• KSII Transactions on Internet and Information Systems
    Monthly Online Journal (eISSN: 1976-7277)

Large-Scale Phase Retrieval via Stochastic Reweighted Amplitude Flow


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.


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Cite this article

[IEEE Style]
Z. Xiao, Y. Zhang and J. Yang, "Large-Scale Phase Retrieval via Stochastic Reweighted Amplitude Flow," KSII Transactions on Internet and Information Systems, vol. 14, no. 11, pp. 4355-4371, 2020. DOI: 10.3837/tiis.2020.11.006.

[ACM Style]
Zhuolei Xiao, Yerong Zhang, and Jie Yang. 2020. Large-Scale Phase Retrieval via Stochastic Reweighted Amplitude Flow. KSII Transactions on Internet and Information Systems, 14, 11, (2020), 4355-4371. DOI: 10.3837/tiis.2020.11.006.