Phaseless PCA: Low-Rank Matrix Recovery from Column-wise Phaseless Measurements

We study the problem of recovering a low-rank matrix, X, from magnitude-only observations of random linear projections of its columns (phaseless measurements). We develop a new approach, called Phase Retrieval Low Rank (PReLow), that borrows ideas from a very recent non-convex phase retrieval approach, called truncated Wirtinger flow (TWF). We show via extensive numerical experiments that, when the rank of X is small compared to its dimensions, PReLow significantly outperforms TWF which operates on one column of X at a time (does not use its low-rank structure).

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