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

Diffusion MRI (dMRI) provides the ability to 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 dictionary 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 an important area of research has focused on finding the sparsest possible representation of dMRI. Current reconstruction methods however, rely on an angular representation per voxel with added spatial regularization, and so, the global level of sparsity can be no less than the number of voxels. Therefore, state-of-the-art dMRI CS frameworks may have a fundamental limit to the rate acceleration that can be achieved. In contrast, we propose a joint spatial-angular representation of dMRI that will allow us to achieve levels of global sparsity that are below the number of voxels. A major challenge, however, is the computational complexity of solving a global sparse coding problem over large-scale dMRI. In this work, we present novel adaptations of popular sparse coding algorithms that become better suited for solving large-scale problems by exploiting spatial-angular separability. Our experiments show that our method achieves significantly sparser representations of HARDI than the state-of-the-art which has the potential to increase HARDI acceleration to new levels.