Learning spectral initialization for phase retrieval via deep neural networks

Phase retrieval (PR) arises from the lack of phase information in the measures recorded by optical sensors. Phase masks that modulate the optical field and reduce ambiguities in the PR problem by producing redundancy in coded diffraction patterns (CDPs) have been included in these diffractive optical systems. Several algorithms have been developed to solve the PR problem from CDPs. Also, deep neural networks (DNNs) are used for solving inverse problems in computational imaging by considering physical constraints in propagation models. However, traditional algorithms based on non-convex formulation include an initialization stage that requires a high number of iterations to properly estimate the optical field. This work proposes an end-to-end (E2E) approach for addressing the PR problem, which jointly learns the spectral initialization and network parameters. Mainly, the proposed deep network approach contains an optical layer that simulates the propagation model in diffractive optical systems, an initialization layer that approximates the underlying optical field from CDPs, and a double branch DNN that improves the obtained initial guess by separately recovering phase and amplitude information. Simulation results show that the proposed E2E approach for PR requires fewer snapshots and iterations than the state of the art.