Rotation-Equivariant Deep Learning for Diffusion MRI
This work addresses the challenge of handling orientation variability in diffusion MRI for medical imaging tasks, representing an incremental advancement by extending existing equivariant methods to a new data domain.
The authors tackled the problem of applying rotation-equivariant neural networks to 6D diffusion MRI data, achieving better results and requiring fewer training scans for multiple-sclerosis lesion segmentation compared to non-rotation-equivariant deep learning.
Convolutional networks are successful, but they have recently been outperformed by new neural networks that are equivariant under rotations and translations. These new networks work better because they do not struggle with learning each possible orientation of each image feature separately. So far, they have been proposed for 2D and 3D data. Here we generalize them to 6D diffusion MRI data, ensuring joint equivariance under 3D roto-translations in image space and the matching 3D rotations in $q$-space, as dictated by the image formation. Such equivariant deep learning is appropriate for diffusion MRI, because microstructural and macrostructural features such as neural fibers can appear at many different orientations, and because even non-rotation-equivariant deep learning has so far been the best method for many diffusion MRI tasks. We validate our equivariant method on multiple-sclerosis lesion segmentation. Our proposed neural networks yield better results and require fewer scans for training compared to non-rotation-equivariant deep learning. They also inherit all the advantages of deep learning over classical diffusion MRI methods. Our implementation is available at https://github.com/philip-mueller/equivariant-deep-dmri and can be used off the shelf without understanding the mathematical background.