Tomographic reconstruction of diffusion propagators from DW-MRI using optimal sampling lattices

This paper exploits the power of optimal sampling lattices in tomography based reconstruction of the diffusion propagator in diffusion weighted magnetic resonance imaging (DW-MRI). Optimal sampling leads to increased accuracy of the tomographic reconstruction approach introduced by Pickalov and Basser [1]. Alternatively, the optimal sampling geometry allows for further reducing the number of samples while maintaining the accuracy of reconstruction of the diffusion propagator. The optimality of the proposed sampling geometry comes from the information theoretic advantages of sphere packing lattices in sampling multidimensional signals. These advantages are in addition to those accrued from the use of the tomographic principle used here for reconstruction. We present comparative results of reconstructions of the diffusion propagator using the Cartesian and the optimal sampling geometry for synthetic and real data sets.