Spatial-Angular Sparse Coding for HARDI

High angular resolution diffusion imaging (HARDI) can produce better estimates of fiber orientation and richer sets of features for disease classification than diffusion tensor imaging. However, existing HARDI reconstruction algorithms require a large number of gradient directions, making the acquisition time too long to be clinically viable. State-of-the-art compressed sensing methods can reduce the number of measurements needed for accurate reconstruction by exploiting angular sparsity at each voxel, but the global sparsity level is therefore bounded below by the number of voxels. In this work, we aim to find a significantly sparser representation of HARDI by exploiting redundancies in both the spatial and angular domains jointly with a global HARDI basis. However, this leads to a massive global optimization problem over the whole brain which cannot be solved using existing sparse coding methods. We present a novel Kronecker extension to ADMM that exploits the separable spatial-angular structure of HARDI data to efficiently find a globally sparse reconstruction. We validate our method on phantom and real HARDI brain data by showing that we can achieve accurate reconstructions with a global sparsity level corresponding to less then one atom per voxel, surpassing the absolute limit of the state-of-the-art.