On approximation of orientation distributions by means of spherical ridgelets

Visualization and analysis of the micro-architecture of brain parenchyma by means of magnetic resonance imaging is nowadays believed to be one of the most powerful tools used for the assessment of various cerebral conditions as well as for understanding the intracerebral connectivity. Unfortunately, the conventional diffusion tensor imaging (DTI) used for estimating the local orientations of neural fibers is incapable of performing reliably in the situations when a voxel of interest accommodates multiple fiber tracts. In this case, a much more accurate analysis is possible using the high angular resolution diffusion imaging (HARDI) that represents local diffusion by its apparent coefficients measured as a discrete function of spatial orientations. In this note, a novel approach to enhancing and modeling the HARDI signals using multiresolution bases of spherical ridgelets is presented. In addition to its desirable properties of being adaptive, sparsifying, and efficiently computable, the proposed modeling leads to analytical computation of the orientation distribution functions associated with the measured diffusion, thereby providing a fast and robust analytical solution for q-ball imaging.