Fourier Phase Retrieval with Extended Support Estimation via Deep Neural Network
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We consider the problem of sparse phase retrieval from Fourier transform magnitudes to recover k-sparse signal vector x^∘ and its support T. To improve the reconstruction performance of x^∘, we exploit extended support estimate E of size larger than k satisfying E⊇T. We propose a learning method for the deep neural network to provide E as an union of equivalent solutions of T by utilizing modulo Fourier invariances and suggest a searching technique for T by iteratively sampling E from the trained network output and applying the hard thresholding to E. Numerical results show that our proposed scheme has a superior performance with a lower complexity compared to the local search-based greedy sparse phase retrieval method and a state-of-the-art variant of the Fienup method.
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