E(3) × SO(3)-Equivariant Networks for Spherical Deconvolution in Diffusion MRI

Axel Elaldi, Guido Gerig, Neel Dey

Research output: Contribution to journalConference articlepeer-review


We present Roto-Translation Equivariant Spherical Deconvolution (RT-ESD), an E(3) × SO(3) equivariant framework for sparse deconvolution of volumes where each voxel contains a spherical signal. Such 6D data naturally arises in diffusion MRI (dMRI), a medical imaging modality widely used to measure microstructure and structural connectivity. As each dMRI voxel is typically a mixture of various overlapping structures, there is a need for blind deconvolution to recover crossing anatomical structures such as white matter tracts. Existing dMRI work takes either an iterative or deep learning approach to sparse spherical deconvolution, yet it typically does not account for relationships between neighboring measurements. This work constructs equivariant deep learning layers which respect to symmetries of spatial rotations, reflections, and translations, alongside the symmetries of voxelwise spherical rotations. As a result, RT-ESD improves on previous work across several tasks including fiber recovery on the DiSCo dataset, deconvolution-derived partial volume estimation on real-world in vivo human brain dMRI, and improved downstream reconstruction of fiber tractograms on the Tractometer dataset. Our implementation is available at https://github.com/AxelElaldi/e3so3_conv.

Original languageEnglish (US)
Pages (from-to)301-319
Number of pages19
JournalProceedings of Machine Learning Research
StatePublished - 2023
Event6th International Conference on Medical Imaging with Deep Learning, MIDL 2023 - Nashville, United States
Duration: Jul 10 2023Jul 12 2023


  • Diffusion MRI
  • Equivariant Networks
  • Spherical Deep Learning

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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