Integrating Reweighted Least Squares with Plug-and-Play Diffusion Priors for Noisy Image Restoration

Abstract

Existing plug-and-play image restoration methods typically employ off-the-shelf Gaussian denoisers as proximal operators within classical optimization frameworks based on variable splitting. Recently, denoisers induced by generative priors have been successfully integrated into regularized optimization methods for image restoration under Gaussian noise. However, their application to non-Gaussian noise--such as impulse noise--remains largely unexplored. In this paper, we propose a plug-and-play image restoration framework based on generative diffusion priors for robust removal of general noise types, including impulse noise. Within the maximum a posteriori (MAP) estimation framework, the data fidelity term is adapted to the specific noise model. Departing from the conventional least-squares loss used for Gaussian noise, we introduce a generalized Gaussian scale mixture-based loss, which approximates a wide range of noise distributions and leads to an $\ell_q$-norm ($0<q\leq2$) fidelity term. This optimization problem is addressed using an iteratively reweighted least squares (IRLS) approach, wherein the proximal step involving the generative prior is efficiently performed via a diffusion-based denoiser. Experimental results on benchmark datasets demonstrate that the proposed method effectively removes non-Gaussian impulse noise and achieves superior restoration performance.