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This paper describes a fast algorithm for recovering low-rank matrices fromtheir linear measurements contaminated with Poisson noise: the Poisson noiseMaximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose aconvex optimization formulation with a cost function consisting of the sum of alikelihood function and a regularization function which the nuclear norm of thematrix. Instead of solving the optimization problem directly by semi-definiteprogram (SDP), we derive an iterative singular value thresholding algorithm byexpanding the likelihood function. We demonstrate the good performance of theproposed algorithm on recovery of solar flare images with Poisson noise: thealgorithm is more efficient than solving SDP using the interior-point algorithmand it generates a good approximate solution compared to that solved from SDP.

Fast Algorithm for Low-rank matrix recovery in Poisson noise