Critically-Sampled Graph Filter Banks with Spectral Domain Sampling

Watanabe, Kana; Sakiyama, Akie; Tanaka, Yuichi; Ortega, Antonio

doi:10.1109/icassp.2018.8461457

Cited by 4 publications

(6 citation statements)

References 19 publications

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“…Spectral domain sampling can be applied to both down-and upsampling of signals. Future work includes devising fast computation methods for spectral domain sampling, conducting experiments using real-world signals on (possibly large-scale) graphs, and designing multirate graph signal processing systems like wavelets [71], [72].…”

Section: Discussionmentioning

confidence: 99%

Spectral Domain Sampling of Graph Signals

Tanaka

2018

IEEE Trans. Signal Process.

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Sampling methods for graph signals in the graph spectral domain are presented. Though the conventional sampling of graph signals can be regarded as sampling in the graph vertex domain, it does not have the desired characteristics in regard to the graph spectral domain. With the proposed methods, the down-and upsampled graph signals inherit the frequency-domain characteristics of the sampled signals defined in the time/spatial domain. The properties of the sampling effects were evaluated theoretically in comparison with those obtained with the conventional sampling method in the vertex domain. Various examples of signals on simple graphs enable precise understanding of the problem considered. Fractional sampling and Laplacian pyramid representation of graph signals are potential applications of these methods.

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Section: Discussionmentioning

confidence: 99%

Spectral Domain Sampling of Graph Signals

Tanaka

2018

IEEE Trans. Signal Process.

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“…The main contribution of this paper is the design of CS graph filter banks (GFBs) using sampling in the graph frequency domain [43]. This paper is a significantly extended version of our preliminary study [44], which first introduced this idea. With respect to [44] we have added theoretical results with proofs as well as much more comprehensive experimental results.…”

Section: A Motivationmentioning

confidence: 99%

“…This paper is a significantly extended version of our preliminary study [44], which first introduced this idea. With respect to [44] we have added theoretical results with proofs as well as much more comprehensive experimental results. The main advantages of our proposed approach are 1 :…”

Section: A Motivationmentioning

confidence: 99%

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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“…In the example above, using the low-pass filter [1100] T does recover the original [1, 2, 0, 0] T , but this is a trivial statement. As shown in Section VII-B, the low-pass filter does not invert the P(M) K K in (50). It only works because in DSP P(M) K K = I K , which does not need inverting.…”

Section: Connection With Other Sampling Methodsmentioning

confidence: 99%

Topics in Graph Signal Processing: Convolution and Modulation

Shi

Moura

2019

2019 53rd Asilomar Conference on Signals, Systems, and Computers

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To analyze data supported by arbitrary graphs G, DSP has been extended to Graph Signal Processing (GSP) by redefining traditional DSP concepts like shift, filtering, and Fourier transform among others. This paper revisits modulation, convolution, and sampling of graph signals as appropriate natural extensions of the corresponding DSP concepts. To define these for both the vertex and the graph frequency domains, we associate with generic data graph G and its graph shift A a graph spectral shift M and a spectral graph G s . This leads to a spectral GSP theory that parallels in the graph frequency domain the existing GSP theory in the vertex domain. The paper applies this to design and recovery sampling techniques for data supported by arbitrary directed graphs.

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Critically-Sampled Graph Filter Banks with Spectral Domain Sampling

Cited by 4 publications

References 19 publications

Spectral Domain Sampling of Graph Signals

Spectral Domain Sampling of Graph Signals

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

Topics in Graph Signal Processing: Convolution and Modulation

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