Compact Support Biorthogonal Wavelet Filterbanks for Arbitrary Undirected Graphs
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Cites background from "Compact Support Biorthogonal Wavele..."
...graphs [68], [102], thus requiring the graph to be decomposed into a series of bipartite subgraphs [68], [103]....
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644 citations
Cites background from "Compact Support Biorthogonal Wavele..."
...The framework models that underlying structure by a graph and signals by graph signals, generalizing concepts and tools from classical discrete signal processing to graph signal processing....
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Cites methods from "Compact Support Biorthogonal Wavele..."
...For example, spectral filters in the form of polynomials of the variation operator are used in the design of wavelet filterbanks for graph signals [21], [17], [18] to offer a trade-off between frequency-domain and vertex-domain localization....
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...It considers a spectral-domain criterion, using minimum singular values of submatrices of the graph Fourier transform matrix, to minimize the effect of sample noise in the worst case....
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"Compact Support Biorthogonal Wavele..." refers background in this paper
...However, it can be shown [2], that filters with polynomial spectral kernels can be implemented iteratively with one-hop operations at each node, and do not require matrix diagonalization....
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...There has been a significant recent interest in the extension of wavelet transforms to graph signals, including wavelets on unweighted graphs for analyzing computer network traffic [5], diffusion wavelets and diffusion wavelet packets [6], [7], the “top-down” wavelet construction of [8], graph dependent basis functions for sensor network graphs [9], lifting based wavelets on graphs [10]–[12], multiscale wavelets on balanced trees [13], spectral graph wavelets [2], and our recent work on graph wavelet filterbanks [3]....
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...This trade-off is being studied for graph signals as well [2]–[4]....
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