Distributed optimization for Generalized Phase Retrieval Over Networks

Ziping Zhao, Songtao Lu, Mingyi Hong, Daniel P. Palomar

Abstract: In this paper, we will solve the generalized phase retrieval (PR) problem over a network, where each agent only has a subset of the measurements. The problem is formulated as minimizing the squared loss between the measurements and linear sensing intensity. To solve the problem in a distributed setting, an algorithm named distributed Wirtinger flow (DWF) is proposed. Theoretical analyses show that the proposed DWF algorithm converges to the (approximate) KKT points of the original problem globally in a sublinear rate. The performance of the DWF algorithm is numerically compared with the state-of-the-art method. Simulation results show that DWF is able to recover a high-quality solution for the original PR problem.