HIGHER ORDER GAUGE EQUIVARIANT CONVOLUTIONS FOR NEURODEGENERATIVE DISORDER CLASSIFICATION.

Diffusion MRI (dMRI) has shown significant promise in capturing subtle changes in neural microstructure caused by neurodegenerative disorders. In this paper, we propose a novel end-to-end compound architecture for processing raw dMRI data. It consists of a 3D convolutional kernel network (CKN) that extracts macro-architectural features across voxels and a gauge equivariant Volterra network (GEVNet) on the sphere that extracts micro-architectural features from within voxels. The use of higher order convolutions enables our architecture to model spatially extended nonlinear interactions across the applied diffusion-sensitizing magnetic field gradients. The compound network is globally equivariant to 3D translations and locally equivariant to 3D rotations. We demonstrate the efficacy of our model on the classification of neurodegenerative disorders.