Gauge equivariant convolutional neural networks for diffusion MRI

Diffusion MRI (dMRI) is an imaging technique widely used in neuroimaging research, where the signal carries directional information of underlying neuronal fibres based on the diffusivity of water molecules. One of the shortcomings of dMRI is that numerous images, sampled at gradient directions on a sphere, must be acquired to achieve a reliable angular resolution for model-fitting, which translates to longer scan times, higher costs, and barriers to clinical adoption. In this work we introduce gauge equivariant convolutional neural network (gCNN) layers for dMRI that overcome the challenges associated with the signal being acquired on a sphere with antipodal points identified. This is done by noting that the domain is equivalent to the real projective plane, [Formula: see text], which is a non-euclidean and a non-orientable manifold. This is in stark contrast to a rectangular grid which typical convolutional neural networks (CNNs) are designed for. We apply our method to upsample angular resolution for predicting diffusion tensor imaging (DTI) parameters from just six diffusion gradient directions. The symmetries introduced allow gCNNs the ability to train with fewer subjects as compared to a baseline model that involves only 3D convolutions.