Sparse and Adaptive Diffusion Dictionary (SADD) for recovering intra-voxel white matter structure.

On the analysis of the Diffusion-Weighted Magnetic Resonance Images, multi-compartment models overcome the limitations of the well-known Diffusion Tensor model for fitting in vivo brain axonal orientations at voxels with fiber crossings, branching, kissing or bifurcations. Some successful multi-compartment methods are based on diffusion dictionaries. The diffusion dictionary-based methods assume that the observed Magnetic Resonance signal at each voxel is a linear combination of the fixed dictionary elements (dictionary atoms). The atoms are fixed along different orientations and diffusivity profiles. In this work, we present a sparse and adaptive diffusion dictionary method based on the Diffusion Basis Functions Model to estimate in vivo brain axonal fiber populations. Our proposal overcomes the following limitations of the diffusion dictionary-based methods: the limited angular resolution and the fixed shapes for the atom set. We propose to iteratively re-estimate the orientations and the diffusivity profile of the atoms independently at each voxel by using a simplified and easier-to-solve mathematical approach. As a result, we improve the fitting of the Diffusion-Weighted Magnetic Resonance signal. The advantages with respect to the former Diffusion Basis Functions method are demonstrated on the synthetic data-set used on the 2012 HARDI Reconstruction Challenge and in vivo human data. We demonstrate that improvements obtained in the intra-voxel fiber structure estimations benefit brain research allowing to obtain better tractography estimations. Hence, these improvements result in an accurate computation of the brain connectivity patterns.