Spatio-Angular Convolutions for Super-resolution in Diffusion MRI

Diffusion MRI (dMRI) is a widely used imaging modality, but requires long scanning times to acquire high resolution datasets. By leveraging the unique geometry present within this domain, we present a novel approach to dMRI angular super-resolution that extends upon the parametric continuous convolution (PCConv) framework. We introduce several additions to the operation including a Fourier feature mapping, global coordinates, and domain specific context. Using this framework, we build a fully parametric continuous convolution network (PCCNN) and compare against existing models. We demonstrate the PCCNN performs competitively while using significantly fewer parameters. Moreover, we show that this formulation generalises well to clinically relevant downstream analyses such as fixel-based analysis, and neurite orientation dispersion and density imaging. This presents an opportunity as typical CNN architectures do not fully utilise the geometric properties present in dMRI data. For example, implicit within the formulation of the CNN is the assumption that data are densely and regularly sampled in a discrete manner. This is only true when considering the three spatial dimensions of dMRI data, whilst the other dimensions would be more suited using approaches like graph convolutional networks (GCNs) [46] , spherical CNNs [7], and point cloud CNNs [22]. Examples of approaches that develop geometrically motivated convolutions in the dMRI 37th Conference on Neural Information Processing Systems (NeurIPS 2023).