Phase Retrieval Using Alternating Minimization In A Batch Setting

Abstract

This paper considers the problem of phase retrieval, where the goal is to recover a signal Z ϵ Cn from the observations yi=|ai∗z|, i=1,2,⋯,m. While many algorithms have been proposed, the alternating minimization algorithm has been one of the most commonly used methods, and it is very simple to implement. Current work [26] has proved that when the observation vectors {a}ii=1m are sampled from a complex Gaussian distribution N(0, I), it recovers the underlying signal with a good initialization when m=O(n), or with random initialization when m=O(n2), and it conjectured that random initialization succeeds with m=O(n). This work proposes a modified alternating minimization method in a batch setting, and proves that when m=O(n log2n), the proposed algorithm with random initialization recovers the underlying signal with high probability. The proof is based on the observation that after each iteration of alternating minimization, with high probability, the angle between the estimated signal and the underlying signal is reduced.

Publication Date

10-23-2018

Publication Title

2018 Information Theory and Applications Workshop, ITA 2018

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/ITA.2018.8503171

Socpus ID

85057219480 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85057219480

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