Higher-Order Tensors in Diffusion Imaging

Diffusion MRI visualization

Modern diffusion magnetic resonance imaging (dMRI) acquires intricate volume datasets and biological meaning can only be found in the relationship between its different measurements. Suitable strategies for visualizing these complicated data have been key to interpretation by physicians and neuroscientists, for drawing conclusions on brain connectivity and for quality control. This article provides an overview of visualization solutions that have been proposed to date, ranging from basic grayscale and color encodings to glyph representations and renderings of fiber tractography. A particular focus is on ongoing and possible future developments in dMRI visualization, including comparative, uncertainty, interactive and dense visualizations.

Learning Compact q -Space Representations for Multi-Shell Diffusion-Weighted MRI

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, while faithfully capturing the micro- and meso-structural information in the signal. Furthermore, we validate the potential of joint radial-spherical as compared with 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.