swMATH ID: 24954
Software Authors: Goldstein, Tom; Studer, Christoph
Description: PhaseMax: convex phase retrieval via basis pursuit. We consider the recovery of a (real- or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods that use semidefinite relaxation and lift the phase retrieval problem to a higher dimension, PhaseMax is a ”non-lifting” relaxation that operates in the original signal dimension. We show that the dual problem to PhaseMax is Basis Pursuit, which implies that phase retrieval can be performed using algorithms initially designed for sparse signal recovery. We develop sharp lower bounds on the success probability of PhaseMax for a broad range of random measurement ensembles, and we analyze the impact of measurement noise on the solution accuracy. We use numerical results to demonstrate the accuracy of our recovery guarantees, and we showcase the efficacy and limits of PhaseMax in practice.
Homepage: https://arxiv.org/abs/1610.07531
Related Software: Wirtinger Flow; PhaseLift; GESPAR; BranchHull; SparsePR; PDCO; PhasePack; PhaseCode; CoSaMP; LIBSVM; RRR; BlockPR; Macaulay2; ProxToolbox; Superflip; iPiano; FASTA; FMS; ADMiRA; minFunc
Cited in: 30 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
PhaseMax: convex phase retrieval via basis pursuit. Zbl 1390.94194
Goldstein, Tom; Studer, Christoph

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