Non-smooth interpolation of graph signals

We consider the problem of signal interpolation on graphs, i.e. recovering one or multiple graph signal values from incomplete measurements. We propose a review of the graph signal interpolation methods, which enlightens the restrictive underlying hypothesis of signal smoothness over the graph. We formulate a new interpolation framework based on a locality criterion designed to handle nonsmooth signals, and provide corresponding specific solutions. We validate the proposed methods on synthetic and real-world interpolation problems, and analyse the stability of our methods regarding the interpolation problem main parameters.