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A Modified Spline Graph Filter Bank

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Abstract

Two-channel critically sampled spline graph filter bank (SGFB) is one of the existing solutions for signal processing on arbitrary graphs. This paper addresses an approach to modify the filter design for SGFB. Our method improves the shape of analysis filters in the spectral domain and also reduces the computational complexity for the synthesis section. Additionally, the proposed method exploits polynomial filters and does not need to compute eigendecomposition for the Laplacian matrix of the underlying graph. Numerical results show the efficacy of our approach by comparing its performance in graph signal decomposition and denoising with the existing solutions.

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Data Availability

The datasets generated during and/or analyzed during the current study are not publicly available due to our future works but 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 multiscale transforms.

  2. \(\rho (A)=\mathrm{max}\{|\lambda |\!:\!\lambda \in \varSigma (A)\}\), \(\varSigma (A)\) contains eigenvalues of matrix A.

  3. The optimal value J and M may differ for different graphs, and an optimal value setting will be an interesting topic in the future.

  4. Although SGFB in [5] can decompose signal in multilevel for arbitrary graphs, it does not maintain the spectral shape of the smooth graph signal after the second level and then denoising of the smooth signal is not possible.

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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. A Modified Spline Graph Filter Bank. Circuits Syst Signal Process 40, 2025–2035 (2021). https://doi.org/10.1007/s00034-020-01543-2

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