Phase Retrieval for Partially Coherent Observations

Phase retrieval is in general a non-convex and non-linear task the corresponding algorithms struggle with issue of local minima. We consider case where measurement samples within typically very small disconnected subsets are coherently linked to each other - which reasonable assumption for our objective antenna measurements. Two classes setups discussed can provide this kind extra information: multi-probe systems holographic measurements multiple reference signals. propose several formulations phase problem. The simplest these poses linear system equations similar an eigenvalue problem unique non-trivial null-space vector needs be found. Accurate reconstruction partially coherent observations is, thus, possible by reliable solution process judgment quality. Under ideal, noise-free conditions, required sampling density less than two times number unknowns. Noise observation errors increase value slightly. Simulations Gaussian random matrices scenarios demonstrate that presented approach.