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.