A statistical framework to characterise microstructure in high angular resolution diffusion imaging

High angular resolution diffusion imaging (HARDI) is an MR acquisition technique that has been used to identify and estimate multi-modal structure in white matter. We introduce a multiresolution estimator of the diffusion density in g-space based on a wavelet lifting scheme for HARDI data. The proposed technique avoids imposing isotropic smoothing with a fixed bandwidth that is a common feature in other higher-order methods. Summary statistics for the properties of the diffusion density are derived entirely in q-space, based on great circle and perpendicular great circle statistics. A framework is developed to characterise structural features of the diffusion using these statistics.