Imaging and Computing Seminar
Vlad Voroninski, Mathematics, UC Berkeley
Title:
Exact Phase Retrieval via Convex Optimization, with connections to
Wright's Conjecture, Sparse Signal Recovery and MAXCUT
Abstract:
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.