An over-complete dictionary based regularized reconstruction of a field of ensemble average propagators

In this paper we present a dictionary-based framework for the reconstruction of a field of ensemble average propagators (EAPs), given a high angular resolution diffusion MRI data set. Existing techniques often consider voxel-wise reconstruction of the EAP field thereby leading to a noisy reconstruction across the field. We present a dictionary learning framework for achieving a smooth EAP reconstruction across the field wherein, the dictionary atoms are learned from the data via an initial regression using adaptive spline kernels. The formulation involves a two stage optimization where the first stage involves optimizing for a sparse dictionary using a K-SVD based updating and the second stage involves a quadratic cost function optimization with a non-local means based regularization across the field. The novelty lies in a dictionary based reconstruction as well as an NLM-based regularization that helps preserving features in the reconstructed field. We document experimental results on synthetic data from crossing fibers and real optic chiasm data set that demonstrate the advantages of the proposed approach.