A Flexible Phase Retrieval Framework for Flux-limited Coherent X-Ray Imaging

TL;DR

This paper introduces a versatile iterative phase retrieval framework for coherent X-ray diffraction imaging that effectively manages noise, missing data, and support constraints, improving accuracy over existing methods.

Contribution

The proposed framework is flexible, incorporates noise modeling, support updates, regularization, and missing data handling, and is efficiently solved using ADMM, outperforming current algorithms.

Findings

Outperforms state-of-the-art algorithms in low-photon phase retrieval

Works effectively on both simulated and experimental data

Handles Gaussian and Poissonian noise, missing data, and support updates

Abstract

Coherent X-ray diffraction imaging (CXDI) experiments are intrinsically limited by shot noise, a lack of prior knowledge about the sample's support, and missing measurements due to the experimental geometry. We propose a flexible, iterative phase retrieval framework that allows for accurate modeling of Gaussian or Poissonian noise statistics, modified support updates, regularization of reconstructed signals, and handling of missing data in the observations. The proposed method is efficiently solved using alternating direction method of multipliers (ADMM) and is demonstrated to consistently outperform state-of-the-art algorithms for low-photon phase retrieval from CXDI experiments, both for simulated diffraction patterns and for experimental measurements.