.pdf:/media/philipp/My Book/Dropbox/mpapers/Bian et al_2016_Fourier ptychographic reconstruction using Poisson maximum likelihood and.pdf:application/pdf;Bian et al_2016_Fourier ptychographic reconstruction using Poisson maximum likelihood and.pdf:/media/philipp/My Book/Dropbox/mpapers/Bian et al_2016_Fourier ptychographic reconstruction using Poisson maximum likelihood and2.pdf:application/pdf;arXiv.org Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/33BJAQ3D/1603.html:text/html}
}

@article{Glaeser1999,
  title = {Review: Electron Crystallography: Present Excitement, a Nod to the Past, Anticipating the Future.},
  volume = {128},
  issn = {1047-8477},
  doi = {10.1006/jsbi.1999.4172},
  abstract = {From a modest beginning with negatively stained samples of the helical T4 bacteriophage tail, electron crystallography has emerged as a powerful tool in structural biology. High-resolution density maps, interpretable in terms of an atomic structure, can be obtained from specimens prepared as well-ordered, two-dimensional crystals, and the resolution achieved with helical specimens and icosahedral viruses is approaching the same goal. A hybrid approach to determining the molecular structure of complex biological assemblies is generating great interest, in which high-resolution structures that have been determined for individual protein components are fitted into a lower resolution envelope of the large complex. With this as background, how much more can be anticipated for the future? Considerable scope still remains to improve the quality of electron microscope images. Automation of data acquisition and data processing, together with the emergence of computational speeds of 10(12) floating point operations per second or higher, will make it possible to extend high-resolution structure determination into the realm of single-particle microscopy. As a result, computational alignment of single particles, i.e., the formation of "virtual crystals," can begin to replace biochemical crystallization. Since single-particle microscopy may remain limited to "large" structures of 200 to 300 kDa or more, however, smaller proteins will continue to be studied as helical assemblies or as two-dimensional crystals. The further development of electron crystallography is thus likely to turn increasingly to the use of single particles and small regions of ordered assemblies, emphasizing more and more the potential for faster, higher throughput.},
  timestamp = {2017-01-11T10:01:25Z},
  journal = {J. Struct. Biol.},
  author = {Glaeser, Robert M},
  year = {1999},
  keywords = {crystallography,diffraction,Electron,imaging,lensless imaging,lowdose,particle},
  pages = {3--14},
  file = {Glaeser_1999_Review.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Glaeser_1999_Review.pdf:application/pdf;ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/MPUQ2W7B/S1047847799941722.html:text/html},
  pmid = {10600552}
}

@article{li_multiple_2016,
  title = {Multiple Mode x-Ray Ptychography Using a Lens and a Fixed Diffuser Optic},
  volume = {18},
  issn = {2040-8986},
  doi = {10.1088/2040-8978/18/5/054008},
  abstract = {We employ a novel combination of a Fresnel lens and a diffuser for x-ray ptychography. The setup uses increased flux by enlarging the width of the coherence-defining slits upstream of the experimental station. In the reconstruction algorithm, modal decomposition is used to account for the resulting partial coherence in the beam. We show that if the object has sparse feactures and large areas of flat contrast, the diffuser facilitates a better reconstruction and the extra diversity in the data also allows cleaner separation of the constituent modes in the illumination. The setup also allows a quick, real-time measure of the beam coherence.},
  language = {en},
  timestamp = {2017-01-13T09:31:31Z},
  number = {5},
  urldate = {2016-03-22},
  journal = {J. Opt.},
  author = {Li, Peng and Batey, Darren J. and Edo, Tega B. and Parsons, Aaron D. and Rau, Christoph and Rodenburg, John M.},
  year = {2016},
  note = {00001},
  keywords = {lowdose},
  pages = {054008}
}

@book{Kirkland2010,
  title = {Advanced Computing in Electron Microscopy},
  isbn = {978-1-4419-6532-5},
  timestamp = {2017-01-10T11:30:11Z},
  url = {http://books.google.com/books?hl=en\&lr=\&id=YscLlyaiNvoC\&oi=fnd\&pg=PR5\&dq=Advanced+Computing+in+Electron+Microscopy\&ots=KA3FApM1kW\&sig=T6oRRFaEMUJuL3d3_GlC2dynwMs},
  author = {Kirkland, EJ},
  year = {2010},
  note = {00000},
  keywords = {algorithms,Electron,lowdose,multi-slice,particle,simulation},
  file = {2010-Advanced_computing_in_electron_microscopy.pdf:/media/philipp/My Book/Dropbox/mpapers/2010-Advanced_computing_in_electron_microscopy.pdf:application/pdf}
}

@article{Godard2012,
  title = {Noise Models for Low Counting Rate Coherent Diffraction Imaging.},
  volume = {20},
  issn = {1094-4087},
  abstract = {Coherent diffraction imaging (CDI) is a lens-less microscopy method that extracts the complex-valued exit field from intensity measurements alone. It is of particular importance for microscopy imaging with diffraction set-ups where high quality lenses are not available. The inversion scheme allowing the phase retrieval is based on the use of an iterative algorithm. In this work, we address the question of the choice of the iterative process in the case of data corrupted by photon or electron shot noise. Several noise models are presented and further used within two inversion strategies, the ordered subset and the scaled gradient. Based on analytical and numerical analysis together with Monte-Carlo studies, we show that any physical interpretations drawn from a CDI iterative technique require a detailed understanding of the relationship between the noise model and the used inversion method. We observe that iterative algorithms often assume implicitly a noise model. For low counting rates, each noise model behaves differently. Moreover, the used optimization strategy introduces its own artefacts. Based on this analysis, we develop a hybrid strategy which works efficiently in the absence of an informed initial guess. Our work emphasises issues which should be considered carefully when inverting experimental data.},
  timestamp = {2017-01-11T10:01:39Z},
  number = {23},
  url = {http://www.ncbi.nlm.nih.gov/pubmed/23187408},
  journal = {Opt. Express},
  author = {Godard, Pierre and Allain, Marc and Chamard, Virginie and Rodenburg, John},
  month = nov,
  year = {2012},
  note = {00024},
  keywords = {cdi,Computer-Assisted,Computer-Assisted: methods,image processing,imaging,lensless imaging,Likelihood Functions,lowdose,Microscopy,Microscopy: methods,Models,Monte Carlo Method,noise,Normal Distribution,optics and photonics,Photons,Physics,Physics: methods,Software,Statistical,Theoretical,theory,X-Ray Diffraction: methods},
  pages = {25914--34},
  file = {Godard et al_2012_Noise models for low counting rate coherent diffraction imaging.pdf:/media/philipp/My Book/Dropbox/mpapers/Godard et al_2012_Noise models for low counting rate coherent diffraction imaging.pdf:application/pdf;Godard et al_2012_Noise models for low counting rate coherent diffraction imaging.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Godard et al_2012_Noise models for low counting rate coherent diffraction imaging.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/82JKFQDF/abstract.html:text/html},
  pmid = {23187408}
}

@article{Diaz2012,
  title = {Quantitative x-Ray Phase Nanotomography},
  volume = {85},
  issn = {1098-0121},
  doi = {10.1103/PhysRevB.85.020104},
  timestamp = {2015-10-14T12:33:56Z},
  number = {2},
  journal = {Phys. Rev. B},
  author = {Diaz, Ana and Trtik, Pavel and Guizar-Sicairos, Manuel and Menzel, Andreas and Thibault, Pierre and Bunk, Oliver},
  month = jan,
  year = {2012},
  keywords = {cdi,hard x-ray,ideas,imaging,lensless imaging,lowdose,particle,photon,ptychography,tomography,x-ray},
  pages = {1--4},
  file = {Diaz et al_2012_Quantitative x-ray phase nanotomography.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Diaz et al_2012_Quantitative x-ray phase nanotomography.pdf:application/pdf}
}

@article{shechtman_phase_2015,
  title = {Phase {{Retrieval}} with {{Application}} to {{Optical Imaging}}: {{A}} Contemporary Overview},
  volume = {32},
  issn = {1053-5888},
  shorttitle = {Phase {{Retrieval}} with {{Application}} to {{Optical Imaging}}},
  doi = {10.1109/MSP.2014.2352673},
  abstract = {This review article provides a contemporary overview of phase retrieval in optical imaging, linking the relevant optical physics to the signal processing methods and algorithms. Our goal is to describe the current state of the art in this area, identify challenges, and suggest future directions and areas where signal processing methods can have a large impact on optical imaging and on the world of imaging at large with applications in a variety of fields ranging from biology and chemistry to physics and engineering.},
  timestamp = {2017-01-11T10:01:38Z},
  number = {3},
  journal = {IEEE Signal Processing Magazine},
  author = {Shechtman, Y. and Eldar, Y.C. and Cohen, O. and Chapman, H.N. and Miao, Jianwei and Segev, M.},
  month = may,
  year = {2015},
  note = {00016},
  keywords = {algorithms,biology,chemistry,Engineering,Extraterrestrial measurements,Holography,Image processing,lowdose,Optical diffraction,Optical imaging,Optical signal processing,Optical variables measurement,Phase measurement,Phase retrieval,phase retrieval,Physics,review,reviews,Signal processing},
  pages = {87--109},
  file = {Shechtman et al_2015_Phase Retrieval with Application to Optical Imaging.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Shechtman et al_2015_Phase Retrieval with Application to Optical Imaging.pdf:application/pdf;Shechtman et al_2015_Phase Retrieval with Application to Optical Imaging2.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Shechtman et al_2015_Phase Retrieval with Application to Optical Imaging2.pdf:application/pdf;IEEE Xplore Abstract Record:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/WBD7AW7V/7078985.html:text/html}
}

@article{Marchesin2014,
  title = {Alternating {{Projection}}, {{Ptychographic Imaging}} and {{Phase Synchronization}}},
  timestamp = {2017-01-10T11:30:14Z},
  url = {http://arxiv.org/abs/1402.0550},
  journal = {arXiv Prepr. arXiv1402.0550},
  author = {Marchesin, S and Tu, YC and Wu, Hau-tieng},
  year = {2014},
  note = {00000},
  keywords = {algorithms,cdi,imaging,lensless imaging,lowdose,particle,phase retrieval,photon,ptychography,x-ray},
  pages = {1--29},
  file = {1402.0550v3.pdf:/media/philipp/My Book/Dropbox/mpapers/1402.0550v3.pdf:application/pdf;Marchesini et al_2014_Alternating projection, ptychographic imaging and phase synchronization.pdf:/media/philipp/My Book/Dropbox/mpapers/Marchesini et al_2014_Alternating projection, ptychographic imaging and phase synchronization.pdf:application/pdf},
  archiveprefix = {arXiv},
  arxivid = {arXiv:1402.0550v1},
  eprint = {arXiv:1402.0550v1},
  mendeley-tags = {cdi,phase retrieval,ptychography}
}

@article{Thibault2012,
  title = {Maximum-Likelihood Refinement for Coherent Diffractive Imaging},
  volume = {14},
  issn = {1367-2630},
  doi = {10.1088/1367-2630/14/6/063004},
  timestamp = {2017-01-10T11:30:16Z},
  number = {6},
  journal = {New J. Phys.},
  author = {Thibault, P and Guizar-Sicairos, M},
  month = jun,
  year = {2012},
  note = {00081},
  keywords = {cdi,imaging,lensless imaging,Low-dose ptychography},
  pages = {063004},
  file = {Thibault_Guizar-Sicairos_2012_Maximum-likelihood refinement for coherent diffractive imaging.pdf:/media/philipp/My Book/Dropbox/mpapers/Thibault_Guizar-Sicairos_2012_Maximum-likelihood refinement for coherent diffractive imaging.pdf:application/pdf;Thibault_Guizar-Sicairos_2012_Maximum-likelihood refinement for coherent diffractive imaging.pdf:/media/philipp/My Book/Dropbox/mpapers/Thibault_Guizar-Sicairos_2012_Maximum-likelihood refinement for coherent diffractive imaging.pdf:application/pdf}
}

@article{Shapiro2005,
  title = {Biological Imaging by Soft x-Ray Diffraction Microscopy.},
  volume = {102},
  issn = {0027-8424},
  doi = {10.1073/pnas.0503305102},
  abstract = {We have used the method of x-ray diffraction microscopy to image the complex-valued exit wave of an intact and unstained yeast cell. The images of the freeze-dried cell, obtained by using 750-eV x-rays from different angular orientations, portray several of the cell's major internal components to 30-nm resolution. The good agreement among the independently recovered structures demonstrates the accuracy of the imaging technique. To obtain the best possible reconstructions, we have implemented procedures for handling noisy and incomplete diffraction data, and we propose a method for determining the reconstructed resolution. This work represents a previously uncharacterized application of x-ray diffraction microscopy to a specimen of this complexity and provides confidence in the feasibility of the ultimate goal of imaging biological specimens at 10-nm resolution in three dimensions.},
  timestamp = {2017-01-10T11:30:17Z},
  number = {43},
  journal = {Proc. Natl. Acad. Sci. U. S. A.},
  author = {Shapiro, David and Thibault, Pierre and Beetz, Tobias and Elser, Veit and Howells, Malcolm and Jacobsen, Chris and Kirz, Janos and Lima, Enju and Miao, Huijie and Neiman, Aaron M and Sayre, David},
  month = oct,
  year = {2005},
  note = {00444},
  keywords = {cdi,Computer-Assisted,farfield cdi,Freeze Drying,image processing,imaging,lensless imaging,Microscopy,particle,photon,Saccharomyces cerevisiae,Saccharomyces cerevisiae: cytology,soft x-ray,Three-Dimensional,x-ray},
  pages = {15343--6},
  pmid = {16219701}
}

@article{burdet_evaluation_2015,
  title = {Evaluation of Partial Coherence Correction in {{X}}-Ray Ptychography},
  volume = {23},
  copyright = {\textcopyright{} 2015 Optical Society of America},
  issn = {1094-4087},
  doi = {10.1364/OE.23.005452},
  abstract = {Coherent X-ray Diffraction Imaging (CDI) and X-ray ptychography both heavily rely on the high degree of spatial coherence of the X-ray illumination for sufficient experimental data quality for reconstruction convergence. Nevertheless, the majority of the available synchrotron undulator sources have a limited degree of partial coherence, leading to reduced data quality and a lower speckle contrast in the coherent diffraction patterns. It is still an open question whether experimentalists should compromise the coherence properties of an X-ray source in exchange for a higher flux density at a sample, especially when some materials of scientific interest are relatively weak scatterers. A previous study has suggested that in CDI, the best strategy for the study of strong phase objects is to maintain a high degree of coherence of the illuminating X-rays because of the broadening of solution space resulting from the strong phase structures. In this article, we demonstrate the first systematic analysis of the effectiveness of partial coherence correction in ptychography as a function of the coherence properties, degree of complexity of illumination (degree of phase diversity of the probe) and sample phase complexity. We have also performed analysis of how well ptychographic algorithms refine X-ray probe and complex coherence functions when those variables are unknown at the start of reconstructions, for noise-free simulated data, in the case of both real-valued and highly-complex objects.},
  language = {EN},
  timestamp = {2017-01-10T11:30:18Z},
  number = {5},
  urldate = {2015-10-13},
  journal = {Opt. Express, OE},
  author = {Burdet, Nicolas and Shi, Xiaowen and Parks, Daniel and Clark, Jesse N. and Huang, Xiaojing and Kevan, Stephen D. and Robinson, Ian K.},
  month = mar,
  year = {2015},
  note = {00005},
  keywords = {cdi,imaging,lensless imaging,lowdose,particle,photon,ptychography,x-ray},
  pages = {5452--5467}
}

@article{dalfonso_dose-dependent_2016,
  title = {Dose-Dependent High-Resolution Electron Ptychography},
  volume = {119},
  issn = {0021-8979, 1089-7550},
  doi = {10.1063/1.4941269},
  abstract = {Recent reports of electron ptychography at atomic resolution have ushered in a new era of coherent diffractiveimaging in the context of electron microscopy. We report and discuss electron ptychography under variable electron dose conditions, exploring the prospects of an approach which has considerable potential for imaging where low dose is needed.},
  timestamp = {2016-07-21T14:05:21Z},
  number = {5},
  urldate = {2016-03-02},
  journal = {Journal of Applied Physics},
  author = {D'Alfonso, A. J. and Allen, L. J. and Sawada, H. and Kirkland, A. I.},
  month = feb,
  year = {2016},
  note = {00000},
  keywords = {Charge coupled devices,Coherence imaging,Electron microscopy,Image reconstruction,Low-dose ptychography,X-ray diffraction},
  pages = {054302},
  file = {Full Text PDF:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/7TANJV82/D'Alfonso et al. - 2016 - Dose-dependent high-resolution electron ptychograp.pdf:application/pdf;D'Alfonso et al_2016_Dose-dependent high-resolution electron ptychography.pdf:/media/philipp/My Book/Dropbox/mpapers/D'Alfonso et al_2016_Dose-dependent high-resolution electron ptychography.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/QWJVBQJJ/1.html:text/html}
}

@article{ophus_efficient_2016,
  title = {Efficient Linear Phase Contrast in Scanning Transmission Electron Microscopy with Matched Illumination and Detector Interferometry},
  volume = {7},
  copyright = {\textcopyright{} 2016 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
  doi = {10.1038/ncomms10719},
  abstract = {The ability to image light elements in soft matter at atomic resolution enables unprecedented insight into the structure and properties of molecular heterostructures and beam-sensitive nanomaterials. In this study, we introduce a scanning transmission electron microscopy technique combining a pre-specimen phase plate designed to produce a probe with structured phase with a high-speed direct electron detector to generate nearly linear contrast images with high efficiency. We demonstrate this method by using both experiment and simulation to simultaneously image the atomic-scale structure of weakly scattering amorphous carbon and strongly scattering gold nanoparticles. Our method demonstrates strong contrast for both materials, making it a promising candidate for structural determination of heterogeneous soft/hard matter samples even at low electron doses comparable to traditional phase-contrast transmission electron microscopy. Simulated images demonstrate the extension of this technique to the challenging problem of structural determination of biological material at the surface of inorganic crystals.},
  language = {en},
  timestamp = {2017-01-11T10:01:30Z},
  urldate = {2016-05-21},
  journal = {Nat Commun},
  author = {Ophus, Colin and Ciston, Jim and Pierce, Jordan and Harvey, Tyler R. and Chess, Jordan and McMorran, Benjamin J. and Czarnik, Cory and Rose, Harald H. and Ercius, Peter},
  month = feb,
  year = {2016},
  note = {00000},
  keywords = {Applied physics,Condensed matter,lowdose,Materials science,Physical Sciences},
  pages = {10719},
  file = {ncomms10719.pdf:/home/philipp/dl/papers/ncomms10719.pdf:application/pdf;Ophus et al_2016_Efficient linear phase contrast in scanning transmission electron microscopy.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Ophus et al_2016_Efficient linear phase contrast in scanning transmission electron microscopy.pdf:application/pdf;Ophus et al_2016_Efficient linear phase contrast in scanning transmission electron microscopy.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Ophus et al_2016_Efficient linear phase contrast in scanning transmission electron microscopy.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/EKX2UEID/ncomms10719.html:text/html;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/P2H7RAR4/ncomms10719.html:text/html}
}

@article{scheres_relion:_2012,
  title = {{{RELION}}: {{Implementation}} of a {{Bayesian}} Approach to Cryo-{{EM}} Structure Determination},
  volume = {180},
  issn = {1047-8477},
  shorttitle = {{{RELION}}},
  doi = {10.1016/j.jsb.2012.09.006},
  abstract = {RELION, for REgularized LIkelihood OptimizatioN, is an open-source computer program for the refinement of macromolecular structures by single-particle analysis of electron cryo-microscopy (cryo-EM) data. Whereas alternative approaches often rely on user expertise for the tuning of parameters, RELION uses a Bayesian approach to infer parameters of a statistical model from the data. This paper describes developments that reduce the computational costs of the underlying maximum a posteriori (MAP) algorithm, as well as statistical considerations that yield new insights into the accuracy with which the relative orientations of individual particles may be determined. A so-called gold-standard Fourier shell correlation (FSC) procedure to prevent overfitting is also described. The resulting implementation yields high-quality reconstructions and reliable resolution estimates with minimal user intervention and at acceptable computational costs.},
  timestamp = {2017-01-10T11:30:21Z},
  number = {3},
  urldate = {2016-07-05},
  journal = {Journal of Structural Biology},
  author = {Scheres, Sjors H. W.},
  month = dec,
  year = {2012},
  note = {00587},
  keywords = {Electron microscopy,Image processing,lowdose,Maximum likelihood,Single-particle analysis,Software development},
  pages = {519--530},
  file = {Scheres_2012_RELION.pdf:/media/philipp/My Book/Dropbox/mpapers/Scheres_2012_RELION.pdf:application/pdf}
}

