Bayesian Formulation of Regularization by Denoising – Model and Monte Carlo Sampling

Image restoration aims at recovering a clean image from degraded observations. This paper presents a novel Bayesian framework for image restoration using a regularization-by-denoising (RED) prior. It introduces a probabilistic counterpart to the RED paradigm, and proposes a new Monte Carlo algorithm to efficiently sample from the resulting posterior distribution. The proposed method benefit from the recent developments of deep learning-based denoisers. Extensive numerical experiments illustrate the efficiency of the proposed method, showcasing its competitive performance against state-of-the-art methods.