Sparse reproducing kernels for modeling fiber crossings in diffusion weighted imaging

Using existing estimators found in High Angular Resolution Diffusion Imaging (HARDI), such as the Orientation Probability Distribution Function (OPDF) of Aganj et al., we develop a new mathematical framework for implementing HARDI. In contrast to traditional methods based on spherical harmonics, the framework is based on a reproducing kernel formalism combined with recently developed Gaussian-like quadratures for the sphere, which leads to an efficient and sparse representation for HARDI estimators. We demonstrate that the new framework results in reconstructions that are more robust to noise and have better angular resolution, compared to spherical harmonic based reconstructions.