Probabilistic Matrix Completion for Image Phase Retrieval

In this paper we address the Phase Retrieval problem, which aims to recover the phase of the Fourier transform of a signal when only magnitude measurements are available. Following recent developments in Phase Retrieval, the problem can be transformed into a convex semidefinite programming optimization problem, which can be solved using Matrix Completion techniques. In this paper the acquisition process is modeled using a likelihood function, which splits the original problem into two convex optimization problems, and alternates between the solution of each of them. To relate both convex problems we introduce a heuristic, which results in fast convergence of the proposed method.