@article{balan_signal_2006,
  title = {On Signal Reconstruction without Phase},
  volume = {20},
  issn = {1063-5203},
  doi = {10.1016/j.acha.2005.07.001},
  abstract = {We will construct new classes of Parseval frames for a Hilbert space which allow signal reconstruction from the absolute value of the frame coefficients. As a consequence, signal reconstruction can be done without using phase or its estimation. This verifies a longstanding conjecture of the speech processing community.},
  timestamp = {2017-01-11T10:01:28Z},
  number = {3},
  urldate = {2016-07-11},
  journal = {Applied and Computational Harmonic Analysis},
  author = {Balan, Radu and Casazza, Pete and Edidin, Dan},
  month = may,
  year = {2006},
  note = {00232},
  keywords = {Frame,lowdose,Phase,Signal reconstruction,Speech recognition},
  pages = {345--356},
  file = {Balan et al_2006_On signal reconstruction without phase.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Balan et al_2006_On signal reconstruction without phase.pdf:application/pdf;ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/GNWSDHNQ/S1063520305000667.html:text/html;ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/RHMTD44B/S1063520305000667.html:text/html}
}

@article{downing_spot-scan_1991,
  title = {Spot-Scan Imaging in Transmission Electron Microscopy},
  volume = {251},
  copyright = {\textcopyright{} 1991},
  issn = {0036-8075, 1095-9203},
  doi = {10.1126/science.1846047},
  abstract = {The determination of the structure of proteins and other organic materials by transmission electron microscopy is a rapidly developing field. Obtaining high-resolution images of these radiation-sensitive specimens has, until recently, been problematic. The development of spot-scan imaging, in which the electron beam is focused to a spot with a diameter of about 1000 angstroms and moved over the specimen to record the image, has overcome some of the most severe problems, which result from beam-induced motion of the specimen and its image. Elimination of this motion greatly enhances the contrast of high-resolution features of the image and promises a significant increase in the speed with which future structural work can be accomplished.},
  language = {en},
  timestamp = {2017-01-13T09:31:31Z},
  number = {4989},
  urldate = {2016-07-11},
  journal = {Science},
  author = {Downing, K. H.},
  month = jan,
  year = {1991},
  note = {00000 PMID: 1846047},
  keywords = {lowdose},
  pages = {53--59},
  file = {Downing_1991_Spot-scan imaging in transmission electron microscopy.pdf:/media/philipp/My Book/Dropbox/mpapers/Downing_1991_Spot-scan imaging in transmission electron microscopy2.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/89WSU8D7/53.html:text/html;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/HJZDP8PS/53.html:text/html}
}

@article{bullough_use_1987,
  title = {Use of Spot-Scan Procedure for Recording Low-Dose Micrographs of Beam-Sensitive Specimens},
  volume = {21},
  issn = {0304-3991},
  doi = {10.1016/0304-3991(87)90147-1},
  abstract = {Electron micrographs of monolayer crystals of paraffin have been recorded with a spot-scan mode of imaging which uses a small 50 nm diameter moving beam. In comparison with normal stationary beam images using 5 $\mu$m illuminating beams, the spot-scan micrographs show a higher and more consistent contrast from the 3.8\textendash{}4.2 {\AA} hydrocarbon chain spacings. On average the improvement in contrast is twofold, but this still leaves scope for further improvement: the best spot-scan images still do not quite reach the level of contrast calculated theoretically from electron diffraction. We believe that the cause of the low contrast in paraffin images must be specimen motion caused by radiation damage rather than a charging effect, for two reasons. First, it does not occur in control images of vermiculite, a non-beam-sensitive mineral, when treated identically. Secondly, although charging might still be a problem with paraffin, when images are taken with the objective aperture in the column, a procedure which is normally expected to reduce charging, no improvement in contrast is found. Thus we think that the use of the small beam minimizes the effect of specimen motion on image contrast by minimizing the specimen area exposed at each instant and therefore the resultant image blurring. Further improvements with even smaller illumination beam diameters might be expected.},
  timestamp = {2017-01-10T11:30:24Z},
  number = {3},
  urldate = {2016-07-11},
  journal = {Ultramicroscopy},
  author = {Bullough, Per and Henderson, Richard},
  month = jan,
  year = {1987},
  note = {00088},
  keywords = {lowdose},
  pages = {223--230},
  file = {Bullough_Henderson_1987_Use of spot-scan procedure for recording low-dose micrographs of beam-sensitive.pdf:/media/philipp/My Book/Dropbox/mpapers/Bullough_Henderson_1987_Use of spot-scan procedure for recording low-dose micrographs of beam-sensitive.pdf:application/pdf;ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/9FNP5ZAR/0304399187901471.html:text/html}
}

@article{bartesaghi_2.2_2015,
  title = {2.2 {{{\AA}}} Resolution Cryo-{{EM}} Structure of $\beta$-Galactosidase in Complex with a Cell-Permeant Inhibitor},
  volume = {348},
  copyright = {Copyright \textcopyright{} 2015, American Association for the Advancement of Science},
  issn = {0036-8075, 1095-9203},
  doi = {10.1126/science.aab1576},
  abstract = {Pushing the limits of electron microscopy
Recent advances in cryo\textendash{}electron microscopy (cryo-EM) allow structures of large macromolecules to be determined at near-atomic resolution. So far, though, resolutions approaching 2 {\AA}, where features key to drug design are revealed, remain the province of x-ray crystallography. Bartesaghi et al. achieved a resolution of 2.2 {\AA} for a 465-kD ligand-bound protein complex using cryo-EM. The density map is detailed enough to show close to 800 water molecules, magnesium and sodium ions, and precise side-chain conformations. These results bring routine use of cryo-EM in rational drug design a step closer.
Science, this issue p. 1147
Cryo\textendash{}electron microscopy (cryo-EM) is rapidly emerging as a powerful tool for protein structure determination at high resolution. Here we report the structure of a complex between Escherichia coli $\beta$-galactosidase and the cell-permeant inhibitor phenylethyl $\beta$-d-thiogalactopyranoside (PETG), determined by cryo-EM at an average resolution of \textasciitilde{}2.2 angstroms ({\AA}). Besides the PETG ligand, we identified densities in the map for \textasciitilde{}800 water molecules and for magnesium and sodium ions. Although it is likely that continued advances in detector technology may further enhance resolution, our findings demonstrate that preparation of specimens of adequate quality and intrinsic protein flexibility, rather than imaging or image-processing technologies, now represent the major bottlenecks to routinely achieving resolutions close to 2 {\AA} using single-particle cryo-EM.
Advances in electron microscopy allow protein structure determination at resolutions useful in drug discovery.
Advances in electron microscopy allow protein structure determination at resolutions useful in drug discovery.},
  language = {en},
  timestamp = {2017-01-10T11:30:23Z},
  number = {6239},
  urldate = {2016-07-11},
  journal = {Science},
  author = {Bartesaghi, Alberto and Merk, Alan and Banerjee, Soojay and Matthies, Doreen and Wu, Xiongwu and Milne, Jacqueline L. S. and Subramaniam, Sriram},
  month = jun,
  year = {2015},
  note = {00141 PMID: 25953817},
  keywords = {Low-dose ptychography},
  pages = {1147--1151},
  file = {Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/AJA9SEZM/1147.html:text/html}
}

@article{scheres_beam-induced_2014,
  title = {Beam-Induced Motion Correction for Sub-Megadalton Cryo-{{EM}} Particles},
  volume = {3},
  copyright = {\textcopyright{} 2014, Scheres. This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.},
  issn = {2050-084X},
  doi = {10.7554/eLife.03665},
  abstract = {In electron cryo-microscopy (cryo-EM), the electron beam that is used for imaging also causes the sample to move. This motion blurs the images and limits the resolution attainable by single-particle analysis. In a previous Research article (Bai et al., 2013) we showed that correcting for this motion by processing movies from fast direct-electron detectors allowed structure determination to near-atomic resolution from 35,000 ribosome particles. In this Research advance article, we show that an improved movie processing algorithm is applicable to a much wider range of specimens. The new algorithm estimates straight movement tracks by considering multiple particles that are close to each other in the field of view, and models the fall-off of high-resolution information content by radiation damage in a dose-dependent manner. Application of the new algorithm to four data sets illustrates its potential for significantly improving cryo-EM structures, even for particles that are smaller than 200 kDa.},
  language = {en},
  timestamp = {2017-01-11T10:01:21Z},
  urldate = {2016-07-11},
  journal = {eLife},
  author = {Scheres, Sjors HW},
  month = aug,
  year = {2014},
  note = {00149},
  keywords = {<italic>E. coli</italic>,<italic>S. cerevisiae</italic>,cryo-EM,Human,image analysis,Low-dose ptychography,Single-particle analysis},
  pages = {e03665},
  file = {Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/FWQRNDQ6/e03665.html:text/html},
  pmid = {25122622}
}

@article{mcmullan_comparison_2014,
  title = {Comparison of Optimal Performance at 300 {{keV}} of Three Direct Electron Detectors for Use in Low Dose Electron Microscopy},
  volume = {147},
  issn = {03043991},
  doi = {10.1016/j.ultramic.2014.08.002},
  abstract = {Low dose electron imaging applications such as electron cyro-microscopy are now benefitting from the improved performance and flexibility of recently introduced electron imaging detectors in which electrons are directly incident on backthinned CMOS sensors. There are currently three commercially available detectors of this type: the Direct Electron DE 20, the FEI Falcon II and the Gatan K2 Summit. These have different characteristics and so it is important to compare their imaging properties carefully with a view to optimising how each is used. Results at 300 keV for both the modulation transfer function (MTF) and detective quantum efficiency (DQE) are presented. Of these, the DQE is the most important in the study of radiation sensitive samples where detector performance is crucial. We find that all three detectors have a better DQE than film. The K2 Summit has the best DQE at low spatial frequencies but with increasing spatial frequency its DQE falls below that of the Falcon II.},
  timestamp = {2017-01-13T09:31:31Z},
  urldate = {2016-07-12},
  journal = {Ultramicroscopy},
  author = {McMullan, G. and Faruqi, A. R. and Clare, D. and Henderson, R.},
  month = dec,
  year = {2014},
  note = {00000 arXiv: 1406.1389},
  keywords = {lowdose,Physics - Instrumentation and Detectors},
  pages = {156--163},
  file = {McMullan et al_2014_Comparison of optimal performance at 300 keV of three direct electron detectors.pdf:/media/philipp/My Book/Dropbox/mpapers/McMullan et al_2014_Comparison of optimal performance at 300 keV of three direct electron detectors.pdf:application/pdf}
}

@article{chen_solving_2015,
  title = {Solving {{Random Quadratic Systems}} of {{Equations Is Nearly}} as {{Easy}} as {{Solving Linear Systems}}},
  abstract = {We consider the fundamental problem of solving quadratic systems of equations in \$n\$ variables, where \$y\_i = |$\backslash$langle $\backslash$boldsymbol\{a\}\_i, $\backslash$boldsymbol\{x\} $\backslash$rangle|\^2\$, \$i = 1, $\backslash$ldots, m\$ and \$$\backslash$boldsymbol\{x\} $\backslash$in $\backslash$mathbb\{R\}\^n\$ is unknown. We propose a novel method, which starting with an initial guess computed by means of a spectral method, proceeds by minimizing a nonconvex functional as in the Wirtinger flow approach. There are several key distinguishing features, most notably, a distinct objective functional and novel update rules, which operate in an adaptive fashion and drop terms bearing too much influence on the search direction. These careful selection rules provide a tighter initial guess, better descent directions, and thus enhanced practical performance. On the theoretical side, we prove that for certain unstructured models of quadratic systems, our algorithms return the correct solution in linear time, i.e. in time proportional to reading the data \$$\backslash$\{$\backslash$boldsymbol\{a\}\_i$\backslash$\}\$ and \$$\backslash$\{y\_i$\backslash$\}\$ as soon as the ratio \$m/n\$ between the number of equations and unknowns exceeds a fixed numerical constant. We extend the theory to deal with noisy systems in which we only have \$y\_i $\backslash$approx |$\backslash$langle $\backslash$boldsymbol\{a\}\_i, $\backslash$boldsymbol\{x\} $\backslash$rangle|\^2\$ and prove that our algorithms achieve a statistical accuracy, which is nearly un-improvable. We complement our theoretical study with numerical examples showing that solving random quadratic systems is both computationally and statistically not much harder than solving linear systems of the same size---hence the title of this paper. For instance, we demonstrate empirically that the computational cost of our algorithm is about four times that of solving a least-squares problem of the same size.},
  timestamp = {2017-01-10T11:30:25Z},
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1505.05114},
  primaryClass = {cs, math, stat},
  urldate = {2016-07-14},
  url = {http://arxiv.org/abs/1505.05114},
  journal = {arXiv:1505.05114 [cs, math, stat]},
  author = {Chen, Yuxin and Candes, Emmanuel J.},
  month = may,
  year = {2015},
  note = {00087 arXiv: 1505.05114},
  keywords = {Computer Science - Information Theory,Computer Science - Learning,lowdose,Mathematics - Numerical Analysis,Mathematics - Statistics Theory,Statistics - Machine Learning},
  file = {Chen_Candes_2015_Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving.pdf:/media/philipp/My Book/Dropbox/mpapers/Chen_Candes_2015_Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving2.pdf:application/pdf}
}

@article{vulovic_image_2013,
  title = {Image Formation Modeling in Cryo-Electron Microscopy},
  volume = {183},
  issn = {1047-8477},
  doi = {10.1016/j.jsb.2013.05.008},
  abstract = {Accurate modeling of image formation in cryo-electron microscopy is an important requirement for quantitative image interpretation and optimization of the data acquisition strategy. Here we present a forward model that accounts for the specimen's scattering properties, microscope optics, and detector response. The specimen interaction potential is calculated with the isolated atom superposition approximation (IASA) and extended with the influences of solvent's dielectric and ionic properties as well as the molecular electrostatic distribution. We account for an effective charge redistribution via the Poisson\textendash{}Boltzmann approach and find that the IASA-based potential forms the dominant part of the interaction potential, as the contribution of the redistribution is less than 10\%. The electron wave is propagated through the specimen by a multislice approach and the influence of the optics is included via the contrast transfer function. We incorporate the detective quantum efficiency of the camera due to the difference between signal and noise transfer characteristics, instead of using only the modulation transfer function. The full model was validated against experimental images of 20S proteasome, hemoglobin, and GroEL. The simulations adequately predict the effects of phase contrast, changes due to the integrated electron flux, thickness, inelastic scattering, detective quantum efficiency and acceleration voltage. We suggest that beam-induced specimen movements are relevant in the experiments whereas the influence of the solvent amorphousness can be neglected. All simulation parameters are based on physical principles and, when necessary, experimentally determined.},
  timestamp = {2017-01-10T11:30:26Z},
  number = {1},
  urldate = {2016-07-22},
  journal = {Journal of Structural Biology},
  author = {Vulovi{\'c}, Milo{\v s} and Ravelli, Raimond B. G. and {\noopsort{vliet}}{van Vliet}, Lucas J. and Koster, Abraham J. and Lazi{\'c}, Ivan and L{\"u}cken, Uwe and Rullg{\aa}rd, Hans and {\"O}ktem, Ozan and Rieger, Bernd},
  month = jul,
  year = {2013},
  note = {00027},
  keywords = {Amplitude contrast,cryo-electron microscopy,image simulation,InSilicoTEM,Interaction potential,lowdose,Phase contrast},
  pages = {19--32},
  file = {Vulović et al_2013_Image formation modeling in cryo-electron microscopy.pdf:/media/philipp/My Book/Dropbox/mpapers/Vulović et al_2013_Image formation modeling in cryo-electron microscopy.pdf:application/pdf;Vulović et al_2013_Image formation modeling in cryo-electron microscopy.pdf:/media/philipp/My Book/Dropbox/mpapers/Vulović et al_2013_Image formation modeling in cryo-electron microscopy.pdf:application/pdf;Vulović et al_2013_Image formation modeling in cryo-electron microscopy2.pdf:/media/philipp/My Book/Dropbox/mpapers/Vulović et al_2013_Image formation modeling in cryo-electron microscopy2.pdf:application/pdf;ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/23W8MFP6/S1047847713001226.html:text/html}
}

@article{yang_simultaneous_2016,
  title = {Simultaneous Atomic-Resolution Electron Ptychography and {{Z}}-Contrast Imaging of Light and Heavy Elements in Complex Nanostructures},
  volume = {7},
  copyright = {\textcopyright{} 2016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.},
  issn = {2041-1723},
  doi = {10.1038/ncomms12532},
  abstract = {The use of ptychography with electrons has been limited. Here, Yang et al. demonstrate that the combination of Z-contrast and phase imaging reveals the structure of complex nanomaterials.},
  language = {en},
  timestamp = {2017-01-13T09:31:31Z},
  urldate = {2016-09-01},
  journal = {Nature Communications},
  author = {Yang, H. and Rutte, R. N. and Jones, L. and Simson, M. and Sagawa, R. and Ryll, H. and Huth, M. and Pennycook, T. J. and Green, M. L. H. and Soltau, H. and Kondo, Y. and Davis, B. G. and Nellist, P. D.},
  month = aug,
  year = {2016},
  note = {00001},
  keywords = {Low-dose ptychography},
  pages = {12532},
  file = {Yang et al_2016_Simultaneous atomic-resolution electron ptychography and Z-contrast imaging of.pdf:/media/philipp/My Book/Dropbox/mpapers/Yang et al_2016_Simultaneous atomic-resolution electron ptychography and Z-contrast imaging of.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/EXRKN9Q4/ncomms12532.html:text/html;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/WMGJD7C5/ncomms12532.html:text/html}
}

@article{glaeser_how_2016,
  title = {How Good Can Cryo-{{EM}} Become?},
  volume = {13},
  copyright = {\textcopyright{} 2016 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
  issn = {1548-7091},
  doi = {10.1038/nmeth.3695},
  abstract = {The suddenness with which single-particle cryo-electron microscopy (cryo-EM) has emerged as a method for determining high-resolution structures of biological macromolecules invites the questions, how much better can this technology get, and how fast is that likely to happen? Though we can rightly celebrate the maturation of cryo-EM as a high-resolution structure-determination tool, I believe there still are many developments to look forward to.},
  language = {en},
  timestamp = {2017-01-11T10:01:24Z},
  number = {1},
  urldate = {2016-09-23},
  journal = {Nat Meth},
  author = {Glaeser, Robert M.},
  month = jan,
  year = {2016},
  note = {00012},
  keywords = {Cryoelectron microscopy,Hardware and infrastructure,lowdose,Proteins},
  pages = {28--32},
  file = {Full Text PDF:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/9X7EUP69/Glaeser - 2016 - How good can cryo-EM become.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/ASF82Z2M/nmeth.3695.html:text/html}
}

