Solving systems of phaseless equations via Kaczmarz methods: A proof of concept study

2015/02/06 by Ke Wei, Wei, Ke · 4 citations
Engineering · Physics and Astronomy · #Advanced X-ray Imaging Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Robotics and Sensor-Based Localization

paper · pdf · doi:10.48550/arxiv.1502.01822

openalex publication_date 2015/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Kaczmarz methods for solving systems of quadratic equations, i.e., the generalized phase retrieval problem. The methods extend the Kaczmarz methods for solving systems of linear equations by integrating a phase selection heuristic in each iteration and overall have the same per iteration computational complexity. Extensive empirical performance comparisons establish the computational advantages of the Kaczmarz methods over other state-of-the-art phase retrieval algorithms both in terms of the number of measurements needed for successful recovery and in terms of computation time. Preliminary convergence analysis is presented for the randomized Kaczmarz methods.

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