Iteratively consistent one-bit phase retrieval

Abstract

We introduce the ICQPhase algorithm for iteratively consistent quantized phase retrieval. ICQPhase addresses the problem of recovering a signal [Formula: see text] or [Formula: see text] from one-bit quantized phaseless measurements [Formula: see text], [Formula: see text], where [Formula: see text] are orthogonal projections and where [Formula: see text] is a one-bit scalar quantizer. We numerically validate the performance of ICQPhase and demonstrate that it experimentally achieves mean squared error of order [Formula: see text] in a variety of settings. We provide a theoretical analysis of the algorithm for the case of rank-one projections of signals in two-dimensional real space and prove that the mean squared error is of order [Formula: see text].