Sparse Multi-Shell Diffusion Imaging

Diffusion magnetic resonance imaging (dMRI) is an important tool that allows non-invasive investigation of neural architecture of the brain. The data obtained from these in-vivo scans provides important information about the integrity and connectivity of neural fiber bundles in the brain. A multi-shell imaging (MSI) scan can be of great value in the study of several psychiatric and neurological disorders, yet its usability has been limited due to the long acquisition times required. A typical MSI scan involves acquiring a large number of gradient directions for the 2 (or more) spherical shells (several b-values), making the acquisition time significantly long for clinical application. In this work, we propose to use results from the theory of compressive sampling and determine the minimum number of gradient directions required to attain signal reconstruction similar to a traditional MSI scan. In particular, we propose a generalization of the single shell spherical ridgelets basis for sparse representation of multi shell signals. We demonstrate its efficacy on several synthetic and in-vivo data sets and perform quantitative comparisons with solid spherical harmonics based representation. Our preliminary results show that around 20-24 directions per shell are enough for robustly recovering the diffusion propagator.