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Coherent diffraction imaging (CDI) is high-resolution lensless microscopythat has been applied to image a wide range of specimens using synchrotronradiation, X-ray free electron lasers, high harmonic generation, soft X-raylaser and electrons. Despite these rapid advances, it remains a challenge toreconstruct fine features in weakly scattering objects such as biologicalspecimens from noisy data. Here we present an effective iterative algorithm,termed oversampling smoothness (OSS), for phase retrieval of noisy diffractionintensities. OSS exploits the correlation information among the pixels orvoxels in the region outside of a support in real space. By properly applyingspatial frequency filters to the pixels or voxels outside the support atdifferent stage of the iterative process (i.e. a smoothness constraint), OSSfinds a balance between the hybrid input-output (HIO) and error reduction (ER)algorithms to search for a global minimum in solution space, while reducing theoscillations in the reconstruction. Both our numerical simulations with Poissonnoise and experimental data from a biological cell indicate that OSSconsistently outperforms the HIO, ER-HIO and noise robust (NR)-HIO algorithmsat all noise levels in terms of accuracy and consistency of thereconstructions. We expect OSS to find application in the rapidly growing CDIfield as well as other disciplines where phase retrieval from noisy Fouriermagnitudes is needed.

Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities