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Design of Time-Vertex Node-Variant Graph Filters

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Abstract

This paper addresses the node-variant graph filter on the joint time-vertex domain. An efficient algorithm is proposed to design the filter that can provide a good approximation to desirable linear operators for the time-varying signals on graphs. As a case study, the application of the designed filter on the signal denoise is addressed, where the filter is designed to approximate an inverse filtering operator. Numerical experiments conducted on the synthetic and real-world datasets demonstrate that the proposed filter is superior to the polynomial counterpart.

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The data used to support the findings of this study are available in [18, 19].

References

  1. E. Abdel-Raheem, A. Tawfik, F. El-Guibaly, Effects of finite word length in two-channel qmf banks, in 1998 IEEE Symposium on Advances in Digital Filtering and Signal Processing. Symposium Proceedings (Cat. No. 98EX185) (IEEE, 1998), pp. 144–148

  2. D. Chan, L. Rabiner, Analysis of quantization errors in the direct form for finite impulse response digital filters. IEEE Trans. Audio Electroacoust. 21(4), 354–366 (1973)

    Article  Google Scholar 

  3. A. Dal Col, P. Valdivia, F. Petronetto, F. Dias, C.T. Silva, L.G. Nonato, Wavelet-based visual analysis for data exploration. Comput. Sci. Eng. 19(5), 85–91 (2017)

    Article  Google Scholar 

  4. F. Grassi, A. Loukas, N. Perraudin, B. Ricaud, A time-vertex signal processing framework: scalable processing and meaningful representations for time-series on graphs. IEEE Trans. Signal Process. 66(3), 817–829 (2018)

    Article  MathSciNet  Google Scholar 

  5. F. Hua, R. Nassifz, C. Richard, H. Wang, A.H. Sayed, Decentralized clustering for node-variant graph filtering with graph diffusion lms, in 2018 52nd Asilomar Conference on Signals, Systems, and Computers (IEEE, 2018), pp. 1418–1422

  6. E. Isufi, G. Leus, P. Banelli, 2-dimensional finite impulse response graph-temporal filters, in 2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP) (IEEE, 2016), pp. 405–409

  7. E. Isufi, A. Loukas, N. Perraudin, G. Leus, Forecasting time series with Varma recursions on graphs. IEEE Trans. Signal Process. 67(18), 4870–4885 (2019)

    Article  MathSciNet  Google Scholar 

  8. E. Isufi, A. Loukas, A. Simonetto, G. Leus, Autoregressive moving average graph filtering. IEEE Trans. Signal Process. 65(2), 274–288 (2017)

    Article  MathSciNet  Google Scholar 

  9. E. Isufi, A. Loukas, A. Simonetto, G. Leus, Separable autoregressive moving average graph-temporal filters, in 2016 24th European Signal Processing Conference (EUSIPCO) (IEEE, 2016), pp. 200–204

  10. J. Jiang, C. Cheng, Q. Sun, Nonsubsampled graph filter banks: theory and distributed algorithms. IEEE Trans. Signal Process. 67(15), 3938–3953 (2019)

    Article  MathSciNet  Google Scholar 

  11. Y.C. Lim, Y.J. Yu, K.L. Teo, T. Saramaki, Frm-based fir filters with optimum finite word-length performance. IEEE Trans. Signal Process. 55(6), 2914–2924 (2007)

    Article  MathSciNet  Google Scholar 

  12. A. Loukas, D. Foucard, Frequency analysis of time-varying graph signals, in 2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP) (IEEE, 2016), pp. 346–350

  13. A. Loukas, N. Perraudin, Stationary time-vertex signal processing. EURASIP J. Adv. Signal Process. 2019(1), 36 (2019)

    Article  Google Scholar 

  14. A. Loukas, A. Simonetto, G. Leus, Distributed autoregressive moving average graph filters. IEEE Signal Process. Lett. 22(11), 1931–1935 (2015)

    Article  Google Scholar 

  15. 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 

  16. I.C.M. Nobre, P. Frossard, Optimized quantization in distributed graph signal filtering (2019). arXiv:1909.12725

  17. M. Onuki, S. Ono, M. Yamagishi, Y. Tanaka, Graph signal denoising via trilateral filter on graph spectral domain. IEEE Trans. Signal Inf. Process. Netw. 2(2), 137–148 (2016)

    MathSciNet  Google Scholar 

  18. N. Perraudin, J. Paratte, D. Shuman, L. Martin, V. Kalofolias, P. Vandergheynst, D.K. Hammond, Gspbox: a toolbox for signal processing on graphs (2014). arXiv:1408.5781

