Phase recovery, MaxCut and complex semidefinite programming

Phase retrieval seeks to recover a signal x ∈ C p from the amplitude | A x | of linear measurements A x ∈ C n . We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called PhaseCut ) similar to the classical MaxCut se...

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Veröffentlicht in:Mathematical programming Jg. 149; H. 1-2; S. 47 - 81
Hauptverfasser: Waldspurger, Irène, d’Aspremont, Alexandre, Mallat, Stéphane
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2015
Springer Nature B.V
Schlagworte:
Algorithms
Amplitudes
Analysis
Blocking
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Fourier transforms
Full Length Paper
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Phase retrieval
Quadratic programming
Semidefinite programming
Studies
Texts
Theoretical
Vectors (mathematics)
Wavelet transforms
94A12
90C22
90C27
ISSN:0025-5610, 1436-4646
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:Phase retrieval seeks to recover a signal x ∈ C p from the amplitude | A x | of linear measurements A x ∈ C n . We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called PhaseCut ) similar to the classical MaxCut semidefinite program. We solve this problem using a provably convergent block coordinate descent algorithm whose structure is similar to that of the original greedy algorithm in Gerchberg and Saxton (Optik 35:237–246, 1972 ), where each iteration is a matrix vector product. Numerical results show the performance of this approach over three different phase retrieval problems, in comparison with greedy phase retrieval algorithms and matrix completion formulations.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-013-0738-9