Phase Recovery, MaxCut and Complex Semidefinite Programming.

TITLE: Phase Recovery, MaxCut and Complex Semidefinite Programming.

AUTHORS: Irène Waldspurger , Alexandre d'Aspremont, Stéphane Mallat

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.

STATUS: Preprint.

ArXiv PREPRINT: 1206.0102

PAPER: Phase Recovery, MaxCut and Complex Semidefinite Programming in pdf