A coherence enhancing penalty for Diffusion MRI: regularizing property and discrete approximation

TL;DR

This paper introduces a novel regularization approach for Diffusion MRI that enhances the coherence of orientation distribution functions by leveraging spatial regularity, with theoretical analysis and numerical validation on real and phantom data.

Contribution

It presents a new regularization method based on fiber continuity, with theoretical convergence analysis and practical demonstration on MRI data.

Findings

The method improves the coherence of ODF reconstructions.

Theoretical convergence is established under smoothness assumptions.

Numerical results show enhanced stability and accuracy.

Abstract

Processing of Diffusion MRI data obtained from High Angular Resolution measurements consists of a series of steps, starting with the estimation of an orientation distribution function (ODF), which is then used as input for e.g. tractography algorithms. It is important that ODF reconstruction methods yield accurate, coherent ODFs, in particular for low SNR or coarsely sampled data sets. As the diffusion process is modelled independently in each voxel, reconstructions are often carried out for each voxel separately, disregarding the observation that neighboring voxels are often quite similar if they belong to the same fiber structure. There are surprisingly few approaches that make use of this kind of spatial regularity to improve coherence and stability of the reconstruction. In this work, we focus on a variation of a method proposed by Reisert and Kiselev based on the concept of fiber continuity. The method has already been shown to yield good numerical results, but has not yet been analyzed theoretically. Under suitable smoothness assumptions, we apply results on constrained Tikhonov-type regularization with approximate operator to show convergence of reconstructions from discrete, noisy data for linear forward models. Further, we numerically illustrate the performance of the method on phantom and in-vivo data.