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Alternating projections for phase retrieval with random sensing vectors

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VMVW02 - Generative models, parameter learning and sparsity

Phase retrieval consists in reconstructing an unknown element in a complex vector space from the modulus of linear measurements. The first reconstruction algorithms for which theoretical guarantees could be proven relied on convexification techniques. It has only recently been realized that similar guarantees hold for non-convex local search methods, that are faster and simpler, provided that their starting point is carefully chosen. We will explain how to establish these guarantees for the most well-known local search method: alternating projections. We will also discuss the role of the initialization method.

This talk is part of the Isaac Newton Institute Seminar Series series.

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