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 (MRI) is currently considered to be one of the most powerful methods for interrogating cerebral tissue. Unfortunately, the diffusion tensor imaging (DTI) which is standardly used for estimating the local orientations of brain fibers, is prone to substantial estimation errors whenever a voxel of interest contains more than one fiber. In such a 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 function of 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.