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<p>This paper focuses on graph signal denoising (GSD), which involves recovering the ground truth from noisy observations. This process can be computationally expensive, especially in large-scale graphs. Therefore, we proposed partitioning the graph using a spectral clustering scheme. Several spectral kernels are designed for each partition, and the corresponding graph signal is filtered, yielding different sets of coefficients corresponding to the number of kernels. Then the Stein’s Unbiased Risk Estimator (SURE) optimization is applied to each of the kernel’s coefficients, enabling us to perform parallel processing. To facilitate the search process and improve computational efficiency, the Imperialist Competitive Algorithm (ICA) was employed to determine the optimal threshold value. This threshold value is then used in two distinct proposed denoising strategies. The kernel coefficients soft thresholding (KCST) and the kernel coefficients block thresholding (KCBT) schemes, which demonstrate competitive performance in terms of accuracy, measured by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Delta\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Δ</mi> </math></EquationSource> </InlineEquation>SNR, and computational efficiency measured in seconds. The experimental results reveal that the proposed approach outperforms in terms of computational complexity, either in normal-sized or large-scale graphs, but is especially effective for large-scale graphs. Furthermore, most schemes are based on bandlimited signals, but the proposed schemes also have proper performance in approximately smooth and bandlimited signals.</p>

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Large-scale Graph Signal Denoising: Spectral Partitioning and Kernel-Based Thresholding

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Mohammadreza Fattahi,
  • Hamid Saeedi-Sourck,
  • Vahid Abootalebi

摘要

This paper focuses on graph signal denoising (GSD), which involves recovering the ground truth from noisy observations. This process can be computationally expensive, especially in large-scale graphs. Therefore, we proposed partitioning the graph using a spectral clustering scheme. Several spectral kernels are designed for each partition, and the corresponding graph signal is filtered, yielding different sets of coefficients corresponding to the number of kernels. Then the Stein’s Unbiased Risk Estimator (SURE) optimization is applied to each of the kernel’s coefficients, enabling us to perform parallel processing. To facilitate the search process and improve computational efficiency, the Imperialist Competitive Algorithm (ICA) was employed to determine the optimal threshold value. This threshold value is then used in two distinct proposed denoising strategies. The kernel coefficients soft thresholding (KCST) and the kernel coefficients block thresholding (KCBT) schemes, which demonstrate competitive performance in terms of accuracy, measured by \(\Delta\) Δ SNR, and computational efficiency measured in seconds. The experimental results reveal that the proposed approach outperforms in terms of computational complexity, either in normal-sized or large-scale graphs, but is especially effective for large-scale graphs. Furthermore, most schemes are based on bandlimited signals, but the proposed schemes also have proper performance in approximately smooth and bandlimited signals.