190280
20190416055537.0
doi
10.1109/Tsp.2015.2424203
1053-587X
ISI
000357778600006
ARTICLE
Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames
2015
Institute of Electrical and Electronics Engineers
2015
Journal Articles
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph wavelet constructions are only adapted to the length of the spectrum, the filters proposed in this paper are adapted to the distribution of graph Laplacian eigenvalues, and therefore lead to atoms with better discriminatory power. Our approach is to first characterize a family of systems of uniformly translated kernels in the graph spectral domain that give rise to tight frames of atoms generated via generalized translation on the graph. We then warp the uniform translates with a function that approximates the cumulative spectral density function of the graph Laplacian eigenvalues. We use this approach to construct computationally efficient, spectrum-adapted, tight vertex-frequency and graph wavelet frames. We give numerous examples of the resulting spectrum-adapted graph filters, and also present an illustrative example of vertex-frequency analysis using the proposed construction.
Filter design
signal processing on graphs
spectrum-based warping
tight frames
vertex-frequency analysis
242930
Shuman, David
201233
Wiesmeyr, Christoph
Holighaus, Nicki
240428
Vandergheynst, Pierre
120906
63
16
4223-4235
IEEE Transactions on Signal Processing
3119273
http://infoscience.epfl.ch/record/190280/files/Shuman_et_al_Spectrum_Adapted_Frames_2013.PDF
Preprint
Preprint
252393
LTS4
U10851
252392
LTS2
U10380
oai:infoscience.tind.io:190280
STI
article
GLOBAL_SET
201233
120906
120906
148230
EPFL-ARTICLE-190280
EPFL
REVIEWED
PUBLISHED
ARTICLE