@article{danev_volta_2014,
  title = {Volta Potential Phase Plate for in-Focus Phase Contrast Transmission Electron Microscopy},
  volume = {111},
  issn = {0027-8424, 1091-6490},
  doi = {10.1073/pnas.1418377111},
  abstract = {We describe a phase plate for transmission electron microscopy taking advantage of a hitherto-unknown phenomenon, namely a beam-induced Volta potential on the surface of a continuous thin film. The Volta potential is negative, indicating that it is not caused by beam-induced electrostatic charging. The film must be heated to $\sim$200 $^\circ$C to prevent contamination and enable the Volta potential effect. The phase shift is created ``on the fly'' by the central diffraction beam eliminating the need for precise phase plate alignment. Images acquired with the Volta phase plate (VPP) show higher contrast and unlike Zernike phase plate images no fringing artifacts. Following installation into the microscope, the VPP has an initial settling time of about a week after which the phase shift behavior becomes stable. The VPP has a long service life and has been used for more than 6 mo without noticeable degradation in performance. The mechanism underlying the VPP is the same as the one responsible for the degradation over time of the performance of thin-film Zernike phase plates, but in the VPP it is used in a constructive way. The exact physics and/or chemistry behind the process causing the Volta potential are not fully understood, but experimental evidence suggests that radiation-induced surface modification combined with a chemical equilibrium between the surface and residual gases in the vacuum play an important role.},
  language = {en},
  timestamp = {2017-01-13T09:31:31Z},
  number = {44},
  urldate = {2016-09-23},
  journal = {PNAS},
  author = {Danev, Radostin and Buijsse, Bart and Khoshouei, Maryam and Plitzko, J{\"u}rgen M. and Baumeister, Wolfgang},
  month = apr,
  year = {2014},
  note = {00077 PMID: 25331897},
  keywords = {cryo-EM,lowdose,Phase contrast,phase plate,TEM,Volta potential},
  pages = {15635--15640},
  file = {Full Text PDF:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/3KSEN5B6/Danev et al. - 2014 - Volta potential phase plate for in-focus phase con.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/PDAXA39E/15635.html:text/html}
}

@article{bai_ribosome_2013,
  title = {Ribosome Structures to near-Atomic Resolution from Thirty Thousand Cryo-{{EM}} Particles},
  volume = {2},
  copyright = {\textcopyright{} 2013, Bai et al. This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.},
  issn = {2050-084X},
  doi = {10.7554/eLife.00461},
  abstract = {Determining the structure of proteins and other biomolecules at the atomic level is central to understanding many aspects of biology. X-ray crystallography is the best-known technique for structural biology but, as the name suggests, it works only with samples that can be crystallized. Electron cryo-microscopy (cryo-EM) could, potentially, be used to determine the atomic structures of biomolecules that cannot be crystallized, but at present the resolution that can be achieved with this approach is sufficient only for imaging certain types of viruses. In cryo-EM, a solution of the biomolecule of interest is frozen in a thin layer of ice, and this layer is imaged in an electron microscope. By combining images of many identical biomolecules in many different orientations, it is possible to work backwards and determine their 3D structure. However, in order to determine this structure at high resolution, it is necessary to make repeated measurements to reduce high levels of noise in the images. Cryo-EM images are usually recorded on a photographic film or a CCD (charge-coupled device) camera. However, photographic film is unsuitable for high-throughput methods because it has to be handled manually, while the efficiency of CCD cameras is limited because the electrons have to be converted into visible light to be detected. Digital cameras that can detect electrons directly have become available recently, and these are more efficient than both film and CCD cameras. They are also much faster, which means that it is possible to record videos of the sample during the time (typically $\sim$1 s) it is being exposed to the electron beam. Processing these videos could then\textemdash{}in theory\textemdash{}compensate for any movements of the biomolecules that are induced by the electron beam. Along with radiation damage caused by the electrons, these beam-induced movements have been a major limitation on the resolution that can be achieved with cryo-EM. Bai et al. demonstrate the potential of direct-electron detectors in cryo-EM by determining the structures of two ribosomes. Using a novel statistical algorithm to accurately follow the movements of the ribosomes during the time they are exposed to the electron beam, they are able to compensate for these movements, and this makes it possible to determine the structures of the ribosomes with near-atomic precision. Moreover, the resolution they achieve with just $\sim$30,000 ribosomes is better than that previously achieved with more than a million ribosomes, allowing small details inside the ribosome \textendash{} such as {\ss}-strands and bulky amino-acid side chains \textendash{} to be resolved with cryo-EM for the first time. The work of Bai et al. could, therefore, allow researchers to use cryo-EM to determine the structure of many more biomolecules with atomic precision.},
  language = {en},
  timestamp = {2017-01-10T11:30:30Z},
  urldate = {2016-09-23},
  journal = {eLife},
  author = {Bai, Xiao-chen and Fernandez, Israel S. and McMullan, Greg and Scheres, Sjors HW},
  month = feb,
  year = {2013},
  note = {00255 PMID: 23427024},
  keywords = {<italic>S. cerevisiae</italic>,Bayesian,Direct electron detector,Electron microscopy,Image processing,lowdose,ribosome,T. thermophilus},
  pages = {e00461},
  file = {Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/RG2Q4IUN/e00461.html:text/html;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/U9WADXZI/e00461.html:text/html}
}

@article{bai_how_2015,
  title = {How Cryo-{{EM}} Is Revolutionizing Structural Biology},
  volume = {40},
  issn = {0968-0004},
  doi = {10.1016/j.tibs.2014.10.005},
  abstract = {For many years, structure determination of biological macromolecules by cryo-electron microscopy (cryo-EM) was limited to large complexes or low-resolution models. With recent advances in electron detection and image processing, the resolution by cryo-EM is now beginning to rival X-ray crystallography. A new generation of electron detectors record images with unprecedented quality, while new image-processing tools correct for sample movements and classify images according to different structural states. Combined, these advances yield density maps with sufficient detail to deduce the atomic structure for a range of specimens. Here, we review the recent advances and illustrate the exciting new opportunities that they offer to structural biology research.},
  timestamp = {2017-01-10T11:30:31Z},
  number = {1},
  urldate = {2016-09-24},
  journal = {Trends in Biochemical Sciences},
  author = {Bai, Xiao-chen and McMullan, Greg and Scheres, Sjors H. W},
  month = jan,
  year = {2015},
  note = {00152},
  keywords = {3D reconstruction,cryo-electron microscopy,electron detection,Image processing,Low-dose ptychography,macromolecular complexes,maximum-likelihood optimization,Single-particle analysis},
  pages = {49--57},
  file = {Bai et al_2015_How cryo-EM is revolutionizing structural biology.pdf:/media/philipp/My Book/Dropbox/mpapers/Bai et al_2015_How cryo-EM is revolutionizing structural biology.pdf:application/pdf}
}

@article{anger_structures_2013,
  title = {Structures of the Human and {{Drosophila 80S}} Ribosome},
  volume = {497},
  copyright = {\textcopyright{} 2013 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
  issn = {0028-0836},
  doi = {10.1038/nature12104},
  abstract = {Protein synthesis in all cells is carried out by macromolecular machines called ribosomes. Although the structures of prokaryotic, yeast and protist ribosomes have been determined, the more complex molecular architecture of metazoan 80S ribosomes has so far remained elusive. Here we present structures of Drosophila melanogaster and Homo sapiens 80S ribosomes in complex with the translation factor eEF2, E-site transfer RNA and Stm1-like proteins, based on high-resolution cryo-electron-microscopy density maps. These structures not only illustrate the co-evolution of metazoan-specific ribosomal RNA with ribosomal proteins but also reveal the presence of two additional structural layers in metazoan ribosomes, a well-ordered inner layer covered by a flexible RNA outer layer. The human and Drosophila ribosome structures will provide the basis for more detailed structural, biochemical and genetic experiments.},
  language = {en},
  timestamp = {2017-01-10T11:30:28Z},
  number = {7447},
  urldate = {2016-10-10},
  journal = {Nature},
  author = {Anger, Andreas M. and Armache, Jean-Paul and Berninghausen, Otto and Habeck, Michael and Subklewe, Marion and Wilson, Daniel N. and Beckmann, Roland},
  month = may,
  year = {2013},
  note = {00169},
  keywords = {Cryoelectron microscopy,lowdose,ribosome},
  pages = {80--85},
  file = {Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/CPIAHRUQ/nature12104.html:text/html}
}

@article{groll_structure_1997,
  title = {Structure of {{20S}} Proteasome from Yeast at 2.{{4{\AA}}} Resolution},
  volume = {386},
  copyright = {\textcopyright{} 1997 Nature Publishing Group},
  issn = {0028-0836},
  doi = {10.1038/386463a0},
  abstract = {The crystal structure of the 20S proteasome from the yeast Saccharomyces cerevisiae shows that its 28 protein subunits are arranged as an ($\alpha$1...$\alpha$7, $\beta$1...$\beta$7)2 complex in four stacked rings and occupy unique locations. The interior of the particle, which harbours the active sites, is only accessible by some very narrow side entrances. The $\beta$-type subunits are synthesized as proproteins before being proteolytically processed for assembly into the particle. The proforms of three of the seven different $\beta$-type subunits, ($\beta$1/PRE3, $\beta$2/PUP1 and $\beta$5/PRE2, are cleaved between the threonine at position 1 and the last glycine of the pro-sequence, with release of the active-site residue Thr 1. These three $\beta$-type subunits have inhibitor-binding sites, indicating that PRE2 has a chymotrypsin-like and a trypsin-like activity and that PRE3 has peptidylglutamyl peptide hydrolytic specificity. Other $\beta$-type subunits are processed to an intermediate form, indicating that an additional nonspecific endopeptidase activity may exist which is important for peptide hydrolysis and for the generation of ligands for class I molecules of the major histocompatibility complex.},
  language = {en},
  timestamp = {2017-01-10T11:30:29Z},
  number = {6624},
  urldate = {2016-10-10},
  journal = {Nature},
  author = {Groll, Michael and Ditzel, Lars and L{\"o}we, Jan and Stock, Daniela and Bochtler, Matthias and Bartunik, Hans D. and Huber, Robert},
  month = apr,
  year = {1997},
  note = {02142},
  keywords = {Acetylcysteine,Calpain,Crystallography; X-Ray,Cysteine Endopeptidases,Endopeptidases,Enzyme Inhibitors,Enzyme Precursors,Glycoproteins,Histocompatibility Antigens Class I,lowdose,Models; Molecular,Multienzyme Complexes,Proteasome Endopeptidase Complex,Protein Conformation,Saccharomyces cerevisiae,Thermoplasma,Threonine},
  pages = {463--471},
  file = {Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/MRX452P2/386463a0.html:text/html}
}

@article{fermi_crystal_1984,
  title = {The Crystal Structure of Human Deoxyhaemoglobin at 1.74 {{A}} Resolution},
  volume = {175},
  issn = {0022-2836},
  abstract = {The structure of human deoxyhaemoglobin was refined at 1.74 A resolution using data collected on film at room temperature from a synchrotron X-ray source. The crystallographic R-factor is 16.0\%. The estimated error in atomic positions is 0.1 A overall, 0.14 A for main-chain atoms of internal segments, and 0.05 A for the iron atoms. The effects of intermolecular contacts on the structure were investigated; such contacts cause only highly localized distortions, as judged from the degree of molecular asymmetry that they induce. The geometry of the iron-nitrogen complex closely resembles that of the deoxymyoglobin structure of Takano (1977) and of the 5-co-ordinated model compounds of Hoard (1975) and Jameson et al. (1980). The distance of the iron from the mean plane of N(porphyrin) is 0.40(5) A and 0.36(5) A, respectively, at the alpha and beta haems, in contrast to the corresponding distance of +0.12(8) A and -0.11(8) A in oxyhaemoglobin ( Shaanan , 1983); the Fe-N epsilon (F8) bond length is 2.12(4) A and the Fe-N(porphyrin) bond length is 2.06(2) A; the last is also in good agreement with extended X-ray fluorescence spectroscopy measurements on deoxyhaemoglobin ( Eisenberger et al., 1978; Perutz et al., 1982). The haems are domed toward the proximal side; the separation between the mean planes of N(porphyrin) and C(porphyrin) being 0.16(6) A and 0.10(6) A, respectively at the alpha and beta haems. At the alpha haems, the normals to the mean pyrrole planes are tilted uniformly toward the haem centre, by about three degrees relative to the haem normal, and there is a folding of about four degrees of the haem about an axis running between the methene carbons that are between the pyrrole rings bearing like-type side-chains. At the beta haems, there is no such folding, and only pyrroles II and IV (those eclipsed by His F8) are appreciably tilted, by about eight degrees. The independence of these parameters from restraints imposed on the model was verified by unrestrained refinement of the entire molecule starting from a structure with modified haem geometry.},
  language = {ENG},
  timestamp = {2017-01-13T09:31:31Z},
  number = {2},
  journal = {J. Mol. Biol.},
  author = {Fermi, G. and Perutz, M. F. and Shaanan, B. and Fourme, R.},
  month = may,
  year = {1984},
  note = {00000 PMID: 6726807},
  keywords = {Crystallography,Hemoglobins,Humans,lowdose,Myoglobin,Protein Conformation,Pyrroles},
  pages = {159--174}
}

@article{yang_enhanced_????,
  title = {Enhanced Phase Contrast Transfer Using Ptychography Combined with a Pre-Specimen Phase Plate in a Scanning Transmission Electron Microscope},
  issn = {0304-3991},
  doi = {10.1016/j.ultramic.2016.09.002},
  abstract = {The ability to image light elements in both crystalline and noncrystalline materials at near atomic resolution with an enhanced contrast is highly advantageous to understand the structure and properties of a wide range of beam sensitive materials including biological specimens and molecular hetero-structures. This requires the imaging system to have an efficient phase contrast transfer at both low and high spatial frequencies. In this work we introduce a new phase contrast imaging method in a scanning transmission electron microscope (STEM) using a pre-specimen phase plate in the probe forming aperture, combined with a fast pixelated detector to record diffraction patterns at every probe position, and phase reconstruction using ptychography. The phase plate significantly enhances the low spatial frequency contrast transfer, and ptychography maximizes the extraction of the phase information at all spatial frequencies. In addition, the STEM probe with the presence of the phase plate remains at atomic resolution, allowing simultaneous incoherent Z-contrast imaging to be obtained along with the ptychographic phase image. Experimental result of imaging Au nanoparticles on a carbon support shows high contrast for both materials. Multislice image simulations of a DNA molecule shows the capability of imaging soft matter at low dose conditions, which implies potential applications of low dose imaging of a wide range of beam sensitive materials.},
  timestamp = {2017-01-11T10:01:48Z},
  urldate = {2016-09-20},
  journal = {Ultramicroscopy},
  author = {Yang, Hao and Ercius, Peter and Nellist, Peter D. and Ophusa, Colin},
  note = {00001},
  keywords = {lowdose,PCTF,Phase contrast,phase plate,Pixelated detectors,Ptychography,STEM},
  file = {Yang et al_2016_Enhanced phase contrast transfer using ptychography combined with a.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Yang et al_2016_Enhanced phase contrast transfer using ptychography combined with a.pdf:application/pdf;ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/BN2W5UA2/S0304399116301966.html:text/html}
}

@article{stark_electron_1996,
  title = {Electron Radiation Damage to Protein Crystals of Bacteriorhodopsin at Different Temperatures},
  volume = {63},
  issn = {0304-3991},
  doi = {10.1016/0304-3991(96)00045-9},
  abstract = {A series of diffraction patterns from two-dimensional protein crystals of bacteriorhodopsin (purple membrane) at different temperatures (294 K, 98 K and 4 K) were recorded as the diffraction spots faded due to radiation damage. The patterns were then computationally evaluated in order to obtain a quantitative measurement of the structural preservation while irradiating the specimen. To provide statistically significant results, diffraction spots corresponding to spacings of 3{\AA}(1200 spots) and 7{\AA}(600 spots) were measured. A substantial increase of the lifetime of high resolution spots was found using liquid nitrogen as a coolant, whereas further structural preservation at liquid helium temperature was significant but smaller. It appears likely therefore that high resolution images are accessible even at liquid nitrogen temperature. Mechanical stability and the absence of thermal specimen drift are certainly of equivalent importance for successful high resolution imaging.},
  timestamp = {2017-01-13T09:31:31Z},
  number = {2},
  urldate = {2016-10-31},
  journal = {Ultramicroscopy},
  author = {Stark, Holger and Zemlin, Friedrich and Boettcher, Christoph},
  month = jun,
  year = {1996},
  note = {00060},
  keywords = {lowdose},
  pages = {75--79},
  file = {ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/4V7HE36C/0304399196000459.html:text/html}
}

@article{danev_cryo-em_2016,
  title = {Cryo-{{EM}} Single Particle Analysis with the {{Volta}} Phase Plate},
  volume = {5},
  copyright = {\textcopyright{} 2016, Danev et al. This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.},
  issn = {2050-084X},
  doi = {10.7554/eLife.13046},
  abstract = {The Volta phase plate enables in-focus single particle analysis at near atomic resolutions, which could expand the capabilities of cryo-EM, especially for small, flexible or heterogeneous macromolecular samples.},
  language = {en},
  timestamp = {2017-01-13T09:31:31Z},
  urldate = {2016-10-31},
  journal = {eLife},
  author = {Danev, Radostin and Baumeister, Wolfgang},
  month = mar,
  year = {2016},
  note = {00016 PMID: 26949259},
  keywords = {cryo-EM,lowdose,phase plate,single particle analysis},
  pages = {e13046},
  file = {Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/CGPJ84WN/e13046.html:text/html}
}

@book{zuo_advanced_2016,
  title = {Advanced {{Transmission Electron Microscopy}}: {{Imaging}} and {{Diffraction}} in {{Nanoscience}}},
  isbn = {978-1-4939-6607-3},
  shorttitle = {Advanced {{Transmission Electron Microscopy}}},
  abstract = {This volume expands and updates the coverage in the authors' popular 1992 book, Electron Microdiffraction. As the title implies, the focus of the book has changed from electron microdiffraction and convergent beam electron diffraction to all forms of advanced transmission electron microscopy. Special attention is given to electron diffraction and imaging, including high-resolution TEM and STEM imaging, and the application of these methods to crystals, their defects, and nanostructures. The authoritative text summarizes and develops most of the useful knowledge which has been gained over the years from the study of the multiple electron scattering problem, the recent development of aberration correctors and their applications to materials structure characterization, as well as the authors' extensive teaching experience in these areas. Advanced Transmission Electron Microscopy: Imaging and Diffraction in Nanoscience is ideal for use as an advanced undergraduate or graduate level text in support of course materials in Materials Science, Physics or Chemistry departments.},
  language = {en},
  timestamp = {2017-01-13T09:31:31Z},
  publisher = {{Springer}},
  author = {Zuo, Jian Min and Spence, John C. H.},
  month = oct,
  year = {2016},
  note = {00000 Google-Books-ID: j41jDQAAQBAJ},
  keywords = {Low-dose ptychography,Science / Chemistry / Analytic,Science / Nanoscience,Science / Physics / Condensed Matter,Technology \& Engineering / Lasers \& Photonics,Technology \& Engineering / Manufacturing,Technology \& Engineering / Materials Science,Technology \& Engineering / Nanotechnology \& MEMS}
}

@article{subramaniam_cryoem_2016,
  title = {{{CryoEM}} at {{IUCrJ}}: A New Era},
  volume = {3},
  copyright = {http://creativecommons.org/licenses/by/2.0/uk},
  issn = {2052-2525},
  shorttitle = {{{CryoEM}} at {{IUCrJ}}},
  doi = {10.1107/S2052252515023738},
  abstract = {In this overview, we briefly outline recent advances in electron cryomicroscopy (cryoEM) and explain why the journal IUCrJ, published by the International Union of Crystallography, could provide a natural home for publications covering many present and future developments in the cryoEM field.},
  language = {en},
  timestamp = {2017-01-10T11:30:33Z},
  number = {1},
  urldate = {2016-11-03},
  journal = {IUCrJ},
  author = {Subramaniam, S. and K{\"u}hlbrandt, W. and Henderson, R.},
  month = jan,
  year = {2016},
  note = {00013},
  keywords = {Low-dose ptychography},
  pages = {3--7},
  file = {Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/H7T2QED9/hi5639.html:text/html}
}

@article{brink_computer-controlled_1992,
  title = {Computer-Controlled Spot-Scan Imaging of Crotoxin Complex Crystals with 400 {{keV}} Electrons at near-Atomic Resolution},
  volume = {46},
  issn = {0304-3991},
  doi = {10.1016/0304-3991(92)90017-E},
  abstract = {400 keV electrons yield a better relative image contrast than 100 keV electrons for a beam-sensitive organic crystal when spot-scan imaging is used [J. Brink and W. Chiu, J. Microscopy 161 (1991) 279]. A FORTRAN 77 program has been written to operate the spot-scan imaging system on a computer workstation under the VMS operating system which is interfaced serially to the JEOL4000 electron microscope. We demonstrate the application of this implementation by imaging crotoxin complex crystals embedded in either vitreous ice or glucose to 2.5 {\AA} resolution. The intensity strength of the structure factors of this protein crystal are different at low ( $>$ 10 {\AA}) resolution but similar at high resolution ( $<$ 10 {\AA}) for the two embedding media as expected from their scattering contrast difference. Based on our experience as judged from the electron diffraction patterns of highly tilted crystals, flat crystals embedded in glucose can be readily obtained. Furthermore, our spot-scan imaging system also has the option of correcting the focus gradient that is present in images of tilted specimens.},
  timestamp = {2017-01-13T09:31:31Z},
  number = {1},
  urldate = {2016-11-03},
  journal = {Ultramicroscopy},
  author = {Brink, Jacob and Chiu, Wah and Dougherty, Matt},
  month = oct,
  year = {1992},
  note = {00034},
  keywords = {lowdose},
  pages = {229--240},
  file = {ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/N68I367H/030439919290017E.html:text/html}
}

