1887
Volume 49, Issue 4
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

[

Noise reduction is important for signal analysis. In this paper, we propose a hybrid denoising method based on thresholding and data-driven signal decomposition. The principle of this method is to reconstruct the signal with previously thresholded intrinsic mode functions (IMFs). Empirical mode decomposition (EMD) based methods decompose a signal into a sum of oscillatory components, while variational mode decomposition (VMD) generates an ensemble of modes with their respective centre frequencies, which enables VMD to further decrease redundant modes and keep less residual noise in the modes. To illustrate its superiority, we compare VMD with EMD as well as its derivations, such as ensemble EMD (EEMD), complete EEMD (CEEMD), improved CEEMD (ICEEMD) using synthetic signals and field seismic traces. Compared with EMD and its derivations, VMD has a solid mathematical foundation and is less sensitive to noise, while both make it more suitable for non-stationary seismic signal decomposition. The determination of mode number is key for successful denoising. We develop an empirical equation, which is based on the detrended fluctuation analysis (DFA), to adaptively determine the number of IMFs for signal reconstruction. Then, a scaling exponent obtained by DFA is used as a threshold to distinguish random noise and signal between IMFs and the reconstruction residual. The proposed thresholded VMD denoising method shows excellent performance on both synthetic and field data applications.

,

In this paper, we propose an adaptive denoising method based on data-driven signal mode decomposition, where the noise is represented by the residual/last mode. The proposed approach adaptively extracts the noise component depending on the data statistics rather than defining a fixed priori threshold.

