A Recursive Solution of the Discrete Phase Retrieval Problem for Fourier Measurements

ABSTRACT In this work, we present a recursive solution of the discrete phase retrieval problem for Fourier measurements. We show that a solution of this problem may be obtained, if we are able to compute a rank one pre‐image of a certain low‐rank Hermitian matrix, under a known linear operator. Based on this observation, we construct a nonlinear recursive sequence of low‐rank Hermitian matrices, and we prove that under certain conditions, there exists a subsequence tending to a solution.