Phase retrieval with random Gaussian sensing vectors by alternating projections

2016/12/13 by Waldspurger, Irène
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1612.04330

Abstract

We consider a phase retrieval problem, where we want to reconstruct a n-dimensional vector from its phaseless scalar products with m sensing vectors, independently sampled from complex normal distributions. We show that, with a suitable initalization procedure, the classical algorithm of alternating projections succeeds with high probability when m≥ Cn, for some C>0. We conjecture that this result is still true when no special initialization procedure is used, and present numerical experiments that support this conjecture.

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