Phase Retrieval by Alternating Minimization with Random Initialization
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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/^3m≥ Mn^3/2^1/2n for some M>0. This is a step toward proving the conjecture in Waldspurger2016, 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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