Compressed sensing HARDI via rotation-invariant concise dictionaries, flexible K-space undersampling, and multiscale spatial regularity

Current methods to reduce acquisition time for high angular resolution diffusion imaging (HARDI) (i) employ large dictionaries where atoms explicitly model finitely-many tract orientations, limiting estimation accuracy of the true tract orientation, (ii) subsample gradient directions only, ignoring k-space undersampling for diffusion-weighted images, (iii) restrict to sparse models that use either frames or dictionaries, and (iv) enforce spatial regularity by penalizing total variation. This paper proposes rotation-invariant dictionaries, enabling a concise dictionary (few atoms representing key diffusion-signal types) by explicitly optimizing the rotation for each atom during sparse fitting. The proposed framework generalizes undersampling strategies to both k-space and gradient directions, thereby enabling a balanced undersampling of k-space over all directions. This paper combines frames and dictionaries for sparse modeling HARDI images. The frame model reduces the need for large intricate dictionaries and enforces spatial regularity over multiple scales. Results on simulated and clinical undersampled HARDI show improved reconstructions via the proposed framework.