@inproceedings{420664a4e0ec427ebce8ef43ddf09193,
title = "Frank-Wolfe works for non-Lipschitz continuous gradient objectives: Scalable poisson phase retrieval",
abstract = "We 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.",
keywords = "Frank-Wolfe algorithm, Phase retrieval, PhaseLift, Poisson noise, non-Lipschitz continuous gradient",
author = "Gergely Odor and Li, \{Yen Huan\} and Alp Yurtsever and Hsieh, \{Ya Ping\} and Quoc Tran-Dinh and Halabi, \{Marwa El\} and Volkan Cevher",
note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 ; Conference date: 20-03-2016 Through 25-03-2016",
year = "2016",
month = may,
day = "18",
doi = "10.1109/ICASSP.2016.7472875",
language = "English",
series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "6230--6234",
booktitle = "2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings",
address = "United States",
}