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Distributed Adaptive Thresholding Graph Recursive Least Squares Algorithm

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Abstract

In this paper, we present a novel approach for the reconstruction of sparse graph signals using a distributed adaptive thresholding recursive least squares algorithm. Our proposed scheme leverages signal measurements across multiple time steps to estimate the underlying graph signal. To achieve this, we define a cost function that combines a weighted least squares term and an \(L_0\) norm. The cost function is then minimized using a surrogate minimization scheme and the recursive least squares technique. The resulting algorithm is an adaptive thresholding recursive least squares scheme that effectively recovers sparse graph signals. Additionally, we apply a consensus-based method to enable distributed recovery, and derive recursive updating relations to speed up the algorithm. Our approach offers a significant novelty in the field of graph signal recovery, providing an efficient and accurate solution for reconstructing sparse graph signals. The numerical simulations show the superiority of the proposed algorithm over the other state-of-the-art algorithms from the point of view of the convergence rate and the mean square deviation (MSD) criterion.

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References

  1. F. Afkhaminia, M. Azghani, Sparsity-based direction of arrival estimation in the presence of gain/phase uncertainty. in 2017 25th European Signal Processing Conference (EUSIPCO) (2017), pp. 2616–2619

  2. F. Afkhaminia, M. Azghani, 2d off-grid doa estimation using joint sparsity. IET Radar Sonar Navig. 13(9), 1580–1587 (2019)

    Article  Google Scholar 

  3. M. Azghani, A. Esmaeili, K. Behdin, F. Marvasti, Missing low-rank and sparse decomposition based on smoothed nuclear norm. IEEE Trans. Circuits Syst. Video Technol. 30(6), 1550–1558 (2020)

    Article  Google Scholar 

  4. M. Azghani, P. Kosmas, F. Marvasti, Microwave medical imaging based on sparsity and an iterative method with adaptive thresholding. IEEE Trans. Med. Imaging 34(2), 357–365 (2014)

    Article  Google Scholar 

  5. M. Azghani, F. Marvasti, L2-regularized iterative weighted algorithm for inverse scattering. IEEE Trans. Antennas Propag. 64(6), 2293–2300 (2016)

    Article  Google Scholar 

  6. T. Blumensath, M.E. Davies, Iterative thresholding for sparse approximations. J. Fourier Anal. Appl. 14(5–6), 629–654 (2008)

    Article  MathSciNet  Google Scholar 

  7. S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al., Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)

    Article  Google Scholar 

  8. M. Brajović, I. Stanković, M. Daković, L. Stanković, Reconstruction of sparse graph signals from reduced sets of samples. in 2023 27th International Conference on Information Technology (IT) (IEEE, 2023), pp. 1–5

  9. S. Chen, R. Varma, A. Sandryhaila, J. Kovačević, Discrete signal processing on graphs: sampling theory. IEEE Trans. Signal Process. 63(24), 6510–6523 (2015)

    Article  MathSciNet  Google Scholar 

  10. Y. Chi, J. Jiang, F. Zhou, S. Xu, A distributed algorithm for reconstructing time-varying graph signals. Circuits Syst. Signal Process. 41(6), 3624–3641 (2022)

    Article  Google Scholar 

  11. P. Di Lorenzo, P. Banelli, S. Barbarossa, Optimal sampling strategies for adaptive learning of graph signals. in 2017 25th European Signal Processing Conference (EUSIPCO) (IEEE, 2017), pp. 1684–1688

  12. P. Di Lorenzo, P. Banelli, E. Isufi, S. Barbarossa, G. Leus, Adaptive graph signal processing: algorithms and optimal sampling strategies. IEEE Trans. Signal Process. 66(13), 3584–3598 (2018)

    Article  MathSciNet  Google Scholar 

  13. P. Di Lorenzo, S. Barbarossa, P. Banelli, S. Sardellitti, Adaptive least mean squares estimation of graph signals. IEEE Trans. Signal Inf. Process. Netw. 2(4), 555–568 (2016)

