A Gibbs posterior sampler for inverse problem based on prior diffusion model. A focus on myopic/blind deconvolution

The talk addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a prior density, and (3) the latter is modeled by a diffusion process adjusted on an available large set of examples. In this context, it is known that the issue of posterior sampling is a thorny one. In http://arxiv.org/abs/2602.11059 we introduce a Gibbs algorithm. It appears that this avenue has not been explored, and we show that this approach is particularly effective and remarkably simple while offering a guarantee of convergence in a clearly identified situation. In addition, based the remarkable flexibility of this Gibbs algorithm, we address the issue of estimating observation parameters (response and error parameters).