Imaging and Computing Seminar

Vlad Voroninski, Mathematics, UC Berkeley

Exact Phase Retrieval via Convex Optimization, with connections to Wright's Conjecture, Sparse Signal Recovery and MAXCUT

PhaseLift is a novel methodology for phase retrieval, combining structured illuminations with convex programming to recover phase from intensity measurements. Recovery of arbitrary signals in C^n from m gaussian or unitary quadratic measurements via PhaseLift is exact and stable to noise with high probability as long as m = O(n). Sparse signal recovery from fewer than n quadratic measurements is also possible via convex optimization and we will discuss sharp theoretical results in this vein. Finally, we will mention applications of PhaseLift to Wright's conjecture in Quantum Mechanics and the Goemans-Williamson relaxation of MAXCUT.