Efficient sampling and robust 3D diffusion magnetic resonance imaging signal reconstruction

TL;DR

This paper introduces efficient sampling schemes and robust reconstruction algorithms for diffusion MRI that reduce scan times and improve accuracy by using fewer measurements and well-conditioned linear systems.

Contribution

It proposes novel single and multi-shell sampling schemes with matching measurements to basis degrees of freedom, along with smaller, well-conditioned reconstruction algorithms incorporating regularization and noise modeling.

Findings

More accurate reconstruction than standard methods at equal sample sizes

Reduced scan times due to fewer required samples

Validated on human brain data with improved robustness

Abstract

This paper presents novel single and multi-shell sampling schemes for diffusion MRI. In diffusion MRI, it is paramount that the number of samples is as small as possible in order that scan times are practical in a clinical setting. The proposed schemes use an efficient number of measurements in that the number of samples is equal to the degrees of freedom in the orthonormal bases used for reconstruction. Novel reconstruction algorithms based on smaller subsystems of linear equations, as compared to the standard regularized least-squares method, are developed for both single and multi-shells sampling schemes. The smaller matrices used in these novel reconstruction algorithms are designed to be well-conditioned, leading to improved reconstruction accuracy. Accurate and robust reconstruction is also achieved through incorporation of regularization into the novel reconstruction algorithms and using a Rician or non-central Chi noise model. We quantitatively validate our single and multi-shell schemes against standard least-squares reconstruction methods to show that they enable more accurate reconstruction when the number of samples is equal to the degrees of freedom in the basis. Human brain data is also used to qualitatively evaluate reconstruction