Solving systems of phaseless equations via Kaczmarz methods: a proof of concept study. (6th November 2015)

• Record Type: Journal Article
• Authors: Wei, Ke
• Is Part Of: Inverse problems. Volume 31:Number 12(2015:Dec.)
• Publication Date: 2015-11-06
• Subjects: generalized phase retrieval -- Kaczmarz methods -- alternating projection -- phase selection heuristic; 49N30 -- 49N45 -- 65F10 -- 65F20 -- 65F22 -- 41A65; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/12/125008
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We study the Kaczmarz methods for solving systems of phaseless 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.