@article{sader_cryomicroscopy_2013,
  title = {Cryomicroscopy of Radiation Sensitive Specimens on Unmodified Graphene Sheets: {{Reduction}} of Electron-Optical Effects of Charging},
  volume = {183},
  issn = {1047-8477},
  shorttitle = {Cryomicroscopy of Radiation Sensitive Specimens on Unmodified Graphene Sheets},
  doi = {10.1016/j.jsb.2013.04.014},
  abstract = {Images of radiation-sensitive specimens obtained by electron microscopy suffer a reduction in quality beyond that expected from radiation damage alone due to electron beam-induced charging or movement of the specimen. For biological specimens, charging and movement are most severe when they are suspended in an insulating layer of vitreous ice, which is otherwise optimal for preserving hydrated specimens in a near native state. We image biological specimens, including a single particle protein complex and a lipid-enveloped virus in thin, vitreous ice films over suspended sheets of unmodified graphene. We show that in such preparations, the charging of ice, as assessed by electron-optical perturbation of the imaging beam, is eliminated. We also use the same specimen supports to record high resolution images at liquid nitrogen temperature of monolayer paraffin crystals grown over graphene.},
  timestamp = {2017-01-13T09:31:31Z},
  number = {3},
  urldate = {2016-11-03},
  journal = {Journal of Structural Biology},
  author = {Sader, Kasim and Stopps, Martyn and Calder, Lesley J. and Rosenthal, Peter B.},
  month = sep,
  year = {2013},
  note = {00007},
  keywords = {Beam induced specimen movement,Charging,Cryomicroscopy,Graphene,Low-dose ptychography,Radiation damage},
  pages = {531--536},
  file = {ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/MXDE7UEK/S1047847713001147.html:text/html}
}

@article{chang_general_2016,
  title = {A General Framework for Denoising Phaseless Diffraction Measurements},
  timestamp = {2017-01-10T11:30:34Z},
  urldate = {2016-11-08},
  url = {https://128.84.21.199/abs/1611.01417},
  author = {Chang, Huibin and Marchesini, Stefano},
  month = nov,
  year = {2016},
  note = {00001},
  keywords = {lowdose},
  file = {Chang_Marchesini_2016_A general framework for denoising phaseless diffraction measurements.pdf:/media/philipp/My Book/Dropbox/mpapers/Chang_Marchesini_2016_A general framework for denoising phaseless diffraction measurements.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/F594SFRM/1611.html:text/html}
}

@article{jaganathan_phase_2015,
  title = {Phase {{Retrieval}}: {{An Overview}} of {{Recent Developments}}},
  shorttitle = {Phase {{Retrieval}}},
  abstract = {The problem of phase retrieval is a classic one in optics and arises when one is interested in recovering an unknown signal from the magnitude (intensity) of its Fourier transform. While there have existed quite a few approaches to phase retrieval, recent developments in compressed sensing and convex optimization-based signal recovery have inspired a host of new ones. This work presents an overview of these approaches. Since phase retrieval, by its very nature, is ill-posed, to make the problem meaningful one needs to either assume prior structure on the signal (e.g., sparsity) or obtain additional measurements (e.g., masks, structured illuminations). For both the cases, we review conditions for the identifiability of the signal, as well as practical algorithms for signal recovery. In particular, we demonstrate that it is possible to robustly and efficiently identify an unknown signal solely from phaseless Fourier measurements, a fact with potentially far-reaching implications.},
  timestamp = {2017-01-18T12:37:16Z},
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1510.07713},
  primaryClass = {cs, math},
  urldate = {2016-11-18},
  url = {http://arxiv.org/abs/1510.07713},
  journal = {Arxiv},
  author = {Jaganathan, Kishore and Eldar, Yonina C. and Hassibi, Babak},
  month = oct,
  year = {2015},
  note = {00024},
  keywords = {Computer Science - Information Theory},
  file = {Jaganathan et al_2015_Phase Retrieval.pdf:/media/philipp/My Book/Dropbox/mpapers/Jaganathan et al_2015_Phase Retrieval.pdf:application/pdf;arXiv.org Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/2443JWTC/1510.html:text/html}
}

@article{kovarik_implementing_2016,
  title = {Implementing an Accurate and Rapid Sparse Sampling Approach for Low-Dose Atomic Resolution {{STEM}} Imaging},
  volume = {109},
  issn = {0003-6951},
  doi = {10.1063/1.4965720},
  abstract = {While aberration correction for scanning transmission electron microscopes (STEMs) dramatically increased the spatial resolution obtainable in the images of materials that are stable under the electron beam, the practical resolution of many STEM images is now limited by the sample stability rather than the microscope. To extract physical information from the images of beam sensitive materials, it is becoming clear that there is a critical dose/dose-rate below which the images can be interpreted as representative of the pristine material, while above it the observation is dominated by beam effects. Here, we describe an experimental approach for sparse sampling in the STEM and in-painting image reconstruction in order to reduce the electron dose/dose-rate to the sample during imaging. By characterizing the induction limited rise-time and hysteresis in the scan coils, we show that a sparse line-hopping approach to scan randomization can be implemented that optimizes both the speed of the scan and the amount of the sample that needs to be illuminated by the beam. The dose and acquisition time for the sparse sampling is shown to be effectively decreased by at least a factor of 5\texttimes{} relative to conventional acquisition, permitting imaging of beam sensitive materials to be obtained without changing the microscope operating parameters. The use of sparse line-hopping scan to acquire STEM images is demonstrated with atomic resolution aberration corrected the Z-contrast images of CaCO3, a material that is traditionally difficult to image by TEM/STEM because of dosage issues.},
  timestamp = {2017-01-13T09:31:31Z},
  number = {16},
  urldate = {2016-12-20},
  journal = {Appl. Phys. Lett.},
  author = {Kovarik, L. and Stevens, A. and Liyu, A. and Browning, N. D.},
  month = oct,
  year = {2016},
  note = {00000},
  keywords = {lowdose},
  pages = {164102}
}

@article{buban_high-resolution_2010,
  title = {High-Resolution Low-Dose Scanning Transmission Electron Microscopy},
  volume = {59},
  issn = {0022-0744},
  doi = {10.1093/jmicro/dfp052},
  abstract = {During the past two decades instrumentation in scanning transmission electron microscopy (STEM) has pushed toward higher intensity electron probes to increase the signal-to-noise ratio of recorded images. While this is suitable for robust specimens, biological specimens require a much reduced electron dose for high-resolution imaging. We describe here protocols for low-dose STEM image recording with a conventional field-emission gun STEM, while maintaining the high-resolution capability of the instrument. Our findings show that a combination of reduced pixel dwell time and reduced gun current can achieve radiation doses comparable to low-dose TEM.},
  timestamp = {2017-02-07T09:34:10Z},
  number = {2},
  urldate = {2016-12-20},
  journal = {J Electron Microsc (Tokyo)},
  author = {Buban, James P. and Ramasse, Quentin and Gipson, Bryant and Browning, Nigel D. and Stahlberg, Henning},
  month = apr,
  year = {2010},
  note = {00000 PMID: 19915208},
  keywords = {Aberration correction,low-dose,lowdose,STEM},
  pages = {103--112},
  file = {Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/CWC8M2FZ/103.html:text/html},
  pmcid = {PMC2857930}
}

@article{sader_quantitative_2010,
  title = {Quantitative Analysis of Image Contrast in Phase Contrast {{STEM}} for Low Dose Imaging},
  volume = {110},
  issn = {0304-3991},
  doi = {10.1016/j.ultramic.2010.06.008},
  abstract = {This work quantitatively evaluates the contrast in phase contrast images of thin vermiculite crystals recorded by TEM and aberration-corrected bright-field STEM. Specimen movement induced by electron irradiation remains a major problem limiting the phase contrast in TEM images of radiation-sensitive specimens. While spot scanning improves the contrast, it does not eliminate the problem. One possibility is to utilise aberration-corrected scanning transmission electron microscopy (STEM) with an {\AA}ngstrom-sized probe to illuminate the sample, and thus further reduce irradiation-induced specimen movement. Vermiculite is relatively radiation insensitive in TEM to electron fluences below 100,000 e-/{\AA}2 and this is likely to be similar for STEM although different damage mechanisms could occur. We compare the performance of a TEM with a thermally assisted field emission electron gun (FEG) and charge coupled device (CCD) image capture to the performance of STEMs with spherical aberration correction, cold field emission electron sources and photomultiplier tube image capture at a range of electron fluences and similar illumination areas. We show that the absolute contrast of the phase contrast images obtained by aberration-corrected STEM is better than that obtained by TEM. Although the STEM contrast is higher, the efficiency of collection of electrons in bright field STEM is still much less than that in bright field TEM (where for thin samples virtually all the electrons contribute to the image), and the SNR of equivalent STEM images is three times lower. This is better than expected, probably due to the absence of a frequency dependent modulation transfer function in the STEM detection system. With optimisation of the STEM bright field collection angles, the efficiency may approach that of bright field TEM, and if reductions in beam-induced specimen movement are found, STEM could surpass the overall performance of TEM.},
  timestamp = {2017-01-13T09:31:31Z},
  number = {10},
  urldate = {2016-12-20},
  journal = {Ultramicroscopy},
  author = {Sader, Kasim and Brown, Andy and Brydson, Rik and Bleloch, Andrew},
  month = sep,
  year = {2010},
  note = {00008},
  keywords = {Absolute image contrast,Beam-induced specimen movement,lowdose,Phase contrast STEM},
  pages = {1324--1331}
}

@article{tsai_x-ray_2016,
  title = {X-Ray Ptychography with Extended Depth of Field},
  volume = {24},
  copyright = {\textcopyright{} 2016 Optical Society of America},
  issn = {1094-4087},
  doi = {10.1364/OE.24.029089},
  abstract = {Ptychographic X-ray computed tomography is a coherent diffractive imaging method that offers nanometer-scale resolution with quantitative contrast. It offers the possibility to study relatively thick samples by using high energy X-ray photons and exploiting the phase contrast. However, the limited depth of field forces a compromise between resolution and sample thickness. Multi-slice techniques have been used to account for propagation effects within the sample, enabling imaging beyond the depth-of-field limit. Here we introduce and experimentally demonstrate our multi-slice algorithms that allow for the reconstruction of multiple object slices and the incident illumination, as well as the retrieval of unknown object thickness. Additionally, through numerical studies, we show that smaller scanning steps surprisingly increase the depth of field, which can be further extended by the use of multi-slice methods under conditions stated by theoretical expressions. The results presented here will be instrumental for the routine implementation of the technique for X-ray nanotomography.},
  language = {EN},
  timestamp = {2017-01-11T10:01:29Z},
  number = {25},
  urldate = {2016-12-13},
  journal = {Opt. Express, OE},
  author = {Tsai, Esther H. R. and Usov, Ivan and Diaz, Ana and Menzel, Andreas and Guizar-Sicairos, Manuel},
  month = dec,
  year = {2016},
  note = {00000},
  keywords = {lowdose},
  pages = {29089--29108},
  file = {Tsai et al_2016_X-ray ptychography with extended depth of field.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Tsai et al_2016_X-ray ptychography with extended depth of field2.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/QSGWAMXH/abstract.html:text/html}
}

@article{guizar-sicairos_role_2012,
  title = {Role of the Illumination Spatial-Frequency Spectrum for Ptychography},
  volume = {86},
  doi = {10.1103/PhysRevB.86.100103},
  abstract = {We demonstrate how the spatial-frequency spectrum of the x-ray illumination affects the reconstruction signal-to-noise ratio and resolution of ptychographic imaging. The spatial-frequency spectrum of a focused x-ray probe is enhanced by partially clipping the beam with an aperture near its focus. This approach presents a simple way of enhancing the illumination spectrum without demanding extra efforts in optics fabrication, and we experimentally demonstrate that it provides an improvement in image quality and resolution.},
  timestamp = {2017-01-13T09:31:31Z},
  number = {10},
  urldate = {2016-12-22},
  journal = {Phys. Rev. B},
  author = {Guizar-Sicairos, Manuel and Holler, Mirko and Diaz, Ana and Vila-Comamala, Joan and Bunk, Oliver and Menzel, Andreas},
  month = sep,
  year = {2012},
  note = {00030},
  keywords = {lowdose},
  pages = {100103},
  file = {APS Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/ZRE5CZCU/PhysRevB.86.html:text/html}
}

@article{maiden_soft_2013,
  title = {Soft {{X}}-Ray Spectromicroscopy Using Ptychography with Randomly Phased Illumination},
  volume = {4},
  copyright = {\textcopyright{} 2016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.},
  issn = {2041-1723},
  doi = {10.1038/ncomms2640},
  abstract = {Ptychographic methods can retrieve the complex sample transmittance from diffraction patterns that may have a large dynamic range. For soft X-ray spectromicroscopy, Maiden et al. use a diffuser to randomize the probe phase, reducing the dynamic range of the diffraction data by an order of magnitude.},
  language = {en},
  timestamp = {2017-01-13T09:31:31Z},
  urldate = {2016-12-22},
  journal = {Nature Communications},
  author = {Maiden, A. M. and Morrison, G. R. and Kaulich, B. and Gianoncelli, A. and Rodenburg, J. M.},
  month = apr,
  year = {2013},
  note = {00042},
  keywords = {lowdose},
  pages = {1669},
  file = {ncomms2640.pdf:/home/philipp/dl/papers/ncomms2640.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/M8GPTCWA/ncomms2640.html:text/html}
}

@article{rosenthal_optimal_2003,
  title = {Optimal {{Determination}} of {{Particle Orientation}}, {{Absolute Hand}}, and {{Contrast Loss}} in {{Single}}-Particle {{Electron Cryomicroscopy}}},
  volume = {333},
  issn = {0022-2836},
  doi = {10.1016/j.jmb.2003.07.013},
  abstract = {A computational procedure is described for assigning the absolute hand of the structure of a protein or assembly determined by single-particle electron microscopy. The procedure requires a pair of micrographs of the same particle field recorded at two tilt angles of a single tilt-axis specimen holder together with the three-dimensional map whose hand is being determined. For orientations determined from particles on one micrograph using the map, the agreement (average phase residual) between particle images on the second micrograph and map projections is determined for all possible choices of tilt angle and axis. Whether the agreement is better at the known tilt angle and axis of the microscope or its inverse indicates whether the map is of correct or incorrect hand. An increased discrimination of correct from incorrect hand (free hand difference), as well as accurate identification of the known values for the tilt angle and axis, can be used as targets for rapidly optimizing the search or refinement procedures used to determine particle orientations. Optimized refinement reduces the tendency for the model to match noise in a single image, thus improving the accuracy of the orientation determination and therefore the quality of the resulting map. The hand determination and refinement optimization procedure is applied to image pairs of the dihydrolipoyl acetyltransferase (E2) catalytic core of the pyruvate dehydrogenase complex from Bacillus stearothermophilus taken by low-dose electron cryomicroscopy. Structure factor amplitudes of a three-dimensional map of the E2 catalytic core obtained by averaging untilted images of 3667 icosahedral particles are compared to a scattering reference using a Guinier plot. A noise-dependent structure factor weight is derived and used in conjunction with a temperature factor (B=-1000 {\AA}2) to restore high-resolution contrast without amplifying noise and to visualize molecular features to 8.7 {\AA} resolution, according to a new objective criterion for resolution assessment proposed here.},
  timestamp = {2017-01-15T21:25:15Z},
  number = {4},
  urldate = {2016-12-23},
  journal = {Journal of Molecular Biology},
  author = {Rosenthal, Peter B. and Henderson, Richard},
  month = oct,
  year = {2003},
  note = {00598},
  keywords = {absolute hand,electron cryomicroscopy,lowdose,pyruvate dehydrogenase,single particle reconstruction,tilt pairs},
  pages = {721--745}
}

@incollection{baker_chapter_2010,
  series = {Cryo-EM Part A Sample Preparation and Data Collection},
  title = {Chapter {{Fifteen}} - {{Radiation Damage}} in {{Electron Cryomicroscopy}}},
  volume = {481},
  abstract = {In an electron microscope, the electron beam used to determine the structures of biological tissues, cells, and molecules destroys the specimen as the image is acquired. This destruction occurs before a statistically well-defined image can be obtained and is consequently the fundamental limit to resolution in biological electron cryomicroscopy (cryo-EM). Damage from the destructive interaction of electrons with frozen-hydrated specimens occurs in three stages: primary damage, as electrons ionize the sample, break bonds, and produce secondary electrons and free radicals; secondary damage, as the secondary electrons and free radicals migrate through the specimen and cause further chemical reactions; and tertiary damage, as hydrogen gas is evolved within the sample, causing gross morphological changes to the specimen. The deleterious effects of radiation are minimized in cryo-EM by limiting the exposure of the specimen to incident electrons and cooling the sample to reduce secondary damage. This review emphasizes practical considerations for minimizing radiation damage, including measurement of electron exposure, estimation of absorbed doses of energy, selection of microscope voltage and specimen temperature, and selection of electron exposure to optimize images.},
  timestamp = {2017-01-13T09:31:31Z},
  urldate = {2017-01-03},
  url = {http://www.sciencedirect.com/science/article/pii/S0076687910810158},
  booktitle = {Methods in {{Enzymology}}},
  publisher = {{Academic Press}},
  author = {Baker, Lindsay A. and Rubinstein, John L.},
  editor = {Jensen, Grant J.},
  year = {2010},
  note = {00035},
  keywords = {lowdose},
  pages = {371--388},
  file = {ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/7RRZH7VB/S0076687910810158.html:text/html}
}

@article{guizar-sicairos_phase_2008,
  title = {Phase Retrieval with Transverse Translation Diversity: A Nonlinear Optimization Approach},
  volume = {16},
  copyright = {\textcopyright{} 2008 Optical Society of America},
  issn = {1094-4087},
  shorttitle = {Phase Retrieval with Transverse Translation Diversity},
  doi = {10.1364/OE.16.007264},
  abstract = {We develop and test a nonlinear optimization algorithm for solving the problem of phase retrieval with transverse translation diversity, where the diverse far-field intensity measurements are taken after translating the object relative to a known illumination pattern. Analytical expressions for the gradient of a squared-error metric with respect to the object, illumination and translations allow joint optimization of the object and system parameters. This approach achieves superior reconstructions, with respect to a previously reported technique [H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004)], when the system parameters are inaccurately known or in the presence of noise. Applicability of this method for samples that are smaller than the illumination pattern is explored.},
  language = {EN},
  timestamp = {2017-01-21T16:03:28Z},
  number = {10},
  urldate = {2017-01-04},
  journal = {Opt. Express, OE},
  author = {Guizar-Sicairos, Manuel and Fienup, James R.},
  month = may,
  year = {2008},
  note = {00219},
  keywords = {lowdose},
  pages = {7264--7278},
  file = {Guizar-Sicairos_Fienup_2008_Phase retrieval with transverse translation diversity.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Guizar-Sicairos_Fienup_2008_Phase retrieval with transverse translation diversity.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/CCMPSB4A/abstract.html:text/html}
}

@article{mises_praktische_1929,
  title = {Praktische {{Verfahren}} Der {{Gleichungsaufl{\"o}sung}} .},
  volume = {9},
  issn = {1521-4001},
  doi = {10.1002/zamm.19290090206},
  language = {en},
  timestamp = {2017-01-21T16:03:37Z},
  number = {2},
  urldate = {2017-01-06},
  journal = {Z. angew. Math. Mech.},
  author = {Mises, R. V. and Pollaczek-Geiringer, H.},
  month = jan,
  year = {1929},
  note = {00185},
  keywords = {lowdose},
  pages = {152--164},
  file = {Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/5Q5CBPNR/abstract.html:text/html}
}

