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Title: Natural Graph Wavelet Packet Dictionaries
Abstract We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their “dual” domains by incorporating the “natural” distances between graph Laplacian eigenvectors, rather than simply using the eigenvalue ordering. These basis dictionaries can be seen as generalizations of the classical Shannon wavelet packet dictionary to arbitrary graphs, and do not rely on the frequency interpretation of Laplacian eigenvalues. We describe the algorithms (involving either vector rotations or orthogonalizations) to construct these basis dictionaries, use them to efficiently approximate graph signals through the best basis search, and demonstrate the strengths of these basis dictionaries for graph signals measured on sunflower graphs and street networks.  more » « less
Award ID(s):
2012266 1912747 1819222 1934568
NSF-PAR ID:
10228778
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Fourier Analysis and Applications
Volume:
27
Issue:
3
ISSN:
1069-5869
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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