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Learning Compact <inline-formula> <tex-math notation="LaTeX">${q}$ </tex-math> </inline-formula>-Space Representations for Multi-Shell Diffusion-Weighted MRI

2018; Institute of Electrical and Electronics Engineers; Volume: 38; Issue: 3 Linguagem: Inglês

10.1109/tmi.2018.2873736

1558-254X

Daan Christiaens, Lucilio Cordero‐Grande, Jana Hutter, Anthony N. Price, Maria Deprez, Joseph V. Hajnal, Jacques‐Donald Tournier,

Tensor decomposition and applications

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.