PHASE RETRIEVAL: FROM CONVEX TO NONCONVEX METHODS
Time: 2015-09-11
Published By:
Speaker(s): Prof. Xiaodong Li, UC Davis
Time: 11:00-12:00 September 11, 2015
Venue: 理科一号楼 1493
Time: 2015-09-11 11:00:00 - 2015-09-11 12:00:00
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.
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.
