Randomized Kaczmarz Method for Single Particle X-ray Image Phase Retrieval

TL;DR

This paper introduces a variance-reduced randomized Kaczmarz algorithm for phase retrieval in single particle X-ray imaging, demonstrating faster convergence, higher accuracy, and robustness to noise compared to existing methods.

Contribution

The paper proposes a novel VR-RK algorithm combining randomized Kaczmarz and SVRG techniques for improved phase retrieval in X-ray imaging.

Findings

Faster convergence than traditional algorithms

Higher phase recovery accuracy

Robust performance in noisy conditions

Abstract

In this paper, we investigate phase retrieval algorithm for the single particle X-ray imaging data. We present a variance-reduced randomized Kaczmarz (VR-RK) algorithm for phase retrieval. The VR-RK algorithm is inspired by the randomized Kaczmarz method and the Stochastic Variance Reduce Gradient Descent (SVRG) algorithm. Numerical experiments show that the VR-RK algorithm has a faster convergence rate than randomized Kaczmarz algorithm and the iterative projection phase retrieval methods, such as the hybrid input output (HIO) and the relaxed averaged alternating reflections (RAAR) methods. The VR-RK algorithm can recover the phases with higher accuracy, and is robust at the presence of noise. Experimental results on the scattering data from individual particles show that the VR-RK algorithm can recover phases and improve the single particle image identification.