Learning compact q-space representations for multi-shell diffusion-weighted MRI

TL;DR

This paper introduces SHARD, a data-driven, orthogonal q-space signal representation for multi-shell diffusion MRI that improves motion correction and outlier rejection by capturing microstructural information efficiently.

Contribution

The paper presents SHARD, a novel radial-spherical decomposition method for q-space signals that outperforms existing models in representing diffusion MRI data.

Findings

SHARD provides a complete orthogonal basis tailored to q-space geometry.

Rank-reduced SHARD outperforms model-based methods in human brain data.

Joint radial-spherical representation improves signal prediction for motion correction.

Abstract

Diffusion-weighted MRI measures the direction and scale of the local diffusion process in every voxel through its spectrum in q-space, typically acquired in one or more shells. Recent developments in microstructure imaging and multi-tissue decomposition have sparked renewed attention in the radial b-value dependence of the signal. Applications in motion correction and outlier rejection therefore require a compact linear signal representation that extends over the radial as well as angular domain. Here, we introduce SHARD, a data-driven representation of the q-space signal based on spherical harmonics and a radial decomposition into orthonormal components. This representation provides a complete, orthogonal signal basis, tailored to the spherical geometry of q-space and calibrated to the data at hand. We demonstrate that the rank-reduced decomposition outperforms model-based alternatives in human brain data, whilst faithfully capturing the micro- and meso-structural information in the signal. Furthermore, we validate the potential of joint radial-spherical as compared to single-shell representations. As such, SHARD is optimally suited for applications that require low-rank signal predictions, such as motion correction and outlier rejection. Finally, we illustrate its application for the latter using outlier robust regression.