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

Poline XIAN, Haiguang Liu, Xue-Cheng TAI, Yang Wang

Research output: Chapter in book/report/conference proceedingChapterpeer-review


In this chapter, 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.
Original languageEnglish
Title of host publicationHandbook of Mathematical Models and Algorithms in Computer Vision and Imaging
EditorsKe Chen, Carola-Bibiane Schönlieb, Xue-Cheng Tai, Laurent Younes
Place of PublicationCham
PublisherSpringer Cham
Number of pages16
ISBN (Electronic)9783030986612
ISBN (Print)9783030986605
Publication statusPublished - 25 Feb 2023

User-Defined Keywords

  • Phase retrieval
  • Randomized Kaczmarz algorithm
  • Stochastic optimization
  • Variance reduction


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