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.

翻译：扩散磁共振成像（dMRI）图像中的每个体素包含一个球形信号，对应大脑中水扩散的方向和强度。本文通过开发对 $\mathbf{E(3) \times SO(3)}$ 群等变的卷积网络层，推进了此类空间-球形数据的分析，该网络层考虑了dMRI的物理对称性，包括空间的旋转、平移和反射以及体素级的旋转。此外，神经纤维通常具有对映对称性，我们利用这一事实构建了高效的空间-半球图卷积，以加速高维dMRI数据的分析。在稀疏球形纤维反卷积以恢复白质微结构的背景下，我们提出的等变网络层在性能和效率上带来了显著提升，从而实现了对交叉神经纤维和纤维束成像更好且更实用的解析。这些提升在模拟和活体人类数据集的实验中均得到一致验证。