Title: Some perspectives on stochastic models for Bayesian image restoration
Abstract: Random image models are central for solving inverse problems in imaging. In a Bayesian formalism, these models can be used as priors or regularisers and combined to an explicit likelihood function to define posterior distributions. Most of the time, these posterior distributions are used to derive Maximum A Posteriori (MAP) estimators, leading to optimization problems that may be convex or not, but are well studied and understood. Sampling schemes can also be used to explore these posterior distributions, to derive Minimum Mean Square Error (MMSE) estimators, quantify uncertainty or perform other advanced inferences. While research on inverse problems has focused for many years on explicit image models (either directly in the image space, or in a transformed space), an important trend nowadays is to use implicit image models encoded by neural networks. This opens the way to restoration algorithms that exploit more powerful and accurate prior models for natural images but raises novel challenges and questions on the corresponding posterior distributions and their resulting estimators. The goal of this presentation is to provide some perspectives and present recent developments on these questions.
