Phase Recovery, MaxCut and Complex Semidefinite Programming

Irène Waldspurger; Alexandre d'Aspremont; Stéphane Mallat

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arXiv · 1206.0102

Phase Recovery, MaxCut and Complex Semidefinite Programming

Irène Waldspurger·Alexandre d'Aspremont·Stéphane Mallat

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Abstract

Phase retrieval seeks to recover a signal x from the amplitude |Ax| of linear measurements. 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-Saxton, 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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Irène Waldspurger, Alexandre d'Aspremont, Stéphane Mallat. 2013-07-22. Phase Recovery, MaxCut and Complex Semidefinite Programming. https://arxiv.org/abs/1206.0102

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