@article{chen_high-resolution_2013,
  title = {High-Resolution Noise Substitution to Measure Overfitting and Validate Resolution in {{3D}} Structure Determination by Single Particle Electron Cryomicroscopy},
  volume = {135},
  issn = {0304-3991},
  doi = {10.1016/j.ultramic.2013.06.004},
  abstract = {Three-dimensional (3D) structure determination by single particle electron cryomicroscopy (cryoEM) involves the calculation of an initial 3D model, followed by extensive iterative improvement of the orientation determination of the individual particle images and the resulting 3D map. Because there is much more noise than signal at high resolution in the images, this creates the possibility of noise reinforcement in the 3D map, which can give a false impression of the resolution attained. The balance between signal and noise in the final map at its limiting resolution depends on the image processing procedure and is not easily predicted. There is a growing awareness in the cryoEM community of how to avoid such over-fitting and over-estimation of resolution. Equally, there has been a reluctance to use the two principal methods of avoidance because they give lower resolution estimates, which some people believe are too pessimistic. Here we describe a simple test that is compatible with any image processing protocol. The test allows measurement of the amount of signal and the amount of noise from overfitting that is present in the final 3D map. We have applied the method to two different sets of cryoEM images of the enzyme beta-galactosidase using several image processing packages. Our procedure involves substituting the Fourier components of the initial particle image stack beyond a chosen resolution by either the Fourier components from an adjacent area of background, or by simple randomisation of the phases of the particle structure factors. This substituted noise thus has the same spectral power distribution as the original data. Comparison of the Fourier Shell Correlation (FSC) plots from the 3D map obtained using the experimental data with that from the same data with high-resolution noise (HR-noise) substituted allows an unambiguous measurement of the amount of overfitting and an accompanying resolution assessment. A simple formula can be used to calculate an unbiased FSC from the two curves, even when a substantial amount of overfitting is present. The approach is software independent. The user is therefore completely free to use any established method or novel combination of methods, provided the HR-noise test is carried out in parallel. Applying this procedure to cryoEM images of beta-galactosidase shows how overfitting varies greatly depending on the procedure, but in the best case shows no overfitting and a resolution of \textasciitilde{}6 {\AA}. (382 words)},
  timestamp = {2017-01-21T16:03:36Z},
  urldate = {2017-01-06},
  journal = {Ultramicroscopy},
  author = {Chen, Shaoxia and McMullan, Greg and Faruqi, Abdul R. and Murshudov, Garib N. and Short, Judith M. and Scheres, Sjors H. W. and Henderson, Richard},
  month = dec,
  year = {2013},
  note = {00156},
  keywords = {Beta-galactosidase,electron cryomicroscopy,lowdose,Overfitting,resolution,Single particle,validation},
  pages = {24--35},
  file = {Chen et al_2013_High-resolution noise substitution to measure overfitting and validate.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Chen et al_2013_High-resolution noise substitution to measure overfitting and validate.pdf:application/pdf;ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/GI4TSSUA/S0304399113001472.html:text/html}
}

@article{diaz_three-dimensional_2015,
  title = {Three-Dimensional Mass Density Mapping of Cellular Ultrastructure by Ptychographic {{X}}-Ray Nanotomography},
  volume = {192},
  issn = {1047-8477},
  doi = {10.1016/j.jsb.2015.10.008},
  abstract = {We demonstrate absolute quantitative mass density mapping in three dimensions of frozen-hydrated biological matter with an isotropic resolution of 180 nm. As model for a biological system we use Chlamydomonas cells in buffer solution confined in a microcapillary. We use ptychographic X-ray computed tomography to image the entire specimen, including the 18 $\mu$m-diameter capillary, thereby providing directly an absolute mass density measurement of biological matter with an uncertainty of about 6\%. The resulting maps have sufficient contrast to distinguish cells from the surrounding ice and several organelles of different densities inside the cells. Organelles are identified by comparison with a stained, resin-embedded specimen, which can be compared with established transmission electron microscopy results. For some identified organelles, the knowledge of their elemental composition reduces the uncertainty of their mass density measurement down to 1\% with values consistent with previous measurements of dry weight concentrations in thin cellular sections by scanning transmission electron microscopy. With prospects of improving the spatial resolution in the near future, we expect that the capability of non-destructive three-dimensional mapping of mass density in biological samples close to their native state becomes a valuable method for measuring the packing of organic matter on the nanoscale.},
  timestamp = {2017-01-13T09:31:31Z},
  number = {3},
  urldate = {2017-01-06},
  journal = {Journal of Structural Biology},
  author = {Diaz, Ana and Malkova, Barbora and Holler, Mirko and Guizar-Sicairos, Manuel and Lima, Enju and Panneels, Valerie and Pigino, Gaia and Bittermann, Anne Greet and Wettstein, Larissa and Tomizaki, Takashi and Bunk, Oliver and Schertler, Gebhard and Ishikawa, Takashi and Wepf, Roger and Menzel, Andreas},
  month = dec,
  year = {2015},
  note = {00005},
  keywords = {Chlamydomonas,lowdose,Ptychography,X-ray microscopy},
  pages = {461--469},
  file = {Diaz et al_2015_Three-dimensional mass density mapping of cellular ultrastructure by.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Diaz et al_2015_Three-dimensional mass density mapping of cellular ultrastructure by.pdf:application/pdf;ScienceDirect Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/QTXEGHPH/S1047847715300873.html:text/html}
}

@article{nogales_development_2016,
  title = {The Development of Cryo-{{EM}} into a Mainstream Structural Biology Technique},
  volume = {13},
  copyright = {\textcopyright{} 2016 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
  issn = {1548-7091},
  doi = {10.1038/nmeth.3694},
  abstract = {Single-particle cryo-electron microscopy (cryo-EM) has emerged over the last two decades as a technique capable of studying challenging systems that otherwise defy structural characterization. Recent technical advances have resulted in a 'quantum leap' in applicability, throughput and achievable resolution that has gained this technique worldwide attention. Here I discuss some of the major historical landmarks in the development of the cryo-EM field, ultimately leading to its present success.},
  language = {en},
  timestamp = {2017-01-13T09:31:36Z},
  number = {1},
  urldate = {2017-01-11},
  journal = {Nat Meth},
  author = {Nogales, Eva},
  month = jan,
  year = {2016},
  note = {00033},
  keywords = {Cryoelectron microscopy,Image processing,lowdose,Proteins},
  pages = {24--27}
}

@misc{hypero,
  title = {Hypero - {{Hyperparameter}} Optimization for Torch},
  timestamp = {2017-01-12T13:33:48Z},
  url = {https://github.com/Element-Research/hypero},
  author = {Leonard, Nicholas},
  note = {00000},
  keywords = {lowdose}
}

@misc{torch.optim,
  title = {Torch.Optim},
  abstract = {torch numerical optimization library},
  timestamp = {2017-01-12T12:49:25Z},
  url = {https://github.com/torch/optim/},
  note = {00000},
  keywords = {lowdose}
}

@techreport{shewchuk_introduction_1994,
  address = {Pittsburgh, PA, USA},
  title = {An {{Introduction}} to the {{Conjugate Gradient Method Without}} the {{Agonizing Pain}}},
  abstract = {The Conjugate Gradient Method is the most prominent iterative method for solving sparse systems of linear equations. Unfortunately, many textbook treatments of the topic are written so that even their own authors would be mystified, if they bothered to read their own writing. For this reason, an understanding of the method has been reserved for the elite brilliant few who have painstakingly decoded the mumblings of their forebears. Nevertheless, the Conjugate Gradient Method is a composite of simple, elegant ideas that almost anyone can understand. Of course, a reader as intelligent as yourself will learn them almost effortlessly. The idea of quadratic forms is introduced and used to derive the methods of Steepest Descent, Conjugate Directions, and Conjugate Gradients. Eigenvectors are explained and used to examine the convergence of the Jacobi Method, Steepest Descent, and Conjugate Gradients. Other topics include preconditioning and the nonlinear Conjugate Gradient Method. I have taken pains to make this article easy to read. Sixty-two illustrations are provided. Dense prose is avoided. Concepts are explained in several different ways. Most equations are coupled with an intuitive interpretation.},
  timestamp = {2017-01-20T13:48:53Z},
  institution = {Carnegie Mellon University},
  author = {Shewchuk, Jonathan R},
  year = {1994},
  note = {01940},
  keywords = {lowdose}
}

@misc{zcutorch,
  title = {Z-Cutorch -  {{Complex}} Number Support for Cutorch},
  timestamp = {2017-01-12T13:41:37Z},
  url = {https://github.com/PhilippPelz/z-cutorch},
  note = {00000},
  keywords = {lowdose}
}

@book{lehoucq1998arpack,
  series = {SIAM e-books},
  title = {{{ARPACK Users}}' {{Guide}}: {{Solution}} of {{Large}}-Scale {{Eigenvalue Problems}} with {{Implicitly Restarted Arnoldi Methods}}},
  isbn = {978-0-89871-962-8},
  timestamp = {2017-01-21T16:03:25Z},
  url = {https://books.google.co.in/books?id=45ZbeycoITcC},
  publisher = {{Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)}},
  author = {Lehoucq, R.B. and Sorensen, D.C. and Yang, C.},
  year = {1998},
  note = {02150},
  keywords = {lowdose}
}

@inproceedings{torch,
  title = {Torch7: {{A Matlab}}-like {{Environment}} for {{Machine Learning}}},
  timestamp = {2017-01-21T16:03:26Z},
  booktitle = {{{BigLearn}}, {{NIPS Workshop}}},
  author = {Collobert, R. and Kavukcuoglu, K. and Farabet, C.},
  year = {2011},
  note = {00445},
  keywords = {lowdose}
}

@article{mcmullan_detective_2009,
  title = {Detective Quantum Efficiency of Electron Area Detectors in Electron Microscopy},
  volume = {109},
  issn = {0304-3991},
  doi = {10.1016/j.ultramic.2009.04.002},
  abstract = {Recent progress in detector design has created the need for a careful side-by-side comparison of the modulation transfer function (MTF) and resolution-dependent detective quantum efficiency (DQE) of existing electron detectors with those of detectors based on new technology. We present MTF and DQE measurements for four types of detector: Kodak SO-163 film, TVIPS 224 charge coupled device (CCD) detector, the Medipix2 hybrid pixel detector, and an experimental direct electron monolithic active pixel sensor (MAPS) detector. Film and CCD performance was measured at 120 and 300 keV, while results are presented for the Medipix2 at 120 keV and for the MAPS detector at 300 keV. In the case of film, the effects of electron backscattering from both the holder and the plastic support have been investigated. We also show that part of the response of the emulsion in film comes from light generated in the plastic support. Computer simulations of film and the MAPS detector have been carried out and show good agreement with experiment. The agreement enables us to conclude that the DQE of a backthinned direct electron MAPS detector is likely to be equal to, or better than, that of film at 300 keV.},
  timestamp = {2017-01-20T13:49:11Z},
  number = {9},
  urldate = {2017-01-11},
  journal = {Ultramicroscopy},
  author = {McMullan, G. and Chen, S. and Henderson, R. and Faruqi, A. R.},
  month = aug,
  year = {2009},
  note = {00137},
  keywords = {CCD,CMOS detector,DQE,Electron backscatter,Film,lowdose,MAPS,Medipix,MTF},
  pages = {1126--1143}
}

@article{zernike_how_1955,
  title = {How {{I Discovered Phase Contrast}}},
  volume = {121},
  copyright = {Copyright \textcopyright{} 1955 by the American Association for the Advancement of Science},
  issn = {0036-8075, 1095-9203},
  doi = {10.1126/science.121.3141.345},
  language = {en},
  timestamp = {2017-01-21T16:03:34Z},
  number = {3141},
  urldate = {2017-01-11},
  journal = {Science},
  author = {Zernike, F.},
  month = mar,
  year = {1955},
  note = {00490},
  keywords = {lowdose},
  pages = {345--349},
  pmid = {13237991}
}

@article{ryll_pnccd-based_2016,
  title = {A {{pnCCD}}-Based, Fast Direct Single Electron Imaging Camera for {{TEM}} and {{STEM}}},
  volume = {11},
  issn = {1748-0221},
  doi = {10.1088/1748-0221/11/04/P04006},
  abstract = {We report on a new camera that is based on a pnCCD sensor for applications in scanning transmission electron microscopy. Emerging new microscopy techniques demand improved detectors with regards to readout rate, sensitivity and radiation hardness, especially in scanning mode. The pnCCD is a 2D imaging sensor that meets these requirements. Its intrinsic radiation hardness permits direct detection of electrons. The pnCCD is read out at a rate of 1,150 frames per second with an image area of 264 x 264 pixel. In binning or windowing modes, the readout rate is increased almost linearly, for example to 4000 frames per second at 4\texttimes{} binning (264 x 66 pixel). Single electrons with energies from 300 keV down to 5 keV can be distinguished due to the high sensitivity of the detector. Three applications in scanning transmission electron microscopy are highlighted to demonstrate that the pnCCD satisfies experimental requirements, especially fast recording of 2D images. In the first application, 65536 2D diffraction patterns were recorded in 70 s. STEM images corresponding to intensities of various diffraction peaks were reconstructed. For the second application, the microscope was operated in a Lorentz-like mode. Magnetic domains were imaged in an area of 256 x 256 sample points in less than 37 seconds for a total of 65536 images each with 264 x 132 pixels. Due to information provided by the two-dimensional images, not only the amplitude but also the direction of the magnetic field could be determined. In the third application, millisecond images of a semiconductor nanostructure were recorded to determine the lattice strain in the sample. A speed-up in measurement time by a factor of 200 could be achieved compared to a previously used camera system.},
  language = {en},
  timestamp = {2017-01-11T11:08:01Z},
  number = {04},
  urldate = {2017-01-11},
  journal = {J. Inst.},
  author = {Ryll, H. and Simson, M. and Hartmann, R. and Holl, P. and Huth, M. and Ihle, S. and Kondo, Y. and Kotula, P. and Liebel, A. and {K. M{\"u}ller-Caspary} and Rosenauer, A. and Sagawa, R. and Schmidt, J. and Soltau, H. and Str{\"u}der, L.},
  year = {2016},
  note = {00003},
  keywords = {lowdose},
  pages = {P04006}
}

@article{bartesaghi_structure_2014,
  title = {Structure of $\beta$-Galactosidase at 3.2-{{{\AA}}} Resolution Obtained by Cryo-Electron Microscopy},
  volume = {111},
  issn = {0027-8424, 1091-6490},
  doi = {10.1073/pnas.1402809111},
  abstract = {We report the solution structure of Escherichia coli $\beta$-galactosidase ($\sim$465 kDa), solved at $\sim$3.2-{\AA} resolution by using single-particle cryo-electron microscopy (cryo-EM). Densities for most side chains, including those of residues in the active site, and a catalytic Mg2+ ion can be discerned in the map obtained by cryo-EM. The atomic model derived from our cryo-EM analysis closely matches the 1.7-{\AA} crystal structure with a global rmsd of $\sim$0.66 {\AA}. There are significant local differences throughout the protein, with clear evidence for conformational changes resulting from contact zones in the crystal lattice. Inspection of the map reveals that although densities for residues with positively charged and neutral side chains are well resolved, systematically weaker densities are observed for residues with negatively charged side chains. We show that the weaker densities for negatively charged residues arise from their greater sensitivity to radiation damage from electron irradiation as determined by comparison of density maps obtained by using electron doses ranging from 10 to 30 e-/{\AA}2. In summary, we establish that it is feasible to use cryo-EM to determine near-atomic resolution structures of protein complexes ($<$500 kDa) with low symmetry, and that the residue-specific radiation damage that occurs with increasing electron dose can be monitored by using dose fractionation tools available with direct electron detector technology.},
  language = {en},
  timestamp = {2017-01-20T13:49:23Z},
  number = {32},
  urldate = {2017-01-11},
  journal = {PNAS},
  author = {Bartesaghi, Alberto and Matthies, Doreen and Banerjee, Soojay and Merk, Alan and Subramaniam, Sriram},
  month = dec,
  year = {2014},
  note = {00063},
  keywords = {3D reconstruction,CTF determination,frame alignment,lowdose,single-particle EM,structure refinement},
  pages = {11709--11714},
  pmid = {25071206}
}

@article{stockmar_near-field_2013,
  title = {Near-Field Ptychography: Phase Retrieval for Inline Holography Using a Structured Illumination},
  volume = {3},
  copyright = {\textcopyright{} 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.},
  issn = {2045-2322},
  shorttitle = {Near-Field Ptychography},
  doi = {10.1038/srep01927},
  abstract = {Inline holography is a common phase-contrast imaging method which uses free-space propagation to encode the phase signal into measured intensities. However, quantitative retrieval of the sample\&\#39;s image remains challenging, imposing constraints on the nature of the sample or on the propagation distance.},
  language = {en},
  timestamp = {2017-02-07T09:34:16Z},
  urldate = {2017-01-13},
  journal = {Scientific Reports},
  author = {Stockmar, Marco and Cloetens, Peter and Zanette, Irene and Enders, Bjoern and Dierolf, Martin and Pfeiffer, Franz and Thibault, Pierre},
  month = may,
  year = {2013},
  note = {00038},
  keywords = {cdi,imaging,lensless imaging,lowdose,particle,photon,ptychography,x-ray},
  pages = {1927},
  file = {Stockmar et al_2013_Near-field ptychography.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Stockmar et al_2013_Near-field ptychography.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/4B7JWGHZ/srep01927.html:text/html}
}

@article{luke_relaxed_2005,
  title = {Relaxed Averaged Alternating Reflections for Diffraction Imaging},
  volume = {21},
  issn = {0266-5611},
  doi = {10.1088/0266-5611/21/1/004},
  abstract = {We report on progress in algorithms for iterative phase retrieval. The theory of convex optimization is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged alternating reflectors and determine the fixed-point set of the related operator in the convex case. A numerical study supports our theoretical observations and demonstrates the effectiveness of the algorithm compared to the current state of the art.},
  language = {en},
  timestamp = {2017-01-21T16:03:41Z},
  number = {1},
  urldate = {2017-01-13},
  journal = {Inverse Problems},
  author = {Luke, D. Russell},
  year = {2005},
  note = {00000},
  keywords = {lowdose},
  pages = {37}
}

@article{lebrun_analysis_2012,
  title = {An {{Analysis}} and {{Implementation}} of the {{BM3D Image Denoising Method}}},
  volume = {2},
  issn = {2105-1232},
  doi = {10.5201/ipol.2012.l-bm3d},
  abstract = {BM3D is a recent denoising method based on the fact that an image has a locally sparse representation in transform domain. This sparsity is enhanced by grouping similar 2D image patches into 3D groups. In this paper we propose an open-source implementation of the method. We discuss the choice of all parameter methods and confirm their actual optimality. The description of the method is rewritten with a a more transparent notation that in the original paper. A final index gives nonetheless the correspondence between the new notation and the original notation.},
  language = {en},
  timestamp = {2017-02-07T09:33:42Z},
  urldate = {2017-01-16},
  journal = {Image Processing On Line},
  author = {Lebrun, Marc},
  month = aug,
  year = {2012},
  note = {00065},
  keywords = {lowdose},
  pages = {175--213},
  file = {Lebrun_2012_An Analysis and Implementation of the BM3D Image Denoising Method.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Lebrun_2012_An Analysis and Implementation of the BM3D Image Denoising Method.pdf:application/pdf;Lebrun_2012_An Analysis and Implementation of the BM3D Image Denoising Method.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Lebrun_2012_An Analysis and Implementation of the BM3D Image Denoising Method2.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/S3DUCGWQ/l-bm3d.html:text/html}
}

@misc{lebrun_bm3d_????,
  title = {Bm3d - {{C}}++ Implementation of {{BM3D}} Denoising},
  timestamp = {2017-02-07T09:19:40Z},
  url = {https://github.com/gfacciol/bm3d},
  author = {Lebrun, Marc},
  note = {00000},
  keywords = {lowdose}
}

