Fast Algorithm for Low-rank matrix recovery in Poisson noise

TL;DR

This paper introduces a fast iterative algorithm for low-rank matrix recovery from Poisson noise, outperforming traditional SDP methods in efficiency and approximation quality.

Contribution

The paper presents the PMLSV algorithm, a novel iterative singular value thresholding method for Poisson noise matrix recovery, avoiding computationally expensive SDP solutions.

Findings

The PMLSV algorithm is more efficient than SDP-based methods.

It provides high-quality approximate solutions for Poisson noise matrix recovery.

Demonstrated effective recovery of solar flare images with Poisson noise.

Abstract

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.