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Can we recover a complex signal from its Fourier magnitudes? More generally, given a set of m measurements, y_k = | a_k^* x| for k = 1, ..., m, is it possible to recover x ∈C^n (i.e., length-n complex vector)? This **generalized phase retrieval** (GPR) problem is a fundamental task in various disciplines, and has been the subject of much recent investigation. Natural nonconvex heuristics often work remarkably well for GPR in practice, but lack clear theoretical explanations. In this paper, wedoi:10.1007/s10208-017-9365-9 fatcat:bu3vvmtyevfz7ccflk5mmcuu7i