GSR-Net: Graph Super-Resolution Network for Predicting High-Resolution from Low-Resolution Functional Brain Connectomes

Abstract

Catchy but rigorous deep learning architectures were tailored for image super-resolution (SR), however, these fail to generalize to non-Euclidean data such as brain connectomes. Specifically, building generative models for super-resolving a low-resolution brain connectome at a higher resolution (i.e., adding new graph nodes/edges) remains unexplored —although this would circumvent the need for costly data collection and manual labelling of anatomical brain regions (i.e. parcellation). To fill this gap, we introduce GSR-Net (Graph Super-Resolution Network), the first super-resolution framework operating on graph-structured data that generates high-resolution brain graphs from low-resolution graphs. First, we adopt a U-Net like architecture based on graph convolution, pooling and unpooling operations specific to non-Euclidean data. However, unlike conventional U-Nets where graph nodes represent samples and node features are mapped to a low-dimensional space (encoding and decoding node attributes or sample features), our GSR-Net operates directly on a single connectome: a fully connected graph where conventionally, a node denotes a brain region, nodes have no features, and edge weights denote brain connectivity strength between two regions of interest (ROIs). In the absence of original node features, we initially assign identity feature vectors to each brain ROI (node) and then leverage the learned local receptive fields to learn node feature representations. Specifically, for each ROI, we learn a node feature embedding by locally averaging the features of its neighboring nodes based on their connectivity weights. Second, inspired by spectral theory, we break the symmetry of the U-Net architecture by topping it up with a graph super-resolution (GSR) layer and two graph convolutional network layers to predict a HR (high-resolution) graph while preserving the characteristics of the LR (low-resolution) input. Our proposed GSR-Net framework outperformed its variants for predicting high-resolution brain functional connectomes from low-resolution connectomes. Our Python GSR-Net code is available on BASIRA GitHub at https://github.com/basiralab/GSR-Net.