Title :
Approximating signals supported on graphs
Author :
Zhu, Xiaofan ; Rabbat, Michael
Author_Institution :
Dept. of Electr. & Comput. Eng., McGill Univ., Montreal, QC, Canada
Abstract :
In this paper, we introduce the concept of smoothness for signals supported on the vertices of a graph. We provide theoretical explanations when and why the Laplacian eigenbasis can be regarded as a meaningful “Fourier” transform of such signals. Moreover, we analyze the desired properties of the underlying graphs for better compressibility of the signals. We verify our theoretical work by experiments on real world data.
Keywords :
Fourier transforms; Laplace transforms; approximation theory; eigenvalues and eigenfunctions; signal processing; Fourier transform; Laplacian eigenbasis; graph vertices; signal approximation; signal compressibility; Compressed sensing; Eigenvalues and eigenfunctions; Fourier transforms; Laplace equations; Linear approximation; Sensors; Fourier transform; Graph Laplacian; compressibility; smoothness;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on
Conference_Location :
Kyoto
Print_ISBN :
978-1-4673-0045-2
Electronic_ISBN :
1520-6149
DOI :
10.1109/ICASSP.2012.6288775
