Abstract:
When we are facing really ill-posed inverse problems such as limited angle compted tomography (CT) image reconstruction, there is a need for regularization. The choice of regularization term is then of great importance. Popular choices are: L2, L1, TV, Hubert and also some non-convex criteria. In some cases, we can make parallel between regularization and Bayesian MAP estimation. But the Bayesian is not limited to MAP. In this talk, first I will present the basics of Bayesian approach. Then I will focus on prior modelling part and in particular a class of hierarchical Gauss-Markov-Potts models well appropriate for industrial Non Destructive Testing (NDT) applications of computed tomography. I will also mention the computational aspects of the Bayesian approach: MCMC and Variational Bayes methods and the implementation of these algorithems on GPU.