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

TL;DR

The paper introduces OSS, an iterative algorithm that improves phase retrieval from noisy diffraction data by leveraging pixel correlation and spatial frequency filtering, outperforming existing methods in accuracy and consistency.

Contribution

The paper presents OSS, a novel phase retrieval algorithm that effectively handles noise by combining smoothness constraints with existing iterative methods.

Findings

OSS outperforms HIO, ER-HIO, and NR-HIO algorithms in noisy conditions.

Numerical simulations and biological data validate OSS's superior accuracy.

OSS maintains robustness across various noise levels.

Abstract

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.