Exploiting structural redundancy in q-space for improved EAP reconstruction from highly undersampled (k, q)-space in DMRI.

Accurate reconstruction of the ensemble average propagators (EAPs) from undersampled diffusion MRI (dMRI) measurements is a well-motivated, actively researched problem in the field of dMRI acquisition and analysis. A number of approaches based on compressed sensing (CS) principles have been developed for this problem, achieving a considerable acceleration in the acquisition by leveraging sparse representations of the signal. Most recent methods in literature apply undersampling techniques in the (k, q)-space for the recovery of EAP in the joint (x, r)-space. Yet, the majority of these methods follow a pipeline of first reconstructing the diffusion images in the (x, q)-space and subsequently estimating the EAPs through a 3D Fourier transform. In this work, we present a novel approach to achieve the direct reconstruction of P(x, r) from partial (k, q)-space measurements, with geometric constraints involving the parallelism of level-sets of diffusion images from proximal q-space points. By directly reconstructing P(x, r)) from (k, q)-space data, we exploit the incoherence between the 6D sensing and reconstruction domains to the fullest, which is consistent with the CS-theory. Further, our approach aims to utilize the inherent structural similarity (parallelism) of the level-sets in the diffusion images corresponding to proximally-located q-space points in a CS framework to achieve further reduction in sample complexity that could facilitate faster acquisition in dMRI. We compare the proposed method to a state-of-the-art CS based EAP reconstruction method (from joint (k, q)-space) on simulated, phantom and real dMRI data demonstrating the benefits of exploiting the structural similarity in the q-space.