Fast variational Bayesian approaches applied to large dimensional problems

This paper introduces two unsupervised approaches for large dimensional ill-posed inverse problems. These approaches are based on improved variational Bayesian (VB) methodologies, where a functional optimization problem is involved. We propose to solve this problem by adapting the subspace optimization methods into the functional space. The application of these approaches to image processing problems is considered thanks to a TV prior. We highlight the efficiency of our approaches through comparisons with a classical VB based one on a super-resolution problem.