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3D Bayesian regularization applied to diffusion tensor MRI is presented here. The approach uses Markov Random Field ideas and is based upon the definition of a 3D neighborhood system in which the spatial interactions of the tensors are modeled. As for the prior, we model the behavior of the tensor fields by means of a 6D multivariate Gaussian local characteristic. As for the likelihood, we model the noise process by means of conditionally independent 6D multivariate Gaussian variables. Those models include inter-tensor correlations, intra-tensor correlations and colored noise. The solution tensor field is obtained by using the simulated annealing algorithm to achieve the maximum a posteriori estimation. Several experiments both on synthetic and real data are presented, and performance is assessed with mean square error measure.

3D Bayesian Regularization of Diffusion Tensor MRI Using Multivariate Gaussian Markov Random Fields