Decomposition of higher-order homogeneous tensors and applications to HARDI

High Angular Resolution Diffusion Imaging (HARDI) holds the promise to provide insight in connectivity of the human brain in vivo. Based on this technique a number of different approaches has been proposed to estimate the ¿ber orientation distribution, which is crucial for ¿ber tracking. A spherical harmonic representation is convenient for regularization and the construction of orientation distribution functions (ODFs), whereas maxima detection and ¿ber tracking techniques are most naturally formulated using a tensor representation. We give an analytical formulation to bridge the gap between the two representations, which admits regularization and ODF construction directly in the tensor basis