Equivariant spatio-hemispherical networks for diffusion MRI deconvolution

• URL: http://arxiv.org/abs/2411.11819v1
• Date: Mon, 18 Nov 2024 18:37:39 GMT
• Title: Equivariant spatio-hemispherical networks for diffusion MRI deconvolution
• Authors: Axel Elaldi, Guido Gerig, Neel Dey,
• Abstract summary: This paper advances the analysis of such sphericalal data by developing convolutional network layers that are equivariant to the $math(3) times SO(3)$ group. In the context of sparse spherical fiber deconvolution to recover white matter, our proposed equivariant network layers yield substantial performance and efficiency gains.
• Score: 5.680416078423551
• License:
• Abstract: Each voxel in a diffusion MRI (dMRI) image contains a spherical signal corresponding to the direction and strength of water diffusion in the brain. This paper advances the analysis of such spatio-spherical data by developing convolutional network layers that are equivariant to the $\mathbf{E(3) \times SO(3)}$ group and account for the physical symmetries of dMRI including rotations, translations, and reflections of space alongside voxel-wise rotations. Further, neuronal fibers are typically antipodally symmetric, a fact we leverage to construct highly efficient spatio-hemispherical graph convolutions to accelerate the analysis of high-dimensional dMRI data. In the context of sparse spherical fiber deconvolution to recover white matter microstructure, our proposed equivariant network layers yield substantial performance and efficiency gains, leading to better and more practical resolution of crossing neuronal fibers and fiber tractography. These gains are experimentally consistent across both simulation and in vivo human datasets.

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