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Spline Graph Filter Bank with Spectral Sampling

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Abstract

In this paper, a two-channel critically sampled spline graph filter bank (SGFB) for an arbitrary undirected graph with spectral domain sampling is proposed. The filters in the analysis section satisfy perfect reconstruction condition, and the synthesis section is implemented with low computational complexity. The proposed SGFB maintains the spectrum of the original signal in multi-level decomposition and then suppresses noise efficiently. It is worth noting that the proposed filter design is performed once for the desired filter shape in the spectral domain with desired cutoff frequency. Since the optimization problem is solved once, it reduces the complexity for large graph significantly. Through numerical analyses, we validate the efficacy of the proposed SGFB using multi-level decomposition of a graph signal and noise suppression in terms of signal-to-noise ratio (SNR) improvement.

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Data Availability

The datasets used in this study are available from the corresponding author on reasonable request.

Notes

  1. Kron reduction is a most widely used method to reduce the graph in GSP, especially in multi-scale transforms.

  2. The spectral sampling requires the number of graph nodes to be even.

  3. Only elements on the counterdiagonal are 1.

  4. All elements in \(\varvec{\mathcal {C}}\) are zeros except the elements that reside on the main diagonal and the counterdiagonal.

  5. Since the eigenvalues are from the decomposition of the graph normalized Laplacian, they are bounded within the interval [0, 2].

  6. The original graph has 2642 vertices, but we add two vertices to run multi-level decomposition. The vertices are added to the left corner at the top of the Minnesota graph.

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Authors and Affiliations

  1. Electrical Engineering Department, Yazd University, Yazd, 89158-18411, Iran

    Amir Miraki & Hamid Saeedi-Sourck

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  1. Amir Miraki
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  2. Hamid Saeedi-Sourck
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Correspondence to Hamid Saeedi-Sourck.

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Miraki, A., Saeedi-Sourck, H. Spline Graph Filter Bank with Spectral Sampling. Circuits Syst Signal Process 40, 5744–5758 (2021). https://doi.org/10.1007/s00034-021-01729-2

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  • DOI: https://doi.org/10.1007/s00034-021-01729-2

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