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 nonconvex 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 GerchbergSaxton, 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
