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PHASE RETRIEVAL: FROM CONVEX TO NONCONVEX METHODS
Date: 2015/9/7             Browse: 448

Speaker: Xiaodong Li

Time: Sept. 7th, 10:00am – 11:00am

Location: Room 220, Building 8

Abstract:

In phase retrieval, one aims to recover a signal from magnitude measurements. In the literature, an effective SDP algorithm, referred to as PhaseLift, was proposed with numerical success as well as strong theoretical guarantees. In this talk, I will first introduce some recent theoretical developments for PhaseLift, which demonstrate the applicability and adaptivity of this convex method.

Although convex methods are provably effective and robust, the computational complexity may be relatively high. Moreover, there is often an issue of storage to solve the lifted problem. To address these issues, we introduce a nonconvex optimization algorithm, named Wirtinger flow, with theoretically guaranteed performance. It is much more efficient than convex methods in terms of computation and memory. Finally, I will introduce how to modify Wirtinger flow when the signal is known to be sparse, in order to improve the accuracy of the recovery.

Bio:

Xiaodong Li is currently an assistant professor in the statistics department at UC Davis. Prior to this, he was a postdoc in the statistics department of Wharton school at University of Pennsylvania from 2013 -- 2015, working with Prof. Tony Cai. In 2013, He received the Ph.D of Mathematics at Stanford University, advised by Prof. Emmanuel Candes. He earned his BS in mathematics from Peking University in 2008. He is currently interested in large data processing/analysis by optimization, compressed sensing and its extensions, and high-dimensional statistics.                                                       

SIST-Seminar 15038