This analysis demonstrates a recursive solution to phase retrieval in Fourier measurements, indicating a path to resolving low-rank matrix challenges.
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.
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Nikolaos Atreas (2025) studied this question.
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