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Compared to other phase retrieval algorithms, methods based on convexification techniques, like PhaseLift or PhaseCut, have the advantage to be more amenable to theoretical analysis. Empirically, they also seem to provide precise reconstructions, even in difficult settings. However, their computational complexity remains prohibitive. This issue is not specific to phase retrieval; a general - but somewhat heuristic - remedy, is the so-called Burer-Monteiro factorization, introduced by Burer and Monteiro, and recently studied in more detail by Boumal, Voroninski and Bandeira. We will discuss the use of this factorization in phase retrieval. This is a preliminary work, in collaboration with Alden Waters (University of Groningen).
This presentation is part of Minisymposium “MS21 - Recent mathematical advances in phase retrieval and computational imaging (2 parts)”
organized by: Mahdi Soltanolkotabi (University of Southern California) , Tamir Bendory (Princeton University) .