A non-commutative viewpoint on graph signal processing

Mahya Ghandehari, Dominique Guillot, Kristopher Hollingsworth

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The emerging field of graph signal processing aims to develop analysis and processing techniques for data that is best represented on irregular domains such as graphs. To this end, important notions of classical signal processing, such as smoothness, band-limitedness, and sampling, should be extended to the case of graph signals. One of the most fundamental concepts in classical signal processing is the Fourier transform. Recently, graph Fourier transform was defined as a generalization of the Fourier transform on Abelian groups, and many of its properties were investigated. However, a graph is usually the manifestation of a non-commutative structure; this can be easily seen in the case of the Cayley graph of a non-Abelian group. In this article, we investigate a new approach to develop concepts of Fourier analysis for graphs. Our point of view is inspired by the theory of non-commutative harmonic analysis, and is founded upon the representation theory of non-Abelian groups.

Original languageEnglish (US)
Title of host publication2019 13th International Conference on Sampling Theory and Applications, SampTA 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728137414
DOIs
StatePublished - Jul 2019
Externally publishedYes
Event13th International Conference on Sampling Theory and Applications, SampTA 2019 - Bordeaux, France
Duration: Jul 8 2019Jul 12 2019

Publication series

Name2019 13th International Conference on Sampling Theory and Applications, SampTA 2019

Conference

Conference13th International Conference on Sampling Theory and Applications, SampTA 2019
CountryFrance
CityBordeaux
Period7/8/197/12/19

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