Low-rank matrix recovery in poisson noise

This paper describes a new algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex optimization formulation with a cost function consisting of the sum of a likelihood function and a regularization function which is proportional to the nuclear norm of the matrix. Instead of solving the optimization problem directly by semi-definite program (SD-P), we derive an iterative singular value thresholding algorithm by expanding the likelihood function. We demonstrate the good performance of the proposed algorithm on recovery of solar flare images with Poisson noise: the algorithm is more efficient than solving SDP using the interior-point algorithm and it generates a good approximate solution compared to that solved from SDP.