Shuman, David
Wiesmeyr, Christoph
Holighaus, Nicki
Vandergheynst, Pierre
Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
63
16
Filter design
signal processing on graphs
spectrum-based warping
tight frames
vertex-frequency analysis
2015
2015
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.
Institute of Electrical and Electronics Engineers
1053-587X
IEEE Transactions on Signal Processing
Journal Articles
10.1109/Tsp.2015.2424203