Alternating projections for phase retrieval with random Gaussian measurements

par Irène Waldspurger (CNRS)

jeudi 9 févr. 2017, 14:30 → 15:30 Europe/Paris

salle 435 (UMPA)

I will present a class of inverse problems called phase retrieval problems. The traditional algorithms used to solve these problems are "iterative methods", that rely on simple heuristics. They are fast and easy to implement. However, because phase retrieval problems are non-convex, these algorithms are in general not guaranteed to return the correct solution. It has recently been shown that some of these methods succeed with high probability for random instances of phase retrieval problems. I will describe this line of work, and its relevance in the more general context of non-convex optimization. I will then explain how to extend these results to the method of alternating projections (the simplest and oldest iterative method used for phase retrieval problems), and discuss open questions.