Poissonian Image Restoration Via the $$L_1/L_2$$ -Based Minimization

Abstract

This study investigates the Poissonian image restoration problems. In particular, we propose a novel model that incorporates \(L_1/L_2\) minimization on the gradient as a regularization term combined with a box constraint and a nonlinear data fidelity term, specifically crafted to address the challenges caused by Poisson noise. We employ a splitting strategy, followed by the alternating direction method of multipliers (ADMM) to find a model solution. Furthermore, we show that under mild conditions, the sequence generated by ADMM has a sub-sequence that converges to a stationary point of the proposed model. Through numerical experiments on image deconvolution, super-resolution, and magnetic resonance imaging (MRI) reconstruction, we demonstrate superior performance made by the proposed approach over some existing gradient-based methods.