Spectral Graph Wavelets and Filter Banks With Low Approximation Error

Sakiyama, Akie; Watanabe, Kana; Tanaka, Yuichi

doi:10.1109/tsipn.2016.2581303

Cited by 42 publications

(40 citation statements)

References 53 publications

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“…By using a method similar to [21], both orthogonal and biorthogonal filters can be designed on the basis of those used in classical signal processing.…”

Section: Design Methodsmentioning

confidence: 99%

“…They can be used on non-bipartite graphs by dividing the original graph into several bipartite graphs and then using a "multidimensional" decomposition. Filter design methods for this class of CS GWT include: GraphQMF [26], which utilizes quadrature mirror filters; GraphBior [27] a biorthogonal and polynomial filter solution with spectral factorization; a frequency conversion method (GraphFC) [21] that transforms time domain filters into graph spectral filters; near-orthogonal polynomial filter design methods (Nearorth) proposed in [28], [29]. Oversampled graph filter banks were introduced in [24], [25] as an extension of CS GWTs for bipartite graphs.…”

Section: Related Workmentioning

confidence: 99%

“…Several CS GFBs that satisfy the above perfect reconstruction condition have been proposed, together with some filter designs [21], [24]- [27].…”

Section: B Filter Designmentioning

confidence: 99%

“…• GraphQMF [26] • GraphBior [27] • GraphFC [21] • Diffusion wavelet (abbreviated as DiffWav) [65] • SubGFB [30] • Graph Laplacian pyramid (abbreviated as GLP) [11] We used MATLAB codes provided by the authors. Note that the existing GraphQMF, GraphBior, and GraphFC require bipartition of the underlying graph.…”

Section: A Setupmentioning

confidence: 99%

“…can achieve different trade-offs in terms of redundancy, performance, computation cost, and storage, are oversampled [21], [23]- [25], critically sampled (CS) [21], [26]- [33] and undersampled transforms [34].…”

mentioning

confidence: 99%

See 4 more Smart Citations

Two-Channel Critically Sampled Graph Filter Banks With Spectral Domain Sampling

Sakiyama

Watanabe

Tanaka

et al. 2019

IEEE Trans. Signal Process.

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We propose two-channel critically-sampled filter banks for signals on undirected graphs that utilize spectral domain sampling. Unlike conventional approaches based on vertex domain sampling, our transforms have the following desirable properties: 1) perfect reconstruction regardless of the characteristics of the underlying graphs and graph variation operators and 2) a symmetric structure; i.e., both analysis and synthesis filter banks are built using similar building blocks. Along with the structure of the filter banks, this paper also proves the general criterion for perfect reconstruction and theoretically shows that the vertex and spectral domain sampling coincide for a special case. The effectiveness of our approach is evaluated by comparing its performance in nonlinear approximation and denoising with various conventional graph transforms.

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“…By using a method similar to [21], both orthogonal and biorthogonal filters can be designed on the basis of those used in classical signal processing.…”

Section: Design Methodsmentioning

confidence: 99%