Odor, GergelyLi, Yen-HuanYurtsever, AlpHsieh, Ya-PingTran Dinh, QuocEl Halabi, MarwaCevher, Volkan2016-02-012016-02-012016-02-01201610.1109/ICASSP.2016.7472875https://infoscience.epfl.ch/handle/20.500.14299/122908WOS:000388373406077We study a phase retrieval problem in the Poisson noise model. Motivated by the PhaseLift approach, we approximate the maximum-likelihood estimator by solving a convex program with a nuclear norm constraint. While the Frank-Wolfe algorithm, together with the Lanczos method, can efficiently deal with nuclear norm constraints, our objective function does not have a Lipschitz continuous gradient, and hence existing convergence guarantees for the Frank-Wolfe algorithm do not apply. In this paper, we show that the Frank-Wolfe algorithm works for the Poisson phase retrieval problem, and has a global convergence rate of O(1/t), where t is the iteration counter. We provide rigorous theoretical guarantee and illustrating numerical results.Phase retrievalPoisson noisePhaseLiftFrank-Wolfe algorithmNon-Lipschitz continuous gradienttext::conference output::conference proceedings::conference paper