Phase retrieval from single biomolecule diffraction pattern

TL;DR

This paper introduces SPR, a Bayesian-based phase retrieval method for coherent x-ray diffraction imaging, capable of reconstructing biomolecular structures from noisy single-shot diffraction patterns without boundary constraints.

Contribution

The SPR method is a novel Bayesian approach that improves phase retrieval in low signal-to-noise conditions without requiring boundary constraints, unlike traditional methods.

Findings

Successfully reconstructs electron density from noisy data

Performs well even when central pixels are masked

Outperforms conventional methods in low SNR scenarios

Abstract

In this paper, we propose the SPR (sparse phase retrieval) method, which is a new phase retrieval method for coherent x-ray diffraction imaging (CXDI). Conventional phase retrieval methods effectively solve the problem for high signal-to-noise ratio measurements, but would not be sufficient for single biomolecular imaging which is expected to be realized with femto-second x-ray free electron laser pulses. The SPR method is based on the Bayesian statistics. It does not need to set the object boundary constraint that is required by the commonly used hybrid input-output (HIO) method, instead a prior distribution is defined with an exponential distribution and used for the estimation. Simulation results demonstrate that the proposed method reconstructs the electron density under a noisy condition even some central pixels are masked.