  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 7.9
\AA$\,$ at a dose of 20 $e^- / \AA^2$. When averaging over only 15 low-dose
datasets, a resolution of 4 \AA$\,$ 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.