@article{meyer_characterisation_2000,
  title = {Characterisation of the Signal and Noise Transfer of {{CCD}} Cameras for Electron Detection},
  volume = {49},
  issn = {1059-910X},
  doi = {10.1002/(SICI)1097-0029(20000501)49:3<269::AID-JEMT5>3.0.CO;2-B},
  abstract = {Methods to characterise the performance of CCD cameras for electron detection are investigated with particular emphasis on the difference between the transfer of signal and noise. Similar to the Modulation Transfer Function MTF, which describes the spatial frequency dependent attenuation of contrast in the image, we introduce a Noise Transfer Function NTF that describes the transfer of the Poisson noise that is inevitably present in any electron image. A general model for signal and noise transfer by an image converter is provided. This allows the calculation of MTF and NTF from Monte-Carlo simulations of the trajectories of electrons and photons in the scintillator and the optical coupling of the camera. Furthermore, accurate methods to measure the modulation and noise transfer functions experimentally are presented. The spatial-frequency dependent Detection Quantum Efficiency DQE, an important figure of merit of the camera which has so far not been measured experimentally, can be obtained from the measured MTF and NTF. The experimental results are in good agreement with the simulations and show that the NTF at high spatial frequencies is in some cases by a factor of four higher than the MTF. This implies that the noise method, which is frequently used to measure the MTF, but in fact measures the NTF, gives over-optimistic results. Furthermore, the spatial frequency dependent DQE is lower than previously assumed.},
  language = {eng},
  timestamp = {2017-01-20T13:49:13Z},
  number = {3},
  journal = {Microsc. Res. Tech.},
  author = {Meyer, R. R. and Kirkland, A. I.},
  month = may,
  year = {2000},
  note = {00112},
  keywords = {Algorithms,Biophysical Phenomena,Biophysics,Electrons,Fourier Analysis,lowdose,Microscopy; Electron,Models; Theoretical,Monte Carlo Method,Photons,Signal Processing; Computer-Assisted},
  pages = {269--280},
  pmid = {10816267}
}

@article{zhang_translation_2013,
  title = {Translation Position Determination in Ptychographic Coherent Diffraction Imaging},
  volume = {21},
  copyright = {\textcopyright{} 2013 OSA},
  issn = {1094-4087},
  doi = {10.1364/OE.21.013592},
  abstract = {Accurate knowledge of translation positions is essential in ptychography to achieve a good image quality and the diffraction limited resolution. We propose a method to retrieve and correct position errors during the image reconstruction iterations. Sub-pixel position accuracy after refinement is shown to be achievable within several tens of iterations. Simulation and experimental results for both optical and X-ray wavelengths are given. The method improves both the quality of the retrieved object image and relaxes the position accuracy requirement while acquiring the diffraction patterns.},
  language = {EN},
  timestamp = {2017-02-07T09:35:01Z},
  number = {11},
  urldate = {2017-01-18},
  journal = {Opt. Express, OE},
  author = {Zhang, Fucai and Peterson, Isaac and Vila-Comamala, Joan and Diaz, Ana and Berenguer, Felisa and Bean, Richard and Chen, Bo and Menzel, Andreas and Robinson, Ian K. and Rodenburg, John M.},
  month = jun,
  year = {2013},
  note = {00085},
  keywords = {algorithms,Electron,Image reconstruction techniques,imaging,lensless imaging,lowdose,particle,Phase retrieval,ptychography,X-ray imaging},
  pages = {13592--13606},
  file = {Zhang et al_2013_Translation position determination in ptychographic coherent diffraction imaging.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Zhang et al_2013_Translation position determination in ptychographic coherent diffraction imaging_2.pdf:application/pdf;Zhang et al_2013_Translation position determination in ptychographic coherent diffraction imaging.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Zhang et al_2013_Translation position determination in ptychographic coherent diffraction imaging.pdf:application/pdf;Snapshot:/home/philipp/.mozilla/firefox/lqlpme75.default/zotero/storage/SFD2572G/abstract.html:text/html}
}

@inproceedings{sun_geometric_2016-1,
  title = {A Geometric Analysis of Phase Retrieval},
  doi = {10.1109/ISIT.2016.7541725},
  abstract = {Given nonlinear measurements yk = |〈ak, x〉| for k = 1,...,m, is it possible to recover x $\in$ $\mathbb{C}$n? This generalized phase retrieval (GPR) problem is a fundamental task in various disciplines. Natural nonconvex methods often work remarkably well for GPR in practice, but lack clear theoretical explanations. In this paper, we take a step towards bridging this gap. We show that when the sensing vectors ak's are generic (i.i.d. complex Gaussian) and the number of measurements is large enough (m $\geq$ Cn log3 n), with high probability (w.h.p.), a natural least-squares formulation for GPR has the following benign geometric structure: (1) all local minimizers are global-they are the target signal x and its equivalent copies; and (2) the objective function has a negative directional curvature around each saddle point. Such structure allows a number of algorithmic possibilities for efficient global optimization. We describe a second-order trust-region algorithm that provably finds a global minimizer in polynomial time, from arbitrary initializations.},
  timestamp = {2017-02-07T09:20:41Z},
  booktitle = {2016 {{IEEE International Symposium}} on {{Information Theory}} ({{ISIT}})},
  author = {Sun, J. and Qu, Q. and Wright, J.},
  month = jul,
  year = {2016},
  note = {00042},
  keywords = {algorithmic possibilities,arbitrary initializations,benign geometric structure,concave programming,Extraterrestrial measurements,generalized phase retrieval problem,Geometry,global minimizer,global optimization,GPR problem,Ground penetrating radar,i.i.d. complex Gaussian,information retrieval,Information theory,least squares approximations,local minimizers,lowdose,natural least-squares formulation,natural nonconvex methods,negative directional curvature,nonlinear measurements,objective function,Optimization,Phase measurement,Radio frequency,second-order trust-region algorithm,sensing vectors,vectors},
  pages = {2379--2383}
}

@article{danielyan_bm3d_2012-1,
  title = {{{BM3D Frames}} and {{Variational Image Deblurring}}},
  volume = {21},
  issn = {1057-7149},
  doi = {10.1109/TIP.2011.2176954},
  abstract = {A family of the block matching 3-D (BM3D) algorithms for various imaging problems has been recently proposed within the framework of nonlocal patchwise image modeling , . In this paper, we construct analysis and synthesis frames, formalizing BM3D image modeling, and use these frames to develop novel iterative deblurring algorithms. We consider two different formulations of the deblurring problem, i.e., one given by the minimization of the single-objective function and another based on the generalized Nash equilibrium (GNE) balance of two objective functions. The latter results in the algorithm where deblurring and denoising operations are decoupled. The convergence of the developed algorithms is proved. Simulation experiments show that the decoupled algorithm derived from the GNE formulation demonstrates the best numerical and visual results and shows superiority with respect to the state of the art in the field, confirming a valuable potential of BM3D-frames as an advanced image modeling tool.},
  timestamp = {2017-02-07T09:33:55Z},
  number = {4},
  journal = {IEEE Transactions on Image Processing},
  author = {Danielyan, A. and Katkovnik, V. and Egiazarian, K.},
  month = apr,
  year = {2012},
  note = {00195},
  keywords = {Adaptation models,Algorithm design and analysis,Algorithms,Artifacts,block matching 3D algorithm,BM3D frame,BM3D image modeling,Computer Simulation,Deblurring,deblurring problem,decoupled algorithm,denoising operation,frames,game theory,generalized Nash equilibrium,image denoising,image enhancement,Image Interpretation; Computer-Assisted,image modeling,Image reconstruction,Image restoration,Imaging; Three-Dimensional,iterative deblurring algorithm,lowdose,Mathematical model,Models; Statistical,Pattern Recognition; Automated,Reproducibility of Results,Sensitivity and Specificity,Signal processing algorithms,Signal Processing; Computer-Assisted,single objective function,sparse representations,sparsity,stereo image processing,theory,Transforms,variational image deblurring,variational techniques},
  pages = {1715--1728},
  file = {Danielyan et al_2012_BM3D Frames and Variational Image Deblurring.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Danielyan et al_2012_BM3D Frames and Variational Image Deblurring_2.pdf:application/pdf}
}

@article{tillmann_dolphin_2016-1,
  title = {{{DOLPHIn}} \#x2014;{{Dictionary Learning}} for {{Phase Retrieval}}},
  volume = {64},
  issn = {1053-587X},
  doi = {10.1109/TSP.2016.2607180},
  abstract = {We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider such a sparse signal prior in the context of phase retrieval, when the sparsifying dictionary is not known in advance. Our algorithm jointly reconstructs the unknown signal-possibly corrupted by noise-and learns a dictionary such that each patch of the estimated image can be sparsely represented. Numerical experiments demonstrate that our approach can obtain significantly better reconstructions for phase retrieval problems with noise than methods that cannot exploit such ``hidden'' sparsity. Moreover, on the theoretical side, we provide a convergence result for our method.},
  timestamp = {2017-01-18T12:28:16Z},
  number = {24},
  journal = {IEEE Transactions on Signal Processing},
  author = {Tillmann, A. M. and Eldar, Y. C. and Mairal, J.},
  month = dec,
  year = {2016},
  note = {00000},
  keywords = {Approximation algorithms,complex-valued linear transformation,Dictionaries,DOLPHIn-dictionary learning,Dolphins,hidden sparsity,image coding,Image reconstruction,lowdose,machine learning,Noise measurement,phase retrieval algorithm,Signal processing algorithms,Signal reconstruction,signal sparse encoding,sparsifying dictionary,squared-magnitude measurements,theoretical side,two-dimensional image estimation},
  pages = {6485--6500},
  file = {Tillmann et al_2016_DOLPHIn #x2014\;Dictionary Learning for Phase Retrieval.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Tillmann et al_2016_DOLPHIn #x2014\;Dictionary Learning for Phase Retrieval.pdf:application/pdf}
}

@article{pelz_--fly_2014,
  title = {On-the-Fly Scans for {{X}}-Ray Ptychography},
  volume = {105},
  issn = {0003-6951},
  doi = {10.1063/1.4904943},
  abstract = {With the increasing importance of nanotechnology, the need for reliable real-time imaging of mesoscopic objects with nanometer resolution is rising. For X-ray ptychography, a scanning microscopy technique that provides nanometric resolution on extended fields of view, and the settling time of the scanning system is one of the bottlenecks for fast imaging. Here, we demonstrate that ptychographic on-the-fly scans, i.e., collecting diffraction patterns while the sample is scanned with constant velocity, can be modelled as a state mixture of the probing radiation and allow for reliable image recovery. Characteristics of the probe modes are discussed for various scan parameters, and the application to significantly reducing the scanning time is considered.},
  timestamp = {2017-02-07T09:34:23Z},
  number = {25},
  urldate = {2017-01-18},
  journal = {Appl. Phys. Lett.},
  author = {Pelz, Philipp M. and Guizar-Sicairos, Manuel and Thibault, Pierre and Johnson, Ian and Holler, Mirko and Menzel, Andreas},
  month = dec,
  year = {2014},
  note = {00011},
  keywords = {cdi,imaging,lensless imaging,lowdose,my papers,mypapers,partial coh.,particle,photon,ptychography,x-ray},
  pages = {251101},
  file = {Pelz et al_2014_On-the-fly scans for X-ray ptychography.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Pelz et al_2014_On-the-fly scans for X-ray ptychography_2.pdf:application/pdf;Pelz et al_2014_On-the-fly scans for X-ray ptychography.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Pelz et al_2014_On-the-fly scans for X-ray ptychography.pdf:application/pdf}
}

@article{marchesini_augmented_2013,
  title = {Augmented Projections for Ptychographic Imaging},
  volume = {29},
  issn = {0266-5611},
  doi = {10.1088/0266-5611/29/11/115009},
  abstract = {Ptychography is a popular technique to achieve diffraction limited resolution images of a two- or three-dimensional sample using high frame rate detectors. We introduce a relaxation of common projection algorithms to account for instabilities given by intensity and background fluctuations, position errors, or poor calibration using multiplexing illumination. This relaxation introduces an additional phasing optimization at every step that enhances the convergence rate of common projection algorithms. Numerical tests exhibit the exact recovery of the object and the perturbations when there is high redundancy in the data.},
  language = {en},
  timestamp = {2017-02-07T09:33:52Z},
  number = {11},
  urldate = {2017-01-18},
  journal = {Inverse Problems},
  author = {Marchesini, Stefano and Schirotzek, Andre and Yang, Chao and Wu, Hau-tieng and Maia, Filipe},
  year = {2013},
  note = {00027},
  keywords = {algorithms,cdi,imaging,lensless imaging,lowdose,Mathematics - Optimization and Control,phase retrieval,Physics - Optics,ptychography},
  pages = {115009},
  file = {Marchesini et al_2013_Augmented projections for ptychographic imaging.pdf:/mnt/wwn-0x50014ee2aaefdace-part1/Dropbox/mpapers/Marchesini et al_2013_Augmented projections for ptychographic imaging_4.pdf:application/pdf}
}

@preamble{ "\newcommand{\noopsort}[1]{} " }


\end{filecontents}

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\title{Low-dose cryo electron ptychography via non-convex Bayesian optimization}

\author[1,2,3,*]{Philipp Michael Pelz}
\author[4]{Wen Xuan Qiu}
\author[1,2]{Robert Buecker}
\author[1,2]{Guenther Kassier}
\author[1,2,3,4]{R.J. Dwayne Miller}


\affil[1]{Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany}
\affil[2]{Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany}
\affil[3]{Department of Physics, University of Hamburg, Hamburg 22761, Germany}
\affil[4]{Departments of Chemistry and Physics, University of Toronto, 80 St. George Street, Toronto M5S 1H6, Canada}
\affil[*]{philipp.pelz@mpsd.mpg.de}

%\affil[+]{these authors contributed equally to this work}

\begin{abstract}
	Electron ptychography has seen a recent surge of interest for phase sensitive imaging at atomic or near-atomic resolution. However, applications are so far mainly limited to radiation-hard samples because the required doses are too high for imaging biological samples at high resolution.
	We propose the use of non-convex, Bayesian optimization to overcome this problem and reduce the dose required for successful reconstruction by two orders of magnitude compared to previous experiments. We suggest to use this method for imaging single biological macromolecules at cryogenic temperatures and demonstrate 2D single-particle reconstructions from simulated data with a resolution of \SI{7.9}{\angstrom} at a dose of \SI{20}{\elementarycharge^-\per\angstrom^2}. When averaging over only 15 low-dose datasets, a resolution of \SI{4}{\angstrom} is possible for large macromolecular complexes. With its independence from microscope transfer function, direct recovery of phase contrast and better scaling of signal-to-noise ratio, cryo-electron ptychography may become a promising alternative to Zernike phase-contrast microscopy.
\end{abstract}



