Fourier Phase Retrieval with Extended Support Estimation via Deep Neural Network

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. Index Terms deep neural network, extended support estimation, Fourier transform, sparse phase retrieval. I. INTRODUCTION Sparse phase retrieval from the magnitude of the Fourier transform (SPRF) [1], [2] has been widely studied in many fields including X-ray crystallography [3], optics [4], [5], and computational biology [6].