]
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2018-08-01
2026-01-21

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References

  1. Bekara M. van der Baan M. 2009 Random and coherent noise attenuation by empirical mode decomposition: Geophysics 74 V89 V98 10.1190/1.3157244
    https://doi.org/10.1190/1.3157244 [Google Scholar]
  2. Berthouze L. Farmer S. F. 2012 Adaptive time-varying detrended fluctuation analysis: Journal of Neuroscience Methods 209 178 188 10.1016/j.jneumeth.2012.05.030
    https://doi.org/10.1016/j.jneumeth.2012.05.030 [Google Scholar]
  3. Chen Z. Ivanov P. C. Hu K. Stanley H. E. 2002 Effect of nonstationarities on detrended fluctuation analysis: Physical Review E 65 041107 10.1103/PhysRevE.65.041107
    https://doi.org/10.1103/PhysRevE.65.041107 [Google Scholar]
  4. Chkeir, A., Marque, C., Terrien, J., and Karlsson, B., 2010, Denoising electrohysterogram via empirical mode decomposition: PSSNIP Biosignals and Biorobotics Conference, 4–6 January 2010, Vitoria, Brazil, 32–35.
  5. Colominas M. A. Schlotthauer G. Torres M. E. 2014 Improved complete ensemble EMD: A suitable tool for biomedical signal processing: Biomedical Signal Processing and Control 14 19 29 10.1016/j.bspc.2014.06.009
    https://doi.org/10.1016/j.bspc.2014.06.009 [Google Scholar]
  6. Donoho D. L. Johnstone J. M. 1994 Ideal spatial adaptation by wavelet shrinkage: Biometrika 81 425 455 10.1093/biomet/81.3.425
    https://doi.org/10.1093/biomet/81.3.425 [Google Scholar]
  7. Dragomiretskiy K. Zosso D. 2014 Variational mode decomposition: IEEE Transactions on Signal Processing 62 531 544 10.1109/TSP.2013.2288675
    https://doi.org/10.1109/TSP.2013.2288675 [Google Scholar]
  8. Fang Y. M. Feng H. L. Li J. Li G. H. 2011 Stress wave signal denoising using ensemble empirical mode decomposition and an instantaneous half period model: Sensors 11 7554 7567 10.3390/s110807554
    https://doi.org/10.3390/s110807554 [Google Scholar]
  9. Gan Y. Sui L. Wu J. Wang B. Zhang Q. Xiao G. 2014 An EMD threshold denoising method for inertial sensors: Measurement 49 34 41 10.1016/j.measurement.2013.11.030
    https://doi.org/10.1016/j.measurement.2013.11.030 [Google Scholar]
  10. Gilles J. 2013 Empirical wavelet transform: IEEE Transactions on Signal Processing 61 3999 4010 10.1109/TSP.2013.2265222
    https://doi.org/10.1109/TSP.2013.2265222 [Google Scholar]
  11. Han J. van der Baan M. 2013 Empirical mode decomposition for seismic time-frequency analysis: Geophysics 78 O9 O19 10.1190/geo2012‑0199.1
    https://doi.org/10.1190/geo2012-0199.1 [Google Scholar]
  12. He, B., and Bai, Y., 2016, Signal-noise separation of sensor signal based on variational mode decomposition: 2016 8th IEEE International Conference on Communication Software and Networks (ICCSN), 132–138.
  13. Hestenes M. R. 1969 Multiplier and gradient methods: Journal of Optimization Theory and Applications 4 303 320 10.1007/BF00927673
    https://doi.org/10.1007/BF00927673 [Google Scholar]
  14. Horvatic D. Stanley H. E. Podobnik B. 2011 Detrended cross-correlation analysis for non-stationary time series with periodic trends: EPL (Europhysics Letters) 94 18007 10.1209/0295‑5075/94/18007
    https://doi.org/10.1209/0295-5075/94/18007 [Google Scholar]
  15. Hu K. Ivanov P. C. Chen Z. Carpena P. Stanley H. E. 2001 Effect of trends on detrended fluctuation analysis: Physical Review E 64 011114 10.1103/PhysRevE.64.011114
    https://doi.org/10.1103/PhysRevE.64.011114 [Google Scholar]
  16. Huang N. E. Shen Z. Long S. R. Wu M. C. Shih H. H. Zheng Q. Liu H. H. 1998 The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 454 903 995
    [Google Scholar]
  17. Kabir M. A. Shahnaz C. 2012 Denoising of ECG signals based on noise reduction algorithms in EMD and wavelet domains: Biomedical Signal Processing and Control 7 481 489 10.1016/j.bspc.2011.11.003
    https://doi.org/10.1016/j.bspc.2011.11.003 [Google Scholar]
  18. Lahmiri, S., and Boukadoum, M., 2014, Biomedical image denoising using variational mode decomposition: IEEE Biomedical Circuits and Systems Conference (BioCAS) Proceedings, 340–343.
  19. Li C. Zhan L. Shen L. 2015 Friction signal denoising using complete ensemble EMD with adaptive noise and mutual information: Entropy 17 5965 5979 10.3390/e17095965
    https://doi.org/10.3390/e17095965 [Google Scholar]
  20. Li F. Zhang B. Zhai R. Zhou H. Marfurt K. J. 2017 Depositional sequence characterization based on seismic variational mode decomposition: Interpretation 5 SE97 SE106 10.1190/INT‑2016‑0069.1
    https://doi.org/10.1190/INT-2016-0069.1 [Google Scholar]
  21. Liu, W., Cao, S., and He, Y., 2015, Ground roll attenuation using variational mode decomposition: 77th Annual International Conference and Exhibition, EAGE, Extended Abstracts, Th P6 06.
  22. Liu W. Cao S. Chen Y. 2016 a Applications of variational mode decomposition in seismic time-frequency analysis: Geophysics 81 V365 V378 10.1190/geo2015‑0489.1
    https://doi.org/10.1190/geo2015-0489.1 [Google Scholar]
  23. Liu Y. Yang G. Li M. Yin H. 2016 b Variational mode decomposition denoising combined the detrended fluctuation analysis: Signal Processing 125 349 364 10.1016/j.sigpro.2016.02.011
    https://doi.org/10.1016/j.sigpro.2016.02.011 [Google Scholar]
  24. Mert A. Akan A. 2014 Detrended fluctuation thresholding for empirical mode decomposition based denoising: Digital Signal Processing 32 48 56 10.1016/j.dsp.2014.06.006
    https://doi.org/10.1016/j.dsp.2014.06.006 [Google Scholar]
  25. Peng C. K. Buldyrev S. V. Havlin S. Simons M. Stanley H. E. Goldberger A. L. 1994 Mosaic organization of DNA nucleotides: Physical Review 49 1685 1689
    [Google Scholar]
  26. Schuster, G. T., 2007, Basics of seismic wave theory: notes for the lecture courses: University of Utah.
  27. Torres, M. E., Colominas, M. A., Schlotthauer, G., and Flandrin, P., 2011, A complete ensemble empirical mode decomposition with adaptive noise: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 4144–4147.
  28. Verma S. Guo S. Ha T. Marfurt K. J. 2016 Highly aliased groundroll suppression using a 3D multiwindow KL filter: application to a legacy Mississippi Lime survey: Geophysics 81 V79 V88 10.1190/geo2014‑0442.1
    https://