Localized Interpolation for Graph Signals

Antoine Mazarguil, Laurent Oudre, Nicolas Vayatis

Abstract: Graph structure is a powerful framework for the characterization of interaction between entities. In the context of graph signal processing, interpolation methods are based on the smoothness assumption that assumes that neighboring nodes present similar values. However, in several contexts, the strong relationship between two connected nodes may express different behaviour. In this paper, we propose a graph signal interpolation algorithm that uses a graph localization penalization on the reconstruction weights. These weights are learned from the data, thus allowing the use of signal anti-correlation on connected nodes in order to perform a more robust interpolation. The results displayed in the paper show that our approach is relevant when dealing with real data, for both smooth and non-smooth signals.