Frank-Wolfe Works for Non-Lipschitz Continuous Gradient Objectives: Scalable Poisson Phase Retrieval

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.


Published in:
2016 Ieee International Conference On Acoustics, Speech And Signal Processing Proceedings, 6230-6234
Presented at:
41st IEEE International Conference on Acoustics, Speech and Signal Processing
Year:
2016
Publisher:
New York, Ieee
ISSN:
1520-6149
ISBN:
978-1-4799-9988-0
Keywords:
Laboratories:




 Record created 2016-02-01, last modified 2018-03-17

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