Frank-Wolfe works for non-Lipschitz continuous gradient objectives: Scalable poisson phase retrieval

Gergely Odor, Yen Huan Li, Alp Yurtsever, Ya Ping Hsieh, Quoc Tran-Dinh, Marwa El Halabi, Volkan Cevher

Research output: Contribution to Book/Report typesConference contributionpeer-review

Abstract (may include machine translation)

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.

Original languageEnglish
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6230-6234
Number of pages5
ISBN (Electronic)9781479999880
DOIs
StatePublished - 18 May 2016
Externally publishedYes
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: 20 Mar 201625 Mar 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Conference

Conference41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Country/TerritoryChina
CityShanghai
Period20/03/1625/03/16

Keywords

  • Frank-Wolfe algorithm
  • non-Lipschitz continuous gradient
  • Phase retrieval
  • PhaseLift
  • Poisson noise

Fingerprint

Dive into the research topics of 'Frank-Wolfe works for non-Lipschitz continuous gradient objectives: Scalable poisson phase retrieval'. Together they form a unique fingerprint.

Cite this