PDMM: A Novel Primal-Dual Majorization-Minimization Algorithm for Poisson Phase-Retrieval Problem

In this paper, we introduce a novel iterative algorithm for the problem of phase-retrieval where measurements consist only magnitude linear function unknown signal, and noise in follow Poisson distribution. The proposed is based on principle majorization-minimization (MM); however, application MM here very distinct from way has been usually used to solve optimization problems literature. More precisely, reformulate original minimization into saddle point by invoking Fenchel dual representation log (.) term likelihood function. We then propose tighter surrogate functions over both primal variables resulting double-loop algorithm, which have named as Primal-Dual Majorization-Minimization (PDMM) algorithm. steps are simple implement involve computing matrix vector products. also extend our handle various L1 regularized (which exploit sparsity). compared with previously algorithms such wirtinger flow (WF), (conventional), alternating direction methods multipliers (ADMM) data model. simulation results under different experimental settings show that PDMM faster than competing methods, its performance recovering signal at par state-of-the-art algorithms.