Efficient Global Spatial-Angular Sparse Coding for Diffusion MRI with Separable Dictionaries

Diffusion MRI (dMRI) can reconstruct neuronal fibers in the brain, in vivo, by measuring water diffusion along angular gradient directions in q-space. High angular resolution diffusion imaging (HARDI) can produce better estimates of fiber orientation than the popularly used diffusion tensor imaging, but the high number of samples needed to estimate diffusivity requires lengthy patient scan times. To accelerate dMRI, compressed sensing (CS) has been utilized by exploiting a sparse representation of the data, discovered through sparse coding. The sparser the representation, the fewer samples are needed to reconstruct a high resolution signal with limited information loss and so a focus of much dMRI research has been finding the sparsest possible dictionary representation. All prior methods, however, rely on an angular model of q-space signals in each voxel which fundamentally limits the global sparsity level since at least one dictionary atom is needed for each voxel. In contrast, we formulate a global spatial-angular representation of dMRI that will allow us to sparsely model an entire dMRI brain signal below the limit of one atom per voxel using joint spatial-angular sparse coding. But a main challenge is optimizing over large-scale dMRI data. In this work, we present extensions to a number of sparse coding algorithms that are better suited for large-scale problems by exploiting the separable Kronecker structure of our global spatial-angular dictionary. We compare the complexity and speed of our methods with prior Kronecker sparse coding algorithms and show promising sparsity results on phantom and real HARDI brain data for various dictionary choices. With great efficiency our method achieves significantly sparser HARDI representations than the state-of-the-art which has the potential achieve new levels of HARDI acceleration within a unified (k,q)-CS framework.