TY - GEN
T1 - Frank-Wolfe works for non-Lipschitz continuous gradient objectives
T2 - 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
AU - Odor, Gergely
AU - Li, Yen Huan
AU - Yurtsever, Alp
AU - Hsieh, Ya Ping
AU - Tran-Dinh, Quoc
AU - Halabi, Marwa El
AU - Cevher, Volkan
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/5/18
Y1 - 2016/5/18
N2 - 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.
AB - 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.
KW - Frank-Wolfe algorithm
KW - non-Lipschitz continuous gradient
KW - Phase retrieval
KW - PhaseLift
KW - Poisson noise
UR - http://www.scopus.com/inward/record.url?scp=84973343777&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2016.7472875
DO - 10.1109/ICASSP.2016.7472875
M3 - Conference contribution
AN - SCOPUS:84973343777
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 6230
EP - 6234
BT - 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 20 March 2016 through 25 March 2016
ER -