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

In: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author

Listed:
  • Yin Xian

    (TCL Research Hong Kong)

  • Haiguang Liu

    (Microsoft Research-Asian)

  • Xuecheng Tai

    (Hong Kong Center for Cerebro-cardiovascular Health Engineering (COCHE))

  • Yang Wang

    (Hong Kong University of Science and Technology)

Abstract

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.

Suggested Citation

  • Yin Xian & Haiguang Liu & Xuecheng Tai & Yang Wang, 2023. "Randomized Kaczmarz Method for Single Particle X-Ray Image Phase Retrieval," Springer Books, in: Ke Chen & Carola-Bibiane Schönlieb & Xue-Cheng Tai & Laurent Younes (ed.), Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, chapter 36, pages 1273-1288, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_112
    DOI: 10.1007/978-3-030-98661-2_112
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