Unifying local and non-local signal processing with graph CNNs

This paper deals with the unification of local and non-local signal processing on graphs within a single convolutional neural network (CNN) framework. Building upon recent works on graph CNNs, we propose to use convolutional layers that take as inputs two variables, a signal and a graph, allowing the network to adapt to changes in the graph structure. This also allows us to learn through training the optimal mixing of locality and non-locality, in cases where the graph is built on the input signal itself. We demonstrate the versatility and the effectiveness of our framework on several types of signals (greyscale and color images, color palettes and speech signals) and on several applications (style transfer, color transfer, and denoising).