Sparse model learning for high dimensional diffusion MRI data in traumatic brain injury

The estimation of multivariate distributions of from high dimensional data with low sample size is at the core of many image analysis applications. Here, we present a method to estimate a multivariate Gaussian distribution of diffusion tensor features in a set of brain regions based on 45 healthy individuals. This distribution is used to identify the imaging abnormalities in subjects with traumatic brain injury (TBI). The model receives apriori knowledge in the form of a neighborhood graph, and maximizes the likelihood of the distribution while putting an additional L1 sparsity constraint on the model parameters. This leads to an interpretable model where the interactions of brain regions are encoded into the estimated model coefficients. The likelihoods of normal and TBI subjects under the estimated distribution are used as features to evaluate discriminatory power of model, using the area under receiver operating characteristic (ROC) curves. Our experiments show that the addition of the neighborhood graph constraint results in significant improvements in classification compared to a model which does not take into account the brain region interactions. In addition, our prior graph leads to a better model than one using a fully connected prior graph as it provides similar classification performance with 10 times fewer parameters (model order), and significantly lower Bayesian information criterion (BIC).