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 $x$ from the amplitude $\left|Ax\right|$ 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 [10] , 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.