Box spline based 3D tomographic reconstruction of diffusion propagators from MRI data

This paper introduces a tomographic approach for reconstruction of diffusion propagators, P(r), in a box spline framework. Box splines are chosen as basis functions for high-order approximation of P(r) from the diffusion signal. Box splines are a generalization of B-splines to multivariate setting that are particularly useful in the context of tomographic reconstruction. The X-Ray or Radon transform of a (tensor-product B-spline or a non-separable) box spline is a box spline - the space of box splines is closed under the Radon transform. We present synthetic and real multi-shell diffusion-weighted MR data experiments that demonstrate the increased accuracy of P(r) reconstruction as the order of basis functions is increased.