Spatially regularized q-ball imaging using spherical ridgelets

In this note, a novel approach to the problem of estimation of orientation distribution functions (ODFs) in q-ball imaging is presented. Rather than recovering the ODFs in a sequential manner, the proposed method performs a concurrent estimation of a set of ODFs pertaining to a specified volume. In this way, the method takes into account the spatial dependencies between different ODFs which are related to the same neural fiber tracts. Such spatial regularization is proven to be a useful tool to use for low SNR data, in which case it allows substantially improving the directional resolution of q-ball imaging. Finally, the reconstruction is based on representing the ODFs using the multi-resolutional basis of spherical ridgelets, which offers a number of additional advantages such as a significant reduction in data dimensionality and remarkable robustness to noises.