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http://dx.doi.org/10.3837/tiis.2020.11.006

Large-Scale Phase Retrieval via Stochastic Reweighted Amplitude Flow  

Xiao, Zhuolei (College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications)
Zhang, Yerong (College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications)
Yang, Jie (College of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications)
Publication Information
KSII Transactions on Internet and Information Systems (TIIS) / v.14, no.11, 2020 , pp. 4355-4371 More about this Journal
Abstract
Phase retrieval, recovering a signal from phaseless measurements, is generally considered to be an NP-hard problem. This paper adopts an amplitude-based nonconvex optimization cost function to develop a new stochastic gradient algorithm, named stochastic reweighted phase retrieval (SRPR). SRPR is a stochastic gradient iteration algorithm, which runs in two stages: First, we use a truncated sample stochastic variance reduction algorithm to initialize the objective function. The second stage is the gradient refinement stage, which uses continuous updating of the amplitude-based stochastic weighted gradient algorithm to improve the initial estimate. Because of the stochastic method, each iteration of the two stages of SRPR involves only one equation. Therefore, SRPR is simple, scalable, and fast. Compared with the state-of-the-art phase retrieval algorithm, simulation results show that SRPR has a faster convergence speed and fewer magnitude-only measurements required to reconstruct the signal, under the real- or complex- cases.
Keywords
Phase retrieval; Nonconvex optimization; sample stochastic variance reduction; stochastic reweighted gradient iteration;
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