Fourier Phase Retrieval With Extended Support Estimation via Deep Neural Network

Abstract

We consider the problem of sparse phase retrieval from Fourier transform magnitudes to recover the k-sparse signal vector and its support T . We exploit extended support estimate E with size larger than k satisfying E ⊇ T and obtained by a trained deep neural network (DNN). To make the DNN learnable, it provides E as the union of equivalent solutions of T by utilizing modulo Fourier invariances. Set E can be estimated with short running time via the DNN, and support T can be determined from the DNN output rather than from the full index set by applying hard thresholding to E. Thus, the DNN-based extended support estimation improves the reconstruction performance of the signal with a low complexity burden dependent on k. Numerical results verify that the proposed scheme has a superior performance with lower complexity compared to local search-based greedy sparse phase retrieval and a state-of-the-art variant of the Fienup method. Index TermsDeep neural network, extended support estimation, Fourier transform, sparse phase retrieval. 1 Signal vector x • is called k-sparse if it has k nonzero elements.

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