# Equivariant spatio-hemispherical networks for diffusion MRI deconvolution

arXiv: https://arxiv.org/abs/2411.11819 · HTML: https://mlsanity.com/paper/2411.11819/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 78 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Builds on (most cited first, 16 of 16)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications](https://mlsanity.com/paper/1810.12186/) (2018)
- [The Lie Derivative for Measuring Learned Equivariance](https://mlsanity.com/paper/2210.02984/) (2022)
- [DDM2: Self-Supervised Diffusion MRI Denoising with Generative Diffusion Models](https://mlsanity.com/paper/2302.03018/) (2023)
- [Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Space](https://mlsanity.com/paper/2310.02970/) (2023)
- [Patch2Self: Denoising Diffusion MRI with Self-Supervised Learning](https://mlsanity.com/paper/2011.01355/) (2020)
- [Rotation-Equivariant Deep Learning for Diffusion MRI](https://mlsanity.com/paper/2102.06942/) (2021)
- [VolterraNet: A higher order convolutional network with group equivariance for homogeneous manifolds](https://mlsanity.com/paper/2106.15301/) (2021)
- [Spatio-Angular Convolutions for Super-resolution in Diffusion MRI](https://mlsanity.com/paper/2306.00854/) (2023)
- [Equivariant Spherical Deconvolution: Learning Sparse Orientation Distribution Functions from Spherical Data](https://mlsanity.com/paper/2102.09462/) (2021)
- [How can spherical CNNs benefit ML-based diffusion MRI parameter estimation?](https://mlsanity.com/paper/2207.00572/) (2022)
- [Deep Learning Estimation of Multi-Tissue Constrained Spherical Deconvolution with Limited Single Shell DW-MRI](https://mlsanity.com/paper/2002.08820/) (2020)

## Built on by (most cited first, 1 of 1)

- [Neural Operators for Biomedical Spherical Heterogeneity](https://mlsanity.com/paper/2601.03561/) (2026)

## Abstract (arXiv)

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 E(3) × 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.