    MathSciNet  Google Scholar 

  14. P. Di Lorenzo, E. Isufi, P. Banelli, S. Barbarossa, G. Leus, Distributed recursive least squares strategies for adaptive reconstruction of graph signals. in 2017 25th European Signal Processing Conference (EUSIPCO) (IEEE, 2017), pp. 2289–2293

  15. E. Isufi, A. Loukas, A. Simonetto, G. Leus, Autoregressive moving average graph filtering. IEEE Trans. Signal Process. 65(2), 274–288 (2016)

    Article  MathSciNet  Google Scholar 

  16. J.R. Khonglah, A. Mukherjee, Kernel-based multilayer graph signal recovery via median truncation of gradient descent. IEEE Trans. Signal Inf. Process. Netw. (2023)

  17. S.K. Narang, A. Ortega, Perfect reconstruction two-channel wavelet filter banks for graph structured data. IEEE Trans. Signal Process. 60(6), 2786–2799 (2012)

    Article  MathSciNet  Google Scholar 

  18. S.K. Narang, A. Ortega, Compact support biorthogonal wavelet filterbanks for arbitrary undirected graphs. IEEE Trans. Signal Process. 61(19), 4673–4685 (2013)

    Article  MathSciNet  Google Scholar 

  19. I. Pesenson, Sampling in paley-wiener spaces on combinatorial graphs. Trans. Am. Math. Soc. 360(10), 5603–5627 (2008)

    Article  MathSciNet  Google Scholar 

  20. D. Romero, V.N. Ioannidis, G.B. Giannakis, Kernel-based reconstruction of space-time functions on dynamic graphs. IEEE J. Select. Top. Signal Process. 11(6), 856–869 (2017)

    Google Scholar 

  21. A. Sandryhaila, J.M. Moura, Discrete signal processing on graphs. IEEE Trans. Signal Process. 61(7), 1644–1656 (2013)

    Article  MathSciNet  Google Scholar 

  22. A. Sandryhaila, J.M. Moura, Big data analysis with signal processing on graphs. IEEE Signal Process. Mag. 31(5), 80–90 (2014)

    Article  Google Scholar 

  23. A. Sandryhaila, J.M. Moura, Discrete signal processing on graphs: frequency analysis. IEEE Trans. Signal Process. 62(12), 3042–3054 (2014)

    Article  MathSciNet  Google Scholar 

  24. A.H. Sayed, Adaptive Filters (Wiley, New York, 2011)

    Google Scholar 

  25. D.I. Shuman, S.K. Narang, P. Frossard, A. Ortega, P. Vandergheynst, The emerging field of signal processing on graphs: extending high-dimensional data analysis to networks and other irregular domains (2012). arXiv preprint arXiv:1211.0053

  26. R. Torkamani, H. Zayyani, M. Korki, Proportionate adaptive graph signal recovery. IEEE Trans. Signal Inf. Process. Netw. (2023)

  27. R. Torkamani, H. Zayyani, F. Marvasti, Joint topology learning and graph signal recovery using variational bayes in non-gaussian noise. IEEE Trans. Circuits Syst. II Express Briefs 69(3), 1887–1891 (2021)

    Google Scholar 

  28. R. Torkamani, H. Zayyani, F. Marvasti, Robust adaptive generalized correntropy-based smoothed graph signal recovery with a kernel width learning (2022). arXiv preprint arXiv:2209.09009

  29. X. Zhu, M. Rabbat, Approximating signals supported on graphs. in 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (IEEE, 2012), pp. 3921–3924

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Authors and Affiliations

  1. Laboratory of Wireless Communication and Signal Processing (WCSP), Faculty of Electrical Engineering, Sahand University of Technology, Tabriz, Iran

    Nafiseh Maleki, Masoumeh Azghani & Nasser Sadeghi

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  1. Nafiseh Maleki
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  2. Masoumeh Azghani
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  3. Nasser Sadeghi
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Correspondence to Masoumeh Azghani.

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Maleki, N., Azghani, M. & Sadeghi, N. Distributed Adaptive Thresholding Graph Recursive Least Squares Algorithm. Circuits Syst Signal Process (2024). https://doi.org/10.1007/s00034-024-02626-0

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