Gauss-Markov-Potts Priors for Images in Computer Tomography Resulting to Joint Optimal Reconstruction and segmentation

Abstract

In many applications of Computed Tomography (CT), we know that the object under the test is composed of a finite number of materials meaning that the images to be reconstructed are composed of a finite number of homogeneous area. To account for this prior knowledge, we propose a family of Gauss-Markov fields with hidden Potts label fields. Then, using these models in a Bayesian inference framework, we are able to jointly reconstruct the image and segment it in an optimal way. In this paper, we first present these prior models, then propose appropriate Bayesian computational methods (MCMC or Variational Bayes) to compute the Joint Maximum A Posteriori (JMAP) or the posterior mean estimators. We finally provide a few results showing the efficiency of the proposed methods for CT with very limited angle and number of projections.