Graph signal processing deals with data processing techniques on irregular domains that can be characterized by means of a graph or a network. The field extends the classical signal processing toolbox to graph signals. It finds applications in a variety of fields and can be used to process data on top of gene, social, communication and brain networks to name a few. One of the cornerstones of the field of graph signal processing is the graph Fourier transform, which will be introduced in this talk. Once a graph Fourier domain has been coined, we can start developing graph filters, which are direct analogues of time-domain filters, but intended for signals defined on graphs. We will give an overview of the graph filtering problem and look at the family of finite impulse response (FIR) and autoregressive moving average (ARMA) graph filters. Finally, the notions of graph stationarity and graph sampling will be introduced. Both are challenging tasks due to the irregularity of the underlying graph domain. Numerical results will accompany the theoretical results, showing that GSP is appealing for many interesting settings.
Geert Leus received the M.Sc. and Ph.D. degree in Electrical Engineering from the KU Leuven, Belgium, in June 1996 and May 2000, respectively. Geert Leus is now an "Antoni van Leeuwenhoek" Full Professor at the Faculty of Electrical Engineering, Mathematics and Computer Science of the Delft University of Technology, The Netherlands. His research interests are in the broad area of signal processing, with a specific focus on wireless communications, array processing, sensor networks, and graph signal processing. Geert Leus received a 2002 IEEE Signal Processing Society Young Author Best Paper Award and a 2005 IEEE Signal Processing Society Best Paper Award. He is a Fellow of the IEEE and a Fellow of EURASIP. Geert Leus was a Member-at-Large of the Board of Governors of the IEEE Signal Processing Society, the Chair of the IEEE Signal Processing for Communications and Networking Technical Committee, a Member of the IEEE Sensor Array and Multichannel Technical Committee, and the Editor in Chief of the EURASIP Journal on Advances in Signal Processing. He was also on the Editorial Boards of the IEEE Transactions on Signal Processing, the IEEE Transactions on Wireless Communications, the IEEE Signal Processing Letters, and the EURASIP Journal on Advances in Signal Processing. Currently, he is the Chair of the EURASIP Special Area Team on Signal Processing for Multisensor Systems, a Member of the IEEE Signal Processing Theory and Methods Technical Committee, a Member of the IEEE Big Data Special Interest Group, an Associate Editor of Foundations and Trends in Signal Processing, and the Editor in Chief of EURASIP Signal Processing.
