Phase retrieval via accelerated gradient descent

Abstract

Phase retrieval, as a non-convex optimization problem arises in many areas of signal processing, is to recover the missed signal phase. Based on the Truncated Wirtinger Flow (TWF), where the updating can be regarded as stochastic gradient descent, we present the Accelerated Wirtinger Flow (AWF), which updates the iterative process with accelerated steepest descent. WF algorithm solves the problem by two steps: (a) initialization signal with truncated spectral initialization method provided in TWF and (b) a series of updates this initial estimate by iteratively applying a novel update rule, AWF. Meanwhile, according to the Amplitude Flow objective, the proximal gradient method is suggested.