Redundant graph Fourier transform

Author

Xianwei Zheng ; Yuanyan Tang ; Jiantao Zhou ; Yang, Lina ; Haoliang Yuan ; Yulong Wang ; Chunli Li

Author_Institution

Dept. of Comput. & Inf. Sci., Univ. of Macau, Macau, China

fYear

2015

fDate

24-26 June 2015

Firstpage

406

Lastpage

409

Abstract

Signal processing on graphs is a new emerging field that processing high-dimensional data by spreading samples on networks or graphs. The new introduced definition of graph Fourier transform shows its importance in establishing the theory of frequency analysis or computational harmonic analysis on graph signal processing. We introduce the definition of redundant graph Fourier transform, which is defined via a Parseval frame transform generated from an extended Laplacian of a given graph. The flexibility and sparsity of the redundant graph Fourier transform are important properties that will be useful in signal processing. In certain applications and by selections of the extended Laplacian, redundant Fourier transform performs better than graph Fourier transform.

Keywords

Fourier transforms; Laplace transforms; data compression; graph theory; matrix algebra; Laplacian matrix; Parseval frame transform; computational harmonic analysis; extended Laplacian selection; frequency analysis theory; graph signal processing; high-dimensional data processing; redundant graph Fourier transform; signal compression; Approximation error; Eigenvalues and eigenfunctions; Fourier transforms; Harmonic analysis; Laplace equations; Graph Fourier transform; graph Laplacian matrix; redundant graph Fourier transform; signal compression;

fLanguage

English

Publisher

ieee

Conference_Titel

Cybernetics (CYBCONF), 2015 IEEE 2nd International Conference on

Conference_Location

Gdynia

Print_ISBN

978-1-4799-8320-9

Type

conf

DOI

10.1109/CYBConf.2015.7175968

Filename

7175968