  Coherent diffraction imaging (CDI) is high-resolution lensless microscopy
that has been applied to image a wide range of specimens using synchrotron
radiation, X-ray free electron lasers, high harmonic generation, soft X-ray
laser and electrons. Despite these rapid advances, it remains a challenge to
reconstruct fine features in weakly scattering objects such as biological
specimens from noisy data. Here we present an effective iterative algorithm,
termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction
intensities. OSS exploits the correlation information among the pixels or
voxels in the region outside of a support in real space. By properly applying
spatial frequency filters to the pixels or voxels outside the support at
different stage of the iterative process (i.e. a smoothness constraint), OSS
finds a balance between the hybrid input-output (HIO) and error reduction (ER)
algorithms to search for a global minimum in solution space, while reducing the
oscillations in the reconstruction. Both our numerical simulations with Poisson
noise and experimental data from a biological cell indicate that OSS
consistently outperforms the HIO, ER-HIO and noise robust (NR)-HIO algorithms
at all noise levels in terms of accuracy and consistency of the
reconstructions. We expect OSS to find application in the rapidly growing CDI
field as well as other disciplines where phase retrieval from noisy Fourier
magnitudes is needed.
