Basis functions for estimating intra-voxel structure in DW-MRI

We present a new method for estimating and recovering the intra-voxel fiber paths, using Diffusion Weighted Magnetic Resonance Images (DW-MRI). The method recovers the intra-voxel information at voxels that contain fiber crossings or bifurcations by means of a combination of a known tensor basis functions (a "multi-tensor" field). In contrast with the state-of-the art methods, our formulation requires a small number of DWMR images and the solution schema is simple. Another advantage is that the solution to our formulation is numerically stable when more than two fiber orientations are present within a voxel. Additionally, we apply a spatial regularization to the multi-tensor field being estimated in order to denoise the data. The regularization uses a generic piece-wise smooth prior on the fiber orientation. Several examples are presented to demonstrate the performance of the proposed algorithm on synthetic and real DW-MRI data