Bayesian regularization of diffusion tensor images using hierarchical MCMC and loopy belief propagation

Based on the theory of Markov Random Fields, a Bayesian regularization model for diffusion tensor images (DTI) is proposed in this paper. The low-degree parameterization of diffusion tensors in our model makes it less computationally intensive to obtain a maximum a posteriori (MAP) estimation. An approximate solution to the problem is achieved efficiently using hierarchical Markov Chain Monte Carlo (HMCMC), and a loopy belief propagation algorithm is applied to a coarse grid to obtain a good initial solution for hierarchical MCMC. Experiments on synthetic and real data demonstrate the effectiveness of our methods.