Diffusion MRI (dMRI) provides the ability to reconstruct neuronal fibers inthe brain, $\textit{in vivo}$, by measuring water diffusion along angulargradient directions in $q$-space. High angular resolution diffusion imaging(HARDI) can produce better estimates of fiber orientation than the popularlyused diffusion tensor imaging, but the high number of samples needed toestimate diffusivity requires lengthy patient scan times. To accelerate dMRI,compressed sensing (CS) has been utilized by exploiting a sparse dictionaryrepresentation of the data, discovered through sparse coding. The sparser therepresentation, the fewer samples are needed to reconstruct a high resolutionsignal with limited information loss, and so an important area of research hasfocused on finding the sparsest possible representation of dMRI. Currentreconstruction methods however, rely on an angular representation $\textit{pervoxel}$ with added spatial regularization, and so, the global level of sparsitycan be no less than the number of voxels. Therefore, state-of-the-art dMRI CSframeworks may have a fundamental limit to the rate acceleration that can beachieved. In contrast, we propose a joint spatial-angular representation ofdMRI that will allow us to achieve levels of global sparsity that are below thenumber of voxels. A major challenge, however, is the computational complexityof solving a global sparse coding problem over large-scale dMRI. In this work,we present novel adaptations of popular sparse coding algorithms that becomebetter suited for solving large-scale problems by exploiting spatial-angularseparability. Our experiments show that our method achieves significantlysparser representations of HARDI than the state-of-the-art which has thepotential to increase HARDI acceleration to new levels.
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