A didactic introduction to Graph Signal Processing techniques and applications

Abstract

Traditional signal processing thrives when applied to uniform, euclidean domains. Even though most DSP tools are built around the fact that signal domains are expected to be uniform e.g. continuous time or an equally spaced discrete domain, many in- teresting problems are defined on top of more irregular structures. When dealing with applications such as social networks, arbitrarily distributed arrays of sensors, neuronal networks, and power grids, one of the mathematical strategies to acknowledge the irregular structure is to interpret the data as being defined on the vertices of a weighted graph. Since these subjacent structures usually carry valueable information, the field of signal processing on graphs, or graph signal processing (GSP), has been active in the recent decade. In this work, we review some of the advances made possible by this new field. We give special focus to time-varying signals in which each graph vertex rep- resents a time-series and the adaptive algorithms designed for this new kind of signal processing. By applying to GSP techniques borrowed from adaptive filtering, one is able to de- rive processing algorithms that learn from the statistics of a graph signal. When the subjacent structure of the irregular domain on which the data reside is accounted for, the results are higher inference power, and better-informed decisions.