Distinguished Symposium Talks

P.P. Vaidyanathan

California Institute of Technology, USA

Graph signals: transforms, filter banks, uncertainty bounds, and sparsity

Abstract
In classical digital signal processing (CSP) signals are defined as functions of discrete time or space, where the domain is a regular lattice such as a uniform grid. In graph signal processing (GSP) the signals are defined on vertices of graphs which are characterized by a graph adjacency matrix or a related matrix such as the Laplacian. The domain of the signal is therefore not necessarily a lattice, in fact it may not even be a domain with the notion of distance. In such cases, all the basic concepts of signal processing have to be revisited. This includes Fourier transforms, filtering, filter banks, and uncertainty relations associated with linear transforms. In recent years many researchers have contributed to the development of such ideas, and this has given birth to the field of graph signal processing. This talk starts with a brief review, and then goes into details of filtering, multirate systems, filter bank theory, and polyphase representations for graph signals. The somewhat unusual interrelationship between shift invariance, alias-free property, and polynomial property of linear systems on graphs is elaborated. Finally, uncertainty relations connecting graph signals and graph Fourier transforms are also discussed, and bounds on sparsity of eigenvectors of graphs are developed and demonstrated with examples.

Biography
Prof. P. P. Vaidyanathan has been with the California Institute of Technology since 1983. He received the B.Tech. and M.Tech. degrees in Radiophysics and Electronics from the University of Calcutta, India, in 1977 and 1979 respectively, and the Ph.D degree in Electrical and Computer Engineering from the University of California at Santa Barbara in 1982. His main research interests are in digital signal processing, multirate systems, filter banks, signal processing for digital communications, genomic signal processing, number theory, sparse array signal processing, and graph signal processing. He has authored many papers and four books in the signal processing area, and has received prizes for excellence in teaching at Caltech multiple times. Prof. Vaidyanathan served as the department head for Electrical Engineering at Caltech for 2002-2005. He is a Fellow of the IEEE, recipient of the F. E. Terman Award of the American Society for Engineering Education, past distinguished lecturer for the IEEE Signal Processing Society, and recipient of the IEEE CAS Society Golden Jubilee Medal. In 2016 he also received the IEEE Gustav Robert Kirchhoff Award (a Technical Field award) for "fundamental contributions to digital signal processing." He is a recipient of the IEEE Signal Processing Society’s Technical Achievement Award (2002), Education Award (2012), and Society Award (2016).

Geert Leus

Delft University of Technology, Netherlands

Stationary Graph Signals: Power Spectral Density Estimation and Sampling

Abstract
Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many contemporary applications the information of interest resides in more irregular domains which can be conveniently represented using a graph. This talk reviews recent advances in extending the notion of stationarity to random graph signals. This is a challenging task due to the irregularity of the underlying graph domain. To that end, we start by presenting coexisting stationarity definitions along with explanations of their genesis, advantages, and disadvantages. Secondly, we introduce the concept of power spectral density for graph processes and propose a number of methods for its estimation. These methods include nonparametric as well as parametric approaches. To account for distributed scenarios where the supporting graph is related to an actual network infrastructure, the last part of the talk discusses how to estimate the power spectral density of a graph process when having access to only a subset of the nodes. We illustrate our findings in synthetic and real-world graphs.

Biography
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 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. 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 the Chair of the IEEE Signal Processing for Communications and Networking Technical Committee, a Member-at-Large to the Board of Governors of the IEEE Signal Processing Society, and an Associate Editor for 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 a member of the IEEE Sensor Array and Multichannel Technical Committee and serves as the Editor in Chief of the EURASIP Journal on Advances in Signal Processing.