\begin{document}
	
	\flushbottom
	\maketitle
	
	\section*{Introduction}
	The advent of direct electron detectors has led to a resolution revolution in the field of cryo-electron microscopy in the last few years, producing three-dimensional atomic potential maps of biological macromolecules of a few \SI{100}{\kilo\dalton} with a resolution better than \SI{3.5}{\angstrom} \cite{bartesaghi_structure_2014,groll_structure_1997}, so that individual amino acid side-chains can be resolved. An important part in this revolution is new image processing algorithms based on a Bayesian approach, which infer important parameters without user intervention \cite{scheres_relion:_2012} and correct beam induced motion \cite{bai_ribosome_2013}. However, several challenges remain to be overcome to routinely reach \SI{3}{\angstrom} resolution also for small complexes \cite{subramaniam_cryoem_2016,bai_how_2015}: Firstly, beam-induced specimen charging and subsequent motion currently still render the high resolution information of the first few frames of a high repetition rate movie recorded with a direct electron detector unusable \cite{scheres_beam-induced_2014}, because the motion is too fast to efficiently correct for it. Secondly, the Detective Quantum Efficiency (DQE) of detectors can still be improved at high spatial frequencies \cite{glaeser_how_2016,bai_how_2015}. Thirdly, the contrast of single images can still be improved to enable reconstructions with fewer particles and increase the throughput \cite{glaeser_how_2016}.\\
	The last of these challenges has recently been addressed with a new phase plate model \cite{danev_cryo-em_2016,danev_volta_2014}, which is comparatively simple to use and provides excellent contrast at low spatial frequencies. In addition to this hardware-based approach to achieve linear phase contrast in the measured amplitudes, discovered by Zernike in the 1930s \cite{zernike_how_1955}, it is also possible to algorithmically retrieve the phase information from a set of coherent diffraction measurements. One such technique, commonly known as \textit{ptychography} or \textit{scanning coherent diffractive microscopy} \cite{Thibault2008}, is becoming increasingly popular in the field of materials science due to experimental robustness and the possibility to obtain quantitative phase contrast with an essentially unlimited field of view \cite{maiden_quantitative_2015,Diaz2012}. The use of ptychography for imaging radiation sensitive samples with electrons at high resolution is however precluded so far by its high dose requirements.\\
	We show here how the use of non-convex Bayesian optimization to solve the ptychographic phase retrieval problem fulfills the dose requirements for imaging biological macromolecules and makes it possible to obtain 2D images from single particles with sub-nanometer resolution. After a short introduction into the technique, we will also mention how ptychography offers improvements for the other two challenges discussed above.\\
	Despite being first proposed as a solution to the phase problem for electrons \cite{hoppe_trace_1982,rodenburg_phase_1989}, ptychography has seen its biggest success in X-ray imaging, due to the less stringent sample requirements and the experimental need for lensless imaging techniques. Recent developments include the introduction of iterative algorithms to enable the reconstruction of datasets collected with an out-of focus probe \cite{Thibault2009,Maiden2009}, which decreases the memory requirements of the method dramatically; the algorithmic corrections of experimental difficulties such as unknown scan positions \cite{guizar-sicairos_phase_2008,zhang_translation_2013,maiden_annealing_2012}, partial coherence \cite{Thibault2012}, probe movement during exposure \cite{pelz_--fly_2014,Clark2014}, intensity fluctuations during the scan \cite{Thibault2012,marchesini_augmented_2013} and reconstruction of background noise \cite{marchesini_augmented_2013,maiden_quantitative_2015}.\\
	In recent years, some of these advances have been applied in the context of electron microscopy and yielded atomic resolution reconstructions of low-atomic number materials \cite{Putkunz2012,yang_simultaneous_2016,dalfonso_dose-dependent_2016} and quantitative phase information \cite{maiden_quantitative_2015}.\\
	\figref{fig:experiment} shows the experimental set-up for an out-of focus ptychography experiment. A ptychographic dataset is collected by scanning a spatially confined, coherent beam, subsequently called 'probe', over the specimen and recording far-field diffraction patterns at a series of positions such that the illuminated regions of neighboring positions overlap. The diffraction limited resolution of the final image is given by the maximum angle subtended by the detector $\mathrm{r_d = \frac{\lambda * \Delta z}{N_{pix}/2*d_{pix}}}$, where $N_{pix}$ is the number of detector pixels, $d_{pix}$ is the detector pixel size, $\lambda$ is the wavelength. Given the set of positions and a realistic forward model which describes the formation of the diffraction pattern, the complex-valued transmission function which describes the atomic properties of the specimen \cite{lubk_phase-space_2015}, can be retrieved by solving a non-convex inverse problem. 
	\begin{figure}[h!]
		\includegraphics[width=1\textwidth]{experiment1}
		\caption{Experimental geometry in ptychography. The coherent electron wave function $\psi(\vec{r})$ illuminates several regions of the sample, characterized by the transmission function $T(\vec{r})$. For every position, a 2D diffraction pattern is recorded in the far field. The sample thickness $t$ can be neglected for biological macromolecules in the reconstruction at the resolutions presented in this paper.}
		\label{fig:experiment}
	\end{figure}
	The electron dose used for successful reconstruction has been above \SI{1e3}{\elementarycharge^-\per\angstrom^2} so far, limiting its usability to radiation-hard specimens. Table \ref{tab:title} lists recently published electron ptychography experiments and the used doses.
	%table was here
	The lowest dose was reported in \cite{Humphry2012}, which used an estimated \SI{3.33e3}{\elementarycharge^-\per\angstrom^2} at a resolution of \SI{58.4}{\pico\metre}, resulting in a dose of \SI{1.1e3}{\elementarycharge^-\per pixel} and achieving a line resolution of \SI{2.3}{\angstrom}, demonstrated by resolving the lattice spacing of gold nanoparticles.
	We demonstrate here via simulations that it is possible to reduce the dose by almost a factor of \num{100} to reach the dose range required for imaging biological macromolecules.\\
	The problem of beam-induced sample movement has already been addressed before the development of fast direct detectors. Scanning with small spots of several \SI{10}{\nano\meter} in size over a vitrified sample has shown to reduce beam induced specimen movement \cite{bullough_use_1987,brink_computer-controlled_1992,downing_spot-scan_1991} in real-space imaging and it has been noted that the remaining movement may be due to radiation damage, not sample charging \cite{bullough_use_1987}. Ptychography naturally operates with a confined beam, thus minimizing the area where charge can build up, such that the movement should be reduced compared to the illumination of large areas in cryo-EM. Additionally we note that due to ptychography being a scanning technique, fast acquisition and rastering is instrumental to achieve high throughput. This and the sampling requirements given by the experimental setup allow to operate the detector with very large effective pixel sizes, such that the DQE and MTF are at near-perfect values.
	\section*{Results}
	\subsection*{Image formation of cryo-TEM and cryo-ptychography}
	We perform multislice simulations of three different biological macromolecules with molecular weights ranging from \SI{64}{\kilo\dalton} to \SI{4}{\mega\dalton}. We choose the \SI{64}{\kilo\dalton} hemoglobin \cite{fermi_crystal_1984}, the \SI{706}{\kilo\dalton} 20S proteasome from yeast \cite{groll_structure_1997}, and the \SI{4}{\mega\dalton} human ribosome \cite{anger_structures_2013}.We create atomic potential maps using the Matlab code InSilicoTem \cite{vulovic_image_2013} with a thickness of \SI{70}{\nano\meter} at an electron energy of \SI{300}{\kilo\electronvolt}. We use the isolated atom superposition approximation, without solving the Poisson-Boltzmann equations for the interaction between the molecule and the ions. We also do not model the amorphousness of the solvent, which was performed in \cite{vulovic_image_2013} using molecular dynamics simulations, but was seen to have a negligible effect at very low doses. As described in \cite{vulovic_image_2013}, we model the imaginary part of the potential via the inelastic mean free path, creating a minimal transmission contrast between the vitreous ice and the protein. Using these potential maps, we simulate a ptychography experiment by cropping three-dimensional slices from this potential at several positions and propagate a coherent incoming wave through the potential slices using the methods described in \cite{Kirkland2010} in custom code. We model the detector properties as in \cite{vulovic_image_2013}, by multiplying the Fourier transform of the exit-wave intensity with $\sqrt{DQE(\vec{q})}$ before applying shot noise. Subsequently we convolve with the noise transfer function of the detector to yield the final intensity.\\
	A notable difference in the simulations and in practice is the fact that for cryo-EM usually no binning is applied to maximize the imaged area and increase throughput. Therefore, the also high spatial-frequency regions with low values of the DQE and NTF are used for image formation. For ptychography on the other hand the detector can be heavily binned until the scanning beam still fits into the real-space patch given by $\mathrm{r_d \cdot N_{pix}}$. We therefore apply a 14x binning to the diffraction patterns and crop to a size of \num{256x256}, i.e. we only use the detector up to \SI{6.7}{\percent} Nyquist frequency. The real-space patch covered by the detector is then \SI{51}{\nano\meter} at for a $\mathrm{r_d}=$\SI{2}{\angstrom}, more than necessary to fit a \SI{10}{\nano\meter} size beam. This leads to a near-constant DQE and a near unity NTF, so that there is no necessity to include them in the ptychography reconstructions, while we still include them in the simulation of the diffraction data. We note, however that a convolution with a detector transfer function can be modeled with a partially coherent beam if necessary, as demonstrated in \cite{Thibault2013b,Enders2014}.
	We choose the Gatan K2 Summit as the detector for our simulations because it has the highest published DQE and MTF values at low spatial frequencies at \SI{300}{\kilo\electronvolt} \cite{mcmullan_comparison_2014}. We note that other direct detection cameras with faster readout may be more suitable for ptychographic scanning experiments \cite{ryll_pnccd-based_2016,mcmullan_detective_2009}, but characteristics for these cameras at \SI{300}{\kilo\electronvolt} are either not published or worse than the K2 Summit. Additionally, the use of the K2 Summit for both ptychography and phase-contrast TEM simulations simplifies a direct comparison between the two methods.\\
	The final model for the formation of the intensity on the detector is then 
	\begin{equation}
	I_0(\vec{q}) = |\f{\psi_{exit}(\vec{r})}|^2 
	\end{equation}
	for the diffraction pattern and 
	\begin{equation}
	I_0(\vec{q}) = |\finv{\f{\psi_{exit}(\vec{r})}\cdot\mathrm{CTF}(\vec{q})}|^2 \\
	\end{equation}
	for the cryo-EM image. The intensity after detection is modeled as 
	\begin{equation}
	I(\vec{q}) =\finv{\f{\mathrm{Poisson}\left(\finv{\f{I_0(\vec{q})}\cdot\sqrt{\mathrm{DQE}(\vec{q})}}\right)}\cdot\mathrm{NTF}(\vec{q})}\, , 
	\end{equation}
	where NTF is the noise transfer function of the detector \cite{meyer_characterisation_2000}.
	\subsection*{Single-particle reconstructions}
	Fig. \ref{fig:reconstructions} shows a comparison of low-dose ptychography reconstructions with currently used methods for single-particle imaging with electrons: defocus-based cryo-EM and Zernike phase contrast cryo-EM with a Volta phase-plate. We choose exemplary doses of \SI{5}{\elementarycharge^-\per\angstrom^2} as the typical threshold where the highest resolution details are destroyed \cite{stark_electron_1996} and \SI{20}{\elementarycharge^-\per\angstrom^2} as a typical dose at which experiments are performed. We have reversed the contrast in the cryo-EM images to simplify the visual comparison with the ptychography reconstructions. It can be seen that ptychography clearly produces the best images for the larger particles at both doses, while it gives roughly the same results as Zernike phase-contrast for very small particles like hemoglobin. To quantitatively assess the image quality, we have computed both the Fourier Shell Correlation (FRC) \cite{Heel2005} and the average signal-to-noise ratio (SNR) in Fig. \ref{fig:reconstructions} h)-i). As ground truth for the cryo-EM images we use the electron counts in a noiseless, aberration-free image. We choose here the 1-bit criterion as a resolution threshold, as the point where the SNR drops to 1 \cite{Heel2005}. With this criterion we achieve resolutions of \SI{14.6}{\angstrom} and \SI{11.5}{\angstrom} for hemoglobin at \SI{5}{\elementarycharge^-\per\angstrom^2} and \SI{20}{\elementarycharge^-\per\angstrom^2}. For 20S proteasome \SI{12.7}{\angstrom} and \SI{10.1}{\angstrom}; and for human ribosome \SI{11.5}{\angstrom} and \SI{7.9}{\angstrom} respectively at doses of \SI{5}{\elementarycharge^-\per\angstrom^2} and \SI{20}{\elementarycharge^-\per\angstrom^2}. Looking at the average SNR values, our ptychography approach seems to have the biggest advantages for particles with molecular weight of several \SI{100}{\kilo\dalton} and larger. Here, the improvements over conventional methods are \SI{8.8}{\decibel} for 20S proteasome at \SI{20}{\elementarycharge^-\per\angstrom^2} and \SI{7.2}{\decibel} for human ribosome at \SI{20}{\elementarycharge^-\per\angstrom^2}, almost an order of magnitude improvement. For the ribosome, the signal is strong enough that the oscillating contrast transfer of the defocus-based method is nicely visible in the FRC.
	\begin{figure}[h!]
		\includegraphics[width=1\textwidth]{recons1.pdf}
		\caption{Cryo-electron ptychography reconstructions from simulated data and simulated cryo-EM images for different doses and 3 macromolecules with growing molecular weights in columns 1-3. Row a): Phase of the transmission function, the ground truth for the ptychography reconstructions. The scale bar above the figures is in rad. Rows b) and e): ptychography reconstruction at doses of \SI{5}{\elementarycharge^-\per\angstrom^2} and \SI{20}{\elementarycharge^-\per\angstrom^2}. Rows c) and f): Simulated cryo-EM image with a defocus of \SI{1.6}{\micro\meter} at a dose of \SI{5}{\elementarycharge^-\per\angstrom^2} and \SI{20}{\elementarycharge^-\per\angstrom^2}. Rows d) and g): Simulated cryo-EM image with a Zernike phase plate and a defocus of \SI{50}{\nano\meter} at doses of \SI{5}{\elementarycharge^-\per\angstrom^2} and \SI{20}{\elementarycharge^-\per\angstrom^2}. Column $\mathrm{(1)}$ hemoglobin, column $\mathrm{(2)}$ 20S proteasome, column $\mathrm{(3)}$ human ribosome. The scale bar is \SI{10}{\nano\meter}. Signal-to-noise ratio over spatial frequency for h) hemoglobin, i) 20S proteasome, j) human ribosome.}
		\label{fig:reconstructions}
	\end{figure}
	\subsection*{Effect of averaging}
	In single-particle 3D cryo-EM, a large ensemble of 2D images is collected and then oriented and averaged in three dimensions to improve the signal-to-noise ratio. A 3D reconstruction from ptychographic data is out of the scope of this paper, because dedicated algorithms need to be developed to achieve optimal results. The reconstructed 2D images do not obey the same noise statistics as cryo-EM micrographs and therefore the use of standard software would lead to suboptimal results. In the best case, a 3D model can be reconstructed directly from the raw diffraction data, while coarse orientation alignment could be done in real space from 2D reconstructions shown here.\\
	To give a rough estimate how the resolution and SNR of our algorithm scales with averaging multiple datasets, we perform here an computer experiment and average over reconstructions of 15 datasets where the particles are in identical orientation. We choose an average of 15 because there is no significant improvement when averaging more datasets. Fig. \ref{fig:averaging} a)-f) shows images of the averaged reconstructions of our three samples, at \SI{5}{\elementarycharge^-\per\angstrom^2} and \SI{20}{\elementarycharge^-\per\angstrom^2} respectively. Comparing the SNR values with the single-particle reconstructions, we see for almost all doses and samples more than an order of magnitude increase in SNR. For hemoglobin, the average SNR increases from \SI{-16.8}{\decibel} to \SI{-0.7}{\decibel} at \SI{5}{\elementarycharge^-\per\angstrom^2} and from \SI{-14}{\decibel} to \SI{3.2}{\decibel} at \SI{20}{\elementarycharge^-\per\angstrom^2}. For the 20S proteasome the SNR increases from \SI{-5.5}{\decibel} to \SI{10}{\decibel} at \SI{5}{\elementarycharge^-\per\angstrom^2} and from \SI{6.2}{\decibel} to \SI{12}{\decibel} at \SI{20}{\elementarycharge^-\per\angstrom^2}. For the human ribosome the SNR increases from \SI{-0.6}{\decibel} to \SI{13.7}{\decibel} at \SI{5}{\elementarycharge^-\per\angstrom^2} and from \SI{3.9}{\decibel} to \SI{16.1}{\decibel} at \SI{20}{\elementarycharge^-\per\angstrom^2}. All in all averaging of reconstructions gives larger improvements for very low doses.\\
	We also FRC curves for the averaged reconstructions of two independently created data sets to give a resolution estimate. We use here the 1/2-bit resolution threshold discussed in \cite{Heel2005}, which gives a slightly more conservative estimate than the 0.143-criterion commonly used in averaged reconstructions for cryo-EM. With averaging, a resolution of \SI{8}{\angstrom} is achieved for hemoglobin, \SI{4.4}{\angstrom} is achieved for 20S proteasome and \SI{3.9}{\angstrom} for human ribosome at a dose of \SI{20}{\elementarycharge^-\per\angstrom^2}.
	\begin{figure}[h!]
		\includegraphics[width=1\textwidth]{averaging1.pdf}
		\caption{Average over 15 ptychographic reconstructions from independent data sets for a) hemoglobin with \SI{5}{\elementarycharge^-\per\angstrom^2}, b) hemoglobin with \SI{20}{\elementarycharge^-\per\angstrom^2}, c) proteasome 20S with \SI{5}{\elementarycharge^-\per\angstrom^2}, d) proteasome 20S with \SI{20}{\elementarycharge^-\per\angstrom^2}, e) human ribosome with \SI{5}{\elementarycharge^-\per\angstrom^2}, f) human ribosome with \SI{20}{\elementarycharge^-\per\angstrom^2}. FRC of averaged reconstructions from independent data sets for g) hemoglobin, h) proteasome 20S i) human ribosome.}
		\label{fig:averaging}
	\end{figure}
	\subsection*{Probe and dose dependence}
	It is well known that the phase profile of the ptychographic probe can heavily influence the reconstruction quality \cite{Marchesin2014,li_multiple_2016,maiden_soft_2013,guizar-sicairos_role_2012,li_ptychographic_2014}. Here we numerically test three different probes, depicted in Fig. \ref{fig:probes}, and their influence on the reconstruction SNR at low and high doses: 1) a standard defocused probe with defocus aberration of 400 nm, 2) a defocused Fresnel Zone Plate (FZP), and 3) a randomized probe generated by a holographic phase plate and a focusing lens. Fig. \ref{fig:probes} depicts these probe in real and Fourier space and typical diffraction patterns at infinite dose and low dose. The FZP was recently suggested as a phase modulator for bright-field STEM \cite{ophus_efficient_2016}, because its simple phase modulation allows analytical retrieval of linear phase contrast. However, diffractive optics typically have imperfections due to the manufacturing process which introduce errors and dose inefficiency if the phase modulation is obtained by a simple fitting procedure. Iterative ptychography algorithms allow for the simultaneous retrieval of the probe wave function \cite{Maiden2009, Thibault2009} and therefore offers full flexibility in the design of the phase profile. Empirically, probes with a diffuse phase profile result in better reconstructions, therefore we test as a third probe a random illumination generated by a holographic phase plate and a focusing lens.\\
	Fig. \ref{fig:probe_snr} shows the SNR of the three proposed probes as a function of spatial frequency. It can be seen that at very low doses of \SI{5}{\elementarycharge^-\per\angstrom^2}, the randomized probe achieves the best SNR. At high doses of \SI{1380}{\elementarycharge^-\per\angstrom^2}, the SNR of the randomized probe at very low frequencies is higher up to a factor of \num{1e4} than the defocused probe and the FZP, whereas the performance at high resolution is only slightly better. We give two qualitative explanations of this fact, but emphasize that a theory for optimal measurement design in ptychography and a practically feasible implementation of it is still outstanding and may drastically improve upon the results presented here.
	\begin{figure}[h!]
		\includegraphics[width=1\textwidth]{probes.pdf}
		\caption{Different probes evaluated in this paper and corresponding diffraction patterns. Row 1: defocused beam with defocus aberration of 400nm, convergence half-angle \SI{7.85}{\milli\radian}; row 2: defocused beam created by a Fresnel zone plate, \SI{600}{\nano\meter} from focus; row 3: randomized beam, generated by a holographic phase plate and focused by a conventional lens. Column a) beam in real space, at the sample position, scale bar is \SI{10}{\nano\meter}; column b) beam at the probe forming aperture, scale bar is \SI{3.85}{\milli\radian}; column c) diffraction pattern of human ribosome at unlimited dose, normalized to the maximum intensity; column d) diffraction pattern for a scan with 589 acquisitions, at an electron dose of \SI{20}{\elementarycharge^-\per\angstrom^2}. The inset in 1a shows the color wheel that is used to represent amplitude and phase in columns a) and b).}
		\label{fig:probes}
	\end{figure} 
	\begin{figure}[h!]
		\includegraphics[width=1\textwidth]{SNR.pdf}
		\caption{Signal to noise ratios of reconstructions of the human ribosome at different radiation doses using a) the defocused probe, b) the Fresnel zone plate, c) the randomized probe}
		\label{fig:probe_snr}
	\end{figure}
	\newpage
	\section*{Methods}
	\subsection*{Mathematical framework of Ptychography}
	The two-dimensional complex transmission function of the object is discretized as a $\mathrm{n_1 \times n_2}$ matrix and denoted as $T : D^{n_1 \times n_2}_{r_d} \rightarrow \mathbb{C}$, where $r_\mathrm{d} > 0$ is the diffraction limited length scale. The object is illuminated by a small beam with known distribution, and discretized as a $\mathrm{m_1 \times m_2}$ matrix denoted as $\psi : D^{M}_{r_d} \rightarrow \mathbb{C}$. For simplicity, in this paper we only consider the case  $\mathrm{n_1 = n_2}$ and $\mathrm{m_1 = m_2}$, i.e. a uniform discretization in both axes.
