On connections between Amplitude Flow and Error Reduction for phase retrieval

Abstract

In this paper, we consider two iterative algorithms for the phase retrieval problem: the well-known Error Reduction method and the Amplitude Flow algorithm, which performs minimization of the amplitude-based squared loss via the gradient descent. We show that Error Reduction can be interpreted as a quasi-Newton method applied to minimize the same amplitude-based squared loss, which allows to establish its convergence properties. Moreover, we show that for a class of measurement scenarios two methods have the same computational complexity and sometimes even coincide.