Phase Retrieval for Partially Coherent Observations
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Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the problem of local minima. We consider the case where portions of the measurement samples are coherently linked to each other - which is a reasonable assumption for our objective of antenna measurements. We propose several formulations of the corresponding phase retrieval problem. The problem may even be reduced to a linear system of equations similar to an eigenvalue problem and to the search for a unique non-trivial null-space vector. Accurate phase reconstruction for partially coherent observations is, thus, possible by a reliable solution process where we are able to judge the solution quality. Under ideal, noise-free conditions, the required sampling density is less than two times the number of unknowns. Noise and other observation errors increase this value slightly. Simulations for Gaussian random matrices and for antenna measurement scenarios demonstrate that reliable phase reconstruction is possible with the presented approach.
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