Bayesian imaging sciences: methods and algorithms

This teaching unit will introduce students to the Bayesian statistical framework for performing inference in high-dimensional inverse problems related to imaging sciences. We will start from basic concepts on probabilistic modelling, Bayesian decision theory, and Monte Carlo integration for Bayesian computation, and progress quickly to modern Bayesian imaging approaches. We will pay special attention to strategies based on stochastic diffusion processes and to Bayesian imaging models that combine elements derived from machine learning with elements derived from the physics of the considered imaging problem. The key ideas and techniques will be illustrated on imaging problems where we will conduct challenges inferences such as uncertainty quantification, hypothesis testing, model self-calibration, and model selection without ground truth.