  19. K. Qiu, X. Mao, X. Shen, X. Wang, T. Li, G. Yuantao, Time-varying graph signal reconstruction. IEEE J. Sel. Top. Signal Process. 11(6), 870–883 (2017)

    Article  Google Scholar 

  20. L.B. Saad, B. Beferull-Lozano, Accurate graph filtering in wireless sensor networks (2020). arXiv:2004.11922

  21. L.B. Saad, B. Beferull-Lozano, E. Isufi, Quantization analysis and robust design for distributed graph filters (2020). arXiv:2004.06692

  22. L.B. Saad, T. Weerasinghe, B. Beferull-Lozano, Topology design to increase network lifetime in wsn for graph filtering in consensus processes, in 2017 25th European Signal Processing Conference (EUSIPCO) (IEEE, 2017), pp. 351–355

  23. A. Sandryhaila, S. Kar, J.M.F. Moura, Finite-time distributed consensus through graph filters, in 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (IEEE, 2014), pp. 1080–1084

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

    Article  MathSciNet  Google Scholar 

  25. A. Sandryhaila, J.M.F. Moura, Discrete signal processing on graphs: graph filters, in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2013), pp. 6163–6166

  26. A. Sandryhaila, J.M.F. Moura, Discrete signal processing on graphs: graph Fourier transform, in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2013), pp. 6167–6170

  27. A. Sandryhaila, J.M.F. Moura, Big data analysis with signal processing on graphs: representation and processing of massive data sets with irregular structure. IEEE Signal Process. Mag. 31(5), 80–90 (2014)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  29. S. Segarra, A.G. Marques, G. Leus, A, Ribeiro, Interpolation of graph signals using shift-invariant graph filters, in 2015 23rd European Signal Processing Conference (EUSIPCO) (IEEE, 2015), pp. 210–214

  30. S. Segarra, A.G. Marques, A. Ribeiro, Optimal graph-filter design and applications to distributed linear network operators. IEEE Trans. Signal Process. 65(15), 4117–4131 (2017)

    Article  MathSciNet  Google Scholar 

  31. 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. IEEE Signal Process. Mag. 30(3), 83–98 (2013)

    Article  Google Scholar 

  32. D.I. Shuman, P. Vandergheynst, D. Kressner, P. Frossard, Distributed signal processing via Chebyshev polynomial approximation. IEEE Trans. Signal Inf. Process. Netw. 4(4), 736–751 (2018)

    MathSciNet  Google Scholar 

  33. P. Siohan, An analysis of coefficient inaccuracy for 2-d fir direct form digital filters. IEEE Trans. Circuits Syst. 37(10), 1308–1313 (1990)

    Article  Google Scholar 

  34. L. Stankovic, D. Mandic, M. Dakovic, M. Brajovic, B. Scalzo, T. Constantinides, Graph signal processing–part I: graphs, graph spectra, and spectral clustering (2019). arXiv:1907.03467

  35. R. Varma, J. Kovačević, Random sampling for bandlimited signals on product graphs, in 2019 13th International conference on Sampling Theory and Applications (SampTA) (IEEE, 2019), pp. 1–5

  36. R.A. Varma, J. Kovacevic, Sampling theory for graph signals on product graphs, in 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP) (IEEE, 2018), pp. 768–772

  37. W. Waheed, D.B.H. Tay, Graph polynomial filter for signal denoising. IET Signal Proc. 12(3), 301–309 (2018)

    Article  Google Scholar 

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (Grant No. 61761011), the Graduate research innovation project of Guilin University of Electronic Technology (Grant No. 2020YCXS018).

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Authors and Affiliations

  1. School of Information and Communication, Guilin University of Electronic Technology, Guilin, 541004, China

    Hairong Feng, Junzheng Jiang & Haitao Wang

  2. School of Life and Environmental Sciences, Guilin University of Electronic Technology, Guilin, 541004, China

    Fang Zhou

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  1. Hairong Feng
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  2. Junzheng Jiang
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  3. Haitao Wang
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Correspondence to Haitao Wang.

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Feng, H., Jiang, J., Wang, H. et al. Design of Time-Vertex Node-Variant Graph Filters. Circuits Syst Signal Process 40, 2036–2049 (2021). https://doi.org/10.1007/s00034-020-01548-x

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  • DOI: https://doi.org/10.1007/s00034-020-01548-x

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