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Phase recovery, MaxCut and complex semidefinite programming

Mathematical programming, 2015-02, Vol.149 (1-2), p.47-81 [Peer Reviewed Journal]

Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013 ;Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2015 ;ISSN: 0025-5610 ;EISSN: 1436-4646 ;DOI: 10.1007/s10107-013-0738-9 ;CODEN: MHPGA4

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Title:
Phase recovery, MaxCut and complex semidefinite programming
Author: Waldspurger, Irène ; d’Aspremont, Alexandre ; Mallat, Stéphane
Subjects: 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
Is Part Of: Mathematical programming, 2015-02, Vol.149 (1-2), p.47-81
Description: 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.
Publisher: Berlin/Heidelberg: Springer Berlin Heidelberg
Language: English
Identifier: ISSN: 0025-5610
EISSN: 1436-4646
DOI: 10.1007/s10107-013-0738-9
CODEN: MHPGA4
Source: ProQuest Central

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Phase recovery, MaxCut and complex semidefinite programming

Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013 ;Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2015 ;ISSN: 0025-5610 ;EISSN: 1436-4646 ;DOI: 10.1007/s10107-013-0738-9 ;CODEN: MHPGA4

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