Bayesian inference for image deblurring at a large scale. (Inférence bayésienne pour la restauration d'images en grande dimension)

Yunshi Huang

Abstract: Image deblurring is an essential image restoration problem arising in several fields from astronomy to medical science. It amounts to restoring an image from a degraded, blurry and noisy, version of it. Bayesian image deblurring seeks for the posterior distribution of the image (and blur kernel, when unknown) given an observation model and some prior knowledge on the unknowns. Closed form for the posterior distribution can rarely be computed analytically, so Bayesian approximation tools are deployed to derive an estimation of it. This thesis brings novel contributions in that topic, by introducing novel Bayesian methods for tackling two important scenarios of image deblurring problems. First, we are interested in the so-called blur identification problem, of estimating spatially varying blur kernels given a clean image and its degraded version. We construct a probabilistic state-space model accounting for the smoothness among the neighboring blur kernels, and propose a novel algorithm based on bootstrap PF (BPF) to sample weighted particles, and thus construct the sought posterior distribution. Numerical experiments on various spatially-variant blur maps and images illustrate the benefits and good stability of our approach. Second, we focus on the blind image deblurring problem of jointly estimating the image and blur kernel given the blurry noisy image. We adopt the variational Bayesian approach, to build an appropriate approximation of the posterior distribution. We introduce majorization steps to maintain closed form updates even for non conjugate priors and non-Gaussian noise. This yields the variational Bayesian algorithm (VBA). We then propose to unfold VBA over neural network layers, following the recently introduced deep unrolling paradigm. This yields the unfolded VBA, benefiting from reduced parameter tuning, fast computations on GPU architecture, and improved quantitative restoration results. The superiority of unfolded VBA over state-of-the-art blind deblurring techniques is illustrated on three datasets involving color/grayscale natural images and various blur shapes