Journal
IEEE TRANSACTIONS ON MEDICAL IMAGING
Volume 38, Issue 3, Pages 834-843Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TMI.2018.2873736
Keywords
Diffusion-weighted imaging; multi-shell HARDI; blind source separation; dimensionality reduction
Categories
Funding
- European Research Council under the European Union's Seventh Framework Programme (FP7/20072013/ERC grant [319456]
- Wellcome Trust/EPSRC Centre for Medical Engineering at King's College London [WT 203148/Z/16/Z]
- Medical Research Council [MR/K006355/1]
- National Institute for Health Research (NIHR) Biomedical Research Centre based at Guy's and St Thomas' NHS Foundation Trust and King's College London
- MRC [MR/K006355/1] Funding Source: UKRI
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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.
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