Odor, GergelyGergelyOdorYen-Huan LiYurtsever, AlpAlpYurtseverHsieh, Ya-PingYa-PingHsiehTran-Dinh, QuocQuocTran-DinhHalabi, Marwa ElMarwa ElHalabiCevher, VolkanVolkanCevher2019-05-072019-05-07201615206149https://doi.org/10.1109/ICASSP.2016.7472875https://scholars.lib.ntu.edu.tw/handle/123456789/406505https://www.scopus.com/inward/record.uri?eid=2-s2.0-84973343777&doi=10.1109%2fICASSP.2016.7472875&partnerID=40&md5=135e51df265aed016f8545c69ee9a961Shanghai, ChinaWe 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. © 2016 IEEE.Frank-Wolfe algorithm; non-Lipschitz continuous gradient; Phase retrieval; PhaseLift; Poisson noiseconference paper10.1109/ICASSP.2016.74728752-s2.0-84973343777