	In the experiment, the beam is moved over the sample to positions $\vec{r}_i$ and illuminates $\mathrm{K > 1}$ subregions to obtain K diffraction images.
	\begin{equation}
	\mathbf{I}_i(\vec{q}) = |\mathcal{F}\left[\psi(\vec{r}+\vec{r}_{i}) \cdot T(\vec{r})\right]|^2, i \in \{0,...,K\}\\,
	\end{equation}
	where the discretized real space coordinates are discretized in steps of $r_\mathrm{d}$  and reciprocal space coordinates are discretized in steps of $\frac{1}{m_i\cdot r_d}$.
	%, &\mu \in \left{0,m_1 -1 \right}, \nu \in \left{0,m_2 -1 \right}, 
	%&\mu \in \left{0,m_1 -1 \right}, \nu \in \left{0,m_2 -1 \right}
	%\begin{eqnarray}
	%\vec{q} &= \left(\frac{\mu}{m_1\cdot r_d}, \frac{\nu}{m_2\cdot r_d} \right),  &\mu \in \{0,m_1 -1\}, \nu \in \{0,m_2 -1 \},\\
	%\vec{r} &= \left(r_d \cdot\mu,r_d \cdot\nu\right),  &\mu \in \{0,m_1 -1\}, \nu \in \{0,m_2 -1 \},  \\
	%\end{eqnarray}
	Mathematically, ptychography can be understood as a special case of the \textit{generalized phase retrieval problem}: given a phase-less vector of measurements $\mathbf{y} \in \mathbb{R}^m_+$
	find a complex vector $\mathbf{z} \in \mathbb{C}^n$ such that 
	\begin{equation}
	\mathbf{y} = |\mathcal{A}\mathbf{z}|^2,
	\end{equation}
	where $\mathcal{A} : \mathbb{C}^n \rightarrow \mathbb{C}^m$ is an arbitrary linear operator. We follow here the notations in \cite{Marchesin2014} to formulate ptychography as a generalized phase retrieval problem. First, we vectorize the transmission function as $\mathbf{T}^V \in \mathbb{C}^N$ with $\mathrm{N = n_1 \cdot n_2 \in \mathbb{N}}$. We introduce the matrix $R_{(i)} \in \mathbb{R}^{M\times N}$, which extracts an $m_1 \times m_2$ sized area centered at position $\vec{r}_i$ from T. With these notations in place, the relationship between the noise-free diffraction measurements collected in a ptychography experiment and $\mathbf{T}^V$ can be represented compactly as
	\begin{eqnarray}
	\mathbf{I} &=& |\mathbf{F}\mathbf{Q}\mathbf{T}^V|^2 = |\mathbf{P}\mathbf{T}^V|^2, \\
	\end{eqnarray}
	where $\mathbf{P}$ is constructed by cropping K regions from T, multiplying by the incoming beam, and a 2D discrete Fourier transform $\mathbf{F}$, i.e. $\mathbf{P}=\mathbf{F}\mathbf{Q}$.
	\begin{eqnarray}
	\overbrace{
		\begin{bmatrix}
		I_{1} \\
		\vdots \\
		I_{KM}
		\end{bmatrix}}^{\mathbf{I}\in\mathbb{R}^{KM}}&=&\left|\overbrace{\begin{bmatrix}
		F & \cdots & 0 \\
		\vdots & \ddots & \vdots \\
		0 & \cdots & F
		\end{bmatrix}}^{\mathbf{F}\in\mathbb{C}^{KM \times KM}}\overbrace{\begin{bmatrix}
		\text{diag}(\psi) R_{(1)} \\
		\vdots \\
		\text{diag}(\psi) R_{(K)}
		\end{bmatrix}}^{\mathbf{Q}\in\mathbb{C}^{KM \times N}}\mathbf{T}^V\right|^2\\.
	\end{eqnarray}
	The matrix $\mathbf{P} \in \mathbb{C}^{KM \times N}$ is sometimes called design matrix because its entries determine the measurement outcome and reflect the experimental design. In the last decades many algorithms to solve this problem have been devised, of which we only review a small fraction  with regards to low-dose reconstruction in the following section. For the subsequent analysis, we denote the KM row vectors of \textbf{P} as $\mathbf{p}_i$.
	\subsection*{Bayesian optimization with truncated gradients}\label{sec:algos}
	The most prominent iterative algorithms to solve the ptychographic phase retrieval problems are the difference map (DM) \cite{Thibault2008} algorithm and the extended ptychographic iterative engine (ePIE) \cite{Maiden2009}. The difference map belongs to the family of algorithms which use projections onto non-convex sets to reach a fix-point, the solution lying at the intersection of the two sets. It can be shown that the standard algorithm of alternating projections is equivalent to steepest descent optimization with a Gaussian likelihood and is not suited for low-dose reconstructions \cite{Marchesin2014} because the Poisson distribution arising from discretized count events differs too strongly from a Gaussian at very low electron counts. While this equality does not hold for the more elaborate projection algorithms like DM and relaxed averaged alternating reflections (RAAR) \cite{luke_relaxed_2005}, they also fail in practice at low doses \cite{Godard2012,pelz_--fly_2014}, and statistical reconstruction methods have to be used. Thibault and Guizar-Sicairos \cite{Thibault2012} have analyzed maximum likelihood methods in conjunction with a conjugate gradient update rule as a refinement step, after the DM algorithm has converged. They demonstrate improved SNR compared to the DM algorithm alone. They note, however, that starting directly with maximum likelihood optimization often poses convergence problems.\\
	The PIE algorithm can be formulated as maximum-a-posteriori (MAP) optimization with a Gaussian likelihood function and an independently weighted Gaussian prior of the object change \cite{Godard2012,Thibault2013b}, combined with a stochastic gradient-like update rule. The noise performance of the PIE algorithm has been investigated in \cite{Godard2012} and found to be worse than the Poissonian likelihood model at low counting statistics.
	While practically very robust, both algorithms can get stuck in local minima and until recently \cite{Marchesin2014}, no proof of convergence to a global minimum existed. \cite{Godard2012} suggest to use a global gradient update at the start to avoid stagnation, and \cite{maiden_quantitative_2015} use a restarted version with the stochastic gradient update rule, after removal of phase vortex artifacts.\\
	Due to the lack of algorithms with provable converge guarantees, the mathematical community has recently picked up the problem and a host of new algorithms with provable convergence has been developed, which we do not elaborate on here but point the interested reader to the summary articles \cite{jaganathan_phase_2015,shechtman_phase_2015} and the article \cite{sun_geometric_2016-1}, which refers to the most recent developments.\\
	Here we focus on developments which specifically target low-dose applications. Notable in this area is the work by Katkovnik et al. \cite{Katkovnik2013a}, which in addition to the maximum likelihood estimate introduces a transform-domain sparsity constraint on the object and optimizes two objective functions in an alternating fashion: one for the maximizing the likelihood and one for obtaining a sparse representation of the transmission function. However, instead of including the Poissonian likelihood directly, an observation filtering step is performed with a Gaussian likelihood. To obtain a sparse representation of the object, the popular BM3D denoising filter is used. Another recent, similar approach uses dictionary learning to obtain a sparse representation of the transmission function \cite{tillmann_dolphin_2016-1}, however only real-valued signals are treated.
	During the writing of this paper, Yang et al. suggested using the one-step inversion technique for low-dose ptychography \cite{yang_enhanced_????}, however no statistical treatment of the measurement process is included so far, which could be a promising avenue for future research.
	We formulate ptychographic phase retrieval as a Bayesian inference problem by introducing the probability of the transmission function $\mathbf{T}^V$, given a set of measurements $\mathbf{y} = \left(y_1, \, y_2, \, ... \, ,y_{KM}\right)^T \in \mathbb{R}_{+}^{KM}$ with the Bayes' rule:
	\begin{equation}
	P(\mathbf{T}^V|\mathbf{y}) = \frac{P(\mathbf{y}|\mathbf{T}^V)\,P(\mathbf{T}^V)}{P(\mathbf{y})}
	\end{equation}
	Since the measurements $y_i$ follow the Poisson distribution
	\begin{equation}
	y_i \sim \mathrm{Poisson}(I_i(\mathbf{T}^V)),
	\end{equation}
	the Likelihood function is given by 
	\begin{equation}
	P(y_i|\mathbf{T}^V) = \frac{I_i(\mathbf{T}^V)^{y_i}}{y_i!}e^{-I_i(\mathbf{T}^V)}.
	\end{equation}
	The prior distribution is usually chosen such that it favors realistic solutions, so that noise is suppressed in the reconstructed image. Here we evaluate two different models. A simple prior, suggested in \cite{Thibault2013b}, penalizes large gradients in the image with a Gaussian distribution on the gradient of the transmission function, which is also known as Tikhonov regularization.
	\begin{equation}
	P_{Tikhonov}(T) = \exp{(-\frac{\mu_0}{\kappa}||\nabla T(\vec{r})||^2)} = \exp{(-\frac{\mu_0}{\kappa}\sum_{i=1}^N (\mathrm{D}_x\mathbf{T}^V)_i^2 + (\mathrm{D}_y\mathbf{T}^V)_i^2)}
	\end{equation}
	with $\kappa = 8\frac{N^2}{N_m ||I||_1}$ chosen as in \cite{Thibault2013b} to scale the numerical value of the prior to be close to the likelihood. $\mathrm{D}_x$ and $\mathrm{D}_y$ are the discrete forward difference operators. The second prior we evaluate is based on the work by Katkovnik et al. \cite{Katkovnik2013a} and uses sparse modeling to denoise the transmission function:
	\begin{equation}
	P_{sparse}(\mathbf{T}^V) = \exp{(- \mu || \mathbf{T}^V - \mathbf{T}^V_{sparse} ||^2)}
	\end{equation}
	Here,  $\mathbf{T}^V_{sparse}$ is built up by applying the BM3D collaborative filtering algorithm \cite{danielyan_bm3d_2012-1}, which we describe here shortly. The BM3D algorithm computes the transform-domain sparse representation in 4 steps: 1$)$ itfinds the image patches similar to a given image patch and groups them in a 3D block 2$)$ 3D linear transform of the 3D block; 3$)$ shrinking of the transform spectrum coefficients; 4$)$ inverse 3D transformation. As input for the BM3D algorithm we transform $\mathbf{T}^V$ into hue-saturation-value format, the phase representing hue and the amplitude representing value, with full saturation. The prior $P_{sparse}(T)$ reduces the difference between the denoised version of the current transmission function and the transmission function itself. We note that during the writing of this manuscript an extensive evaluation of denoising phase retrieval algorithms was published \cite{chang_general_2016}, which also evaluates BM3D denoising using an algorithm similar to the one presented here and finds superior performance compared to other denoising strategies such as total variation or nonlocal means.
	We do not take into account the marginal likelihood $P(\mathbf{y})$ due to the high dimensionality of the problem. 
	Given the likelihood function and the prior distribution, one can write down the objective function for the MAP estimate:
	\begin{equation}
	\mathbf{T}^V_{MAP} := \underset{\mathbf{T}^V}{\mathrm{arg min}}\,\,\mathcal{L}_{MAP}(\mathbf{T}^V)
	\end{equation}
	The gradient of the likelihood is given as 
	\begin{equation}
	\mathcal{L}(\mathbf{T}^V) = \sum_{i=1}^{KM}\left[|\mathbf{p}_i\, \mathbf{T}^V|^2- y_i\, \mathrm{log}(|\mathbf{p}_i\, \mathbf{T}^V|^2)\right].
	\label{equ:LMAP1}
	\end{equation}
	and the MAP objective functions are
	%= \underset{\mathbf{T}^V}{\mathrm{arg min}}\left(-\log\left(\frac{P(\mathbf{y}|\mathbf{T}^V)P(\mathbf{T}^V)}{P(\mathbf{y})}\right) \right)
	\begin{equation}
	\mathcal{L}_{MAP}(\mathbf{T}^V) = -\log\left(\frac{P(\mathbf{y}|\mathbf{T}^V)P(\mathbf{T}^V)}{P(\mathbf{y})}\right) =  \mathcal{L}(\mathbf{T}^V) + \frac{\mu_0}{\kappa}||\nabla T(\vec{r})||^2
	\label{equ:LMAP2}
	\end{equation}
	and 
	\begin{equation}
	\mathcal{L}_{BM3D-MAP}(\mathbf{T}^V) = \mathcal{L}(\mathbf{T}^V) + \mu_1 || \mathbf{T}^V - \mathbf{T}^V_{sparse} ||^2
	\label{equ:LMAP3}
	\end{equation}
	We calculate the gradient of $\mathcal{L}_{MAP}(T)$
	\begin{equation}
	\nabla\mathcal{L}_{MAP}(T) = \sum^{KM}_{i=1} 2 \, \mathbf{p}_i\, \mathbf{T}^V \left(1-\frac{y_i }{|\mathbf{p}_i\, \mathbf{T}^V|^2}\right)\mathbf{p}_i^{\dagger} +  2 \frac{\mu_0}{\kappa}\sum_{i=1}^N (\mathrm{D}_x\mathbf{T}^V)_i + (\mathrm{D}_y\mathbf{T}^V)_i
	\end{equation}
	\begin{equation}
	\nabla\mathcal{L}_{BM3D-MAP}(T) = \sum^{KM}_{i=1} 2 \, \mathbf{p}_i\, \mathbf{T}^V \left( 1 -\frac{y_i}{|\mathbf{p}_i\, \mathbf{T}^V|^2}\right)\mathbf{p}_i^{\dagger} + \mu_1 \left(\mathbf{T}^V - \mathbf{T}^V_{sparse} \right)
	\end{equation}
	Since \ref{equ:LMAP2} and \ref{equ:LMAP3} are non-convex functions, there is no guarantee that standard gradient descent converges to a global minimum. Recently, a non-convex algorithm for the generalized phase retrieval problem with Poisson noise was presented \cite{chen_solving_2015} that provably converges to a global minimum with suitable initialization. It introduces a iteration-dependent regularization on the gradients of the likelihood to remove terms which have a negative effect on the search direction. Namely, it introduces a truncation criterion 
	\begin{equation}
	\mathcal{E}^i(\mathbf{T}^V) = \left\lbrace \left|y_i - \left|\mathbf{p}_i \mathbf{T}^V\right|^2\right| \leq \frac{\alpha_h}{KM} 
	\norm{\mathbf{y} - \mathbf{I}}{1} \frac{\left|\mathbf{p}_i \mathbf{T}^V\right|}{\norm{\mathbf{T}^V}{2}} \right\rbrace
	\end{equation}
	that acts on the gradient of the likelihood and suppresses the influence of measurements that are too incompatible with the reconstruction. The regularized likelihood gradient is then 
	\begin{equation}
	\nabla\mathcal{L}_{\mathcal{E}^i}(\mathbf{T}^V) = \sum_{i \in \mathcal{E}^i(\mathbf{T}^V)}^{KM}\left[|\mathbf{p}_i\, \mathbf{T}^V|^2- y_i\, \mathrm{log}(|\mathbf{p}_i\, \mathbf{T}^V|^2)\right].
	\label{equ:LMAP4}
	\end{equation}
	We compute the next step using conjugate gradient descent \cite{shewchuk_introduction_1994,torch.optim}, since this lead to much faster convergence compared to the update procedure described in \cite{chen_solving_2015}.
	\subsubsection*{Initialization}
	Truncated spectral initialization for ptychography was first proposed by Marchesini et al. \cite{Marchesin2014}, based on the notion that the highest intensities in the diffraction pattern carry the strongest phase information. They compute the phase of the largest eigenvector of the following hermitian operator:
	\begin{equation}
	\mathbf{1}_{|y_i|>\epsilon} \mathbf{F} \mathbf{Q}(\mathbf{Q}^{\dagger}\mathbf{Q})^{-1}\mathbf{Q}^{\dagger}\mathbf{F}^{\dagger}\mathbf{1}_{|y_i|>\epsilon}\, ,
	\end{equation}
	where $\mathbf{1}_{\mathbf{y}>\epsilon}$ is an indicator vector of the same dimension as $\mathbf{y}$ and $\epsilon$ is chosen so that the largest 20 percent of the intensities are allowed to contribute.
	The largest eigenvalue of a sparse hermitian matrix can be efficiently computed either with power iterations \cite{mises_praktische_1929}, or with the Arnoldi method \cite{lehoucq1998arpack}. In \cite{chen_solving_2015}, truncated spectral initialization with a truncation rule  with $\mathbf{1}_{|y_i|<\alpha_0^2\, \lambda_0^2}$ is used, with $\lambda_0=\sqrt{\sum_{i=1}^{KM} y_i}$. We  found the initialization of Marchesini et al. to produce better initializations for ptychographic datasets. This may be due to the nature of the ptychographic measurement vectors $\mathbf{p}_i$, which are different from the measurement vectors used in \cite{chen_solving_2015}. We leave further analysis of this matter for future research. It is also important to note that the truncated spectral initialization only produces visually correct initial phase to a dose of roughly \SI{100}{\elementarycharge^-\per\angstrom^2}. Fig. \ref{fig:algos} b) shows an example initialization for a dose of \SI{100}{\elementarycharge^-\per\angstrom^2}. For doses below this value, we initialized the transmission function with unity transmission and normal-distributed phase with mean \num{0.1}, \num{0.2}, and \num{0.3} for hemoglobin, 20S proteasome and ribosome respectively, and variance of \num{0.1}, which usually provides a lower starting error than the spectral initialization. With this sample-dependent random initialization we found no problem of convergence for all algorithms tested in this paper.
	\begin{figure}[h!]
		\includegraphics[width=1\textwidth]{algos_init.pdf}
		\caption{a) Convergence behavior of different gradient update rules b) Example for the transmission function initialization $T^0$ after 70 power iterations, for an electron dose of \SI{100}{\elementarycharge^-\per\angstrom^2}, intensities were truncated at the 80th percentile. c) $\mathbf{T}^V_{sparse}$ for human ribosome after 60 iterations of BM3D-MAP. Scale bar is \SI{10}{\nano\meter}.}
		\label{fig:algos}
	\end{figure}
	\subsubsection*{Reconstruction parameters}
	All ptychography reconstructions were performed with a probe area overlap of \SI{75}{\percent} in real-space, where the probe area is defined by all pixels contributing more than \SI{1}{\percent} of the maximum intensity. This corresponds to a step size of roughly \SI{3}{\nano\meter}, depending on the probe used. For the reconstructions shown in Fig. \ref{fig:reconstructions} a total of 589 diffraction patterns were created using the random illumination. At a dose of \SI{20}{\elementarycharge^-\per\angstrom^2}, this corresponds to \num{5000} electrons per diffraction pattern.
	For the regularization parameters we performed a grid search evaluating the final NRMSE and found the values to be $\mathrm{\mu_1=4e-2}$, $\mathrm{\mu_2=1e-1}$. We choose the biorthogonal spline wavelet transform as the linear transform for BM3D as it achieves the best PSNR for high noise \cite{lebrun_analysis_2012}.
	\subsubsection*{Implementation Details}
	The algorithms presented in this paper were implemented with the torch scientific computing framework \cite{torch}. The gradient update routines were adapted from the optim package for torch \cite{torch.optim}. For efficient  computing on the graphics processing unit (GPU) with complex numbers, the zcutorch library for cuda was developed \cite{zcutorch}. hyperparameter optimization was done with the hypero \cite{hypero} package for torch. For BM3D denoising we use the C++ implementation \cite{lebrun_bm3d_????}.
	The code was run on an Intel i7-6700 processor with 32GB RAM and a NVidia Titan X GPU with 12GB RAM. The runtime for optimization with $\mathcal{L}_{MAP}$ was \SI{26}{\second}, and for optimization with $\mathcal{L}_{BM3D-MAP}$ \SI{35}{\second}, because the BM3D algorithm used here is not implemented on the GPU and the BM3D denoising is computationally more intensive.
	\section*{Conclusion}
	In this paper we have demonstrated via numerical experiments the possibility to retrieve high resolution electron transmission phase information of biological macromolecules using ptychography and Bayesian optimization. Using the methods presented in this paper, it should be possible to achieve resolutions below \SI{1}{\nano\meter} for true single particle imaging of large molecular complexes like human ribosome and a resolution around \SI{4}{\angstrom} with simple averaging of 15 datasets. We have given a detailed explanation of the optimization and initialization procedures used and have emphasized the importance of choosing an appropriate illumination function. We note that, while the high data redundancy in a ptychographic dataset empirically makes it experimentally very robust, there is much room for improvements in terms of measurement complexity. For the results presented here, the measurement dimension $\mathrm{KM}$ is larger than the problem dimension $\mathrm{N}$ by a factor of at least 30, while the theoretical limit for successful phase retrieval is $\mathrm{KM=4N}$ \cite{balan_signal_2006}. By reducing the number of measurements the variance of each individual measurement could be reduced, yielding an improved SNR in the reconstruction. Therefore the development of an optimized experimental scheme including design of the illumination function and scanning scheme is a promising direction of research and may enable significant improvement to the results presented here.\\
	We would like to point out two obstacles that one may have to overcome in the experimental realization of our results. Firstly the best results are to be expected when recoding zero-loss diffraction patterns with the use of an energy filter. The energy filter may introduce phase distortions into the diffraction patterns which may need to be accounted for in the reconstruction algorithm. One could achieve this by first reconstructing the incoming wavefront in characterization experiment without energy filter and then reconstructing the aberration induced by the energy filter with a fixed, known incoming wavefront. Secondly, although beam induced movements are expected to be reduced by a large amount due to spot-scanning, the remaining movement may cause problems in the reconstruction. Statistically stationary sample movements can be accounted for in the reconstruction algorithm \cite{pelz_--fly_2014,Clark2011}, but beam induced motions are likely to be non-stationary, and dedicated algorithms may need to be developed to account for it. Cryogenic ptychographic imaging of biological samples is also being developed in the X-ray sciences \cite{diaz_three-dimensional_2015}, and our results could equally be implemented there to improve the dose-effectiveness.
	Finally, the methods presented here may find application in electron phase imaging of radiation-sensitive samples under non-cryogenic conditions and the incorporation of Bayesian methods into in-focus ptychographic reconstruction procedures \cite{yang_enhanced_????,rodenburg_phase_1989} may provide similar gains in SNR as the ones discussed here while also keeping the analytical capabilities of traditional STEM imaging.
	\section*{Acknowledgements}
	This work was funded by the Max Planck Society through institutional support. P.M.P. acknowledges support from the International Max Planck Research School for Ultrafast Imaging \& Structural Dynamics.
	\section*{Author contributions statement}
	P.M.P., R.J.D.M. and R.B. conceived the idea. P.M.P and W.Q wrote the simulation code. P.M.P wrote the ptychographic reconstruction code. P.M.P wrote the paper with input and discussions from R.B, G.K, and R.J.D.M.
	\section*{Competing financial interests}
	The authors declare no competing financial interests.
	\begin {table}[h!]
	\begin{center}
		\begin{tabular}{|l|c|c|c|c|}
			\hline			
			Reference                                           & resolution  & \SI{}{\elementarycharge^-\per\angstrom^2} \\
			\hline
			D'Alfonso et al. \cite{dalfonso_dose-dependent_2016} & $\sim$\SI{1.5}{\angstrom}  & \num{3.98e4}\\ % & \num{2.69e4} \\
			Yang et al. \cite{yang_simultaneous_2016}           & atomic & \num{1.3e4}\\ % & \num{8.1e3} \\
			Putkunz et al.\cite{Putkunz2012}           &  $\sim$\SI{1}{\angstrom}   & \num{9.2e6}\\ % & \num{5.4e6} \\
			Humphry et al. \cite{Humphry2012} & $\sim$\SI{2.3}{\angstrom}    & \num{3.33e3} \\ %& \num{1.1e3} \\
			\hline  		
		\end{tabular}
		\caption{List of previously published electron ptychography experiments and used electron dose}\label{tab:title} 
	\end{center}
	\end {table}
	%\bibliographystyle{plainnat}
	\bibliography{\jobname}
%\listoftodos

\end{document}
main.bbl
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