  This paper describes a fast 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 the nuclear norm of the
matrix. Instead of solving the optimization problem directly by semi-definite
program (SDP), 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.
