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Graph Normalized-LMP Algorithm for Signal Estimation Under Impulsive Noise

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Abstract

We introduce an adaptive graph normalized least mean pth power (GNLMP) algorithm that utilizes graph signal processing (GSP) techniques, including bandlimited filtering and node sampling, to estimate sampled graph signals under impulsive noise. Different from least-squares-based algorithms, such as the adaptive GSP Least Mean Squares (GLMS) algorithm and the normalized GLMS (GNLMS) algorithm, the GNLMP algorithm has the ability to reconstruct a graph signal that is corrupted by non-Gaussian noise with heavy-tailed characteristics. Compared to the recently introduced adaptive GSP least mean pth power (GLMP) algorithm, the GNLMP algorithm reduces the number of iterations to converge to a steady graph signal. The convergence condition of the GNLMP algorithm is derived, and the ability of the GNLMP algorithm to process multidimensional time-varying graph signals with multiple features is demonstrated. Simulations show that the performance of the GNLMP algorithm in estimating steady-state and time-varying graph signals is faster than GLMP and is more robust in comparison to GLMS and GNLMS.

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Code and Data Availability Statements

The code and the data set are available at https://github.com/yan2yi4/GSP_NLMP_paper.

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Acknowledgements

This work has been funded by High-end Foreign Expert Talent Introduction Plan under Grant G2021032021L.

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Authors and Affiliations

  1. Tsinghua-Berkeley Shenzhen Institute, Shenzhen International Graduate School, Tsinghua University, Shenzhen, China

    Yi Yan, Radwa Adel & Ercan Engin Kuruoglu

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  1. Yi Yan
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  2. Radwa Adel
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  3. Ercan Engin Kuruoglu
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Correspondence to Ercan Engin Kuruoglu.

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Yan, Y., Adel, R. & Kuruoglu, E.E. Graph Normalized-LMP Algorithm for Signal Estimation Under Impulsive Noise. J Sign Process Syst 95, 25–36 (2023). https://doi.org/10.1007/s11265-022-01802-2

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  • DOI: https://doi.org/10.1007/s11265-022-01802-2

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