Section: New Results
Phase Recovery, MaxCut and Complex Semidefinite Programming
Participant : Alexandre d'Aspremont [correspondent] .
Collaboration with Irène Waldspurger and Stéphane Mallat.
Phase retrieval seeks to recover a signal from the amplitude 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. In  , 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.