Phase Retrieval by Alternating Minimization with Random Initialization

2018/12/04 by Zhang, Teng
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1812.01255

Abstract

We consider a phase retrieval problem, where the goal is to reconstruct a n-dimensional complex vector from its phaseless scalar products with m sensing vectors, independently sampled from complex normal distributions. We show that, with a random initialization, the classical algorithm of alternating minimization succeeds with high probability as n,m→∞ when m/log³m≥ Mn^3/2log^1/2n for some M>0. This is a step toward proving the conjecture in \citeWaldspurger2016, which conjectures that the algorithm succeeds when m=O(n). The analysis depends on an approach that enables the decoupling of the dependency between the algorithmic iterates and the sensing vectors.

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