Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling

Elhadji C. Faye (1) , Mame Diarra Fall (1) , Nicolas Dobigeon (2, 3)

1 IDP - Institut Denis Poisson
2 IRIT-SC - Signal et Communications
3 Toulouse INP - Institut National Polytechnique (Toulouse)

This paper introduces a Bayesian framework for image inversion by deriving a probabilistic counterpart to the regularization-by-denoising (RED) paradigm. It additionally implements a Monte Carlo algorithm specifically tailored for sampling from the resulting posterior distribution, based on an asymptotically exact data augmentation (AXDA). The proposed algorithm is an approximate instance of split Gibbs sampling (SGS) which embeds one Langevin Monte Carlo step. The proposed method is applied to common imaging tasks such as deblurring, inpainting and super-resolution, demonstrating its efficacy through extensive numerical experiments. These contributions advance Bayesian inference in imaging by leveraging datadriven regularization strategies within a probabilistic framework.

Keywords: Bayesian; image processing; RED; MCMC; Deep-learning

Domains: Signal and Image processing; Machine Learning [stat.ML]

Elhadji C. Faye, Mame Diarra Fall, Nicolas Dobigeon. Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling. 2024. ⟨hal-04480090⟩