PGPAL: A Monotonic Iterative Algorithm for Phase-Retrieval Under the Presence of Poisson-Gaussian Noise

Abstract

In this paper, we propose an iterative algorithm named PGPAL for the phase-retrieval problem under the scenario when the measurements follow Poisson plus Gaussian (PG) distribution, which is a more realistic model in applications like astronomy, microscopy, medical imaging, and remote sensing. The proposed algorithm is based on majorization-minimization (MM) framework, in which a simple surrogate function that tightly upperbounds the challenging underlying maximum-likelihood (ML) objective is constructed and minimized iteratively. The proposed algorithm monotonically decreases the ML objective and the algorithm is guaranteed to converge to a stationary point of the ML objective. Numerical simulations are performed for the one-dimensional phase-retrieval case, and the performance of the proposed method is compared with the recently proposed Poisson phase-retrieval algorithm, which assumes the measurement model to be only Poisson distributed. The performance of the proposed MM-based algorithm in terms of the normalized root mean square error (NRMSE) is found to be much better in comparison to the method for Poisson phase-retrieval.