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A Mixed-Mode Decomposition Denoising Algorithm Based on Variance Estimation

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Abstract

Conventional denoising algorithms have poor effect when dealing with nonlinear or non-stationary signals, and it is also difficult to select appropriate threshold parameters for denoising. This paper proposes a mixed-mode decomposition denoising algorithm based on variance estimation, which combines empirical mode decomposition (EMD) and variational mode decomposition (VMD). The algorithm performs a single EMD decomposition on an original signal, calculates an energy sequence of the first-order intrinsic mode functions, and estimates a noise variance in the original signal according to the noise energy attenuation characteristics, and the estimated variance value serves as the threshold for VMD denoising completion. Nonlinear signals and actual speech signals are selected to carry out experimental comparisons of various denoising algorithms. The results show that the mixed-mode decomposition denoising algorithm is not constrained by the selection of threshold parameters, and its denoising performance is better than that of conventional mode decomposition threshold denoising algorithms.

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References

  1. B. Aka, C. Cpg, A. Ht, et al, Adaptive sensitive frequency band selection for VMD to identify defective components of an axial piston pump. Chin. J. Aeronaut. (2021)

  2. A. Boudraa, J.C. Cexus, Denoising via empirical mode decomposition, in Proceedings of IEEE Isccsp (2006)

  3. A.O. Boudraa, J.C. Cexus, EMD-based signal filtering. IEEE Trans. Instrum. Meas. 56(6), 2196–2202 (2007)

    Article  Google Scholar 

  4. K. Dragomiretskiy, D. Zosso, Variational mode decomposition. IEEE Trans Signal Process 62(3), 531–544 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. D.L. Donoho, De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41(3), 613–627 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. P. Flandrin, G. Rilling, P. Goncalves, Empirical mode decomposition as a filter bank. IEEE Signal Process. Lett. 11(2), 112–114 (2004)

    Article  Google Scholar 

  7. N.E. Huang, S.S.P. Shen, Hilbert-Huang Transform and Its Applications (World Scientific, 2005)

  8. X. Hu, S. Peng, W.L. Hwang, E.M.D. Revisited, A new understanding of the envelope and resolving the mode-mixing problem in AM-FM signals. IEEE Trans. Signal Process. 60(3), 1075–1086 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. N.E. Huang, Z. Wu, A review on Hilbert-Huang transform: method and its applications to geophysical studies. Rev. Geophys. 46(2), 6 (2008)

    Article  MathSciNet  Google Scholar 

  10. N.E. Huang, A study of the characteristics of white noise using the empirical mode decomposition method. Proc. Math. Phys. Eng. Sci. 460(2046), 1597–1611 (2004)

    Article  MATH  Google Scholar 

  11. Y. Kopsinis, S. Mclaughlin, Development of EMD-based denoising methods inspired by wavelet thresholding. IEEE Trans. Signal Process. 57(4), 1351–1362 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Li, L. Li, H.M. Tai, Variable step size LMS algorithm based on function control. Circuits Syst. Signal Process. 32(6), 3121–3130 (2013)

    Article  MathSciNet  Google Scholar 

  13. H. Li, X. Wang, L. Chen et al., Denoising and R-peak detection of electrocardiogram signal based on EMD and improved approximate envelope. Circuits Syst. Signal Process. 33(4), 1261–1276 (2014)

    Article  Google Scholar 

  14. M. Li, X. Wu, X. Liu, An improved EMD method for time-frequency feature extraction of telemetry vibration signal based on multi-scale median filtering. Circuits Syst. Signal Process. 34(3), 815–830 (2015)

    Article  Google Scholar 

  15. J.X. Lv, G.Q. Liu, Magneto-acousto-electrical NDT and improved EMD denoising algorithm. Trans. China Electrotech. Soc. 1(5), 1–9 (2018)

    Google Scholar 

  16. S. Mckinley, M. Levine, Cubic Spline Interpolation, Methods of Shape-Preserving Spline Approximation, pp. 37–59 (2011)

  17. Y.M. Ni, N.H. Yang, Speech denoising application based on Hilbert-Huang transform. Comput. Simul. 28(4), 408–412 (2011)

    Google Scholar 

  18. H.E. Peng-Fei, L.I. Bo-Quan, X.U. Xiao-Jing, Denoise study on improved empirical mode decomposition based on modified threshold. Inf. Technol. 1, 50–52 (2015)

    Google Scholar 

  19. G. Rilling, P. Flandrin, P. Goncalves, On empirical mode decomposition and its algorithms, in IEEEEURASIP Workshop on Non-linear Signal and Image Processing, vol. 10, no. 3, pp. 180–185(1999)

  20. Y.Z. Sun, W. Huang, Y.U. Bo, Adaptive analysis of non-linear signal base on EMD. J. Univ. Electron. Sci. Technol. China 36(1), 24–26 (2007)

    Google Scholar 

  21. R. Wang, S. Sun, X. Guo, D. Yan, EMD threshold denoising algorithm based on variance estimation. Circuits Syst. Signal Process. 37, 5369–5388 (2018)

    Article  MathSciNet  Google Scholar 

  22. S. Zhao, D.L. Jones, S. Khoo et al., New variable step-sizes minimizing mean-square deviation for the LMS-type algorithms. Circuits Syst. Signal Process. 33(7), 2251–2265 (2014)

    Article  Google Scholar 

  23. Q. Zhang, H.Y. Xing, Adaptive denoising algorithm based on the variance characteristics of EMD. Tien Tzu Hsueh Pao/Acta Electronica Sinica 43(5), 901–906 (2015)

    MathSciNet  Google Scholar 

  24. J.P. Zhao, D.J. Huang, Mirror extending and circular spline function for empirical mode decomposition method. J. Zhejiang Univ. Sci. 2(3), 247–252 (2001)

    Article  MATH  Google Scholar 

  25. Y. Zhao, C. Li, W. Fu et al., A modified variational mode decomposition method based on envelope nesting and multicriteria evaluation. J. Sound Vib. 468, 115099 (2020)

    Article  Google Scholar 

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Authors and Affiliations

  1. Suzhou Power Supply Branch Company, State Grid Jiangsu Power Co. Ltd, Suzhou, 215004, China

    Rong Cai, Bo Yang & Xiaofeng Dong

  2. College of Information Science and Engineering, Huaqiao University, Xiamen, 361000, China

    Rongkun Wang & Sigun Sun

  3. NARI Technology Development Co. Ltd, Nanjing, 211106, China

    Feng Xie

  4. Nanjing NR Electric Co. Ltd, Nanjing, 211102, China

    Jianyang Lian

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  1. Rong Cai
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  2. Rongkun Wang
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  4. Bo Yang
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  5. Xiaofeng Dong
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Correspondence to Rongkun Wang.

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Cai, R., Wang, R., Sun, S. et al. A Mixed-Mode Decomposition Denoising Algorithm Based on Variance Estimation. Circuits Syst Signal Process 42, 1011–1033 (2023). https://doi.org/10.1007/s00034-022-02161-w

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  • DOI: https://doi.org/10.1007/s00034-022-02161-w

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