Geert Leus, Elvin Isufi and Mario Coutino
Although processing and analyzing audio, images and video is still of great importance in current society, more and more data is originating from networks with an irregular structure, e.g., social networks, brain networks, sensor networks, and communications networks to name a few. To handle such signals, graph signal processing has recently been coined as a proper tool set. In graph signal processing the irregular structure of the network is captured by means of a graph, and the data is viewed as a signal on top of this graph, i.e., a graph signal. Graph signal processing extends concepts and tools from classical signal processing to the field of graph signals, e.g., the Fourier transform, filtering, sampling, stationarity, etc. Since nowadays many researchers and engineers work in the field of network data processing, this tutorial is attractive, timely and critical. Further, most existing tutorials in this field focus on the basics of graph signal processing. Hence, it is urgent to go one step beyond and discuss the latest advances in graph signal processing as well as connections to the exciting fields of distributed optimization and neural networks, both of which draw inspiration from fundamental signal processing techniques.
More specifically, in this tutorial, we will emphasize the concept of graph filtering, one of the cornerstones of the field of graph signal processing. Graph filters are direct analogues of time-domain filters but intended for signals defined on graphs. They find applications in image denoising, network data interpolation, signal and link prediction, learning of graph signals and building recommender systems. More recently, connections to distributed optimization as well as neural networks have been established. These last two applications rely heavily on core signal processing techniques such as iterative inversion algorithms and linear time-invariant filters. Graph filters extend these concepts to graphs, leading to key developments in distributed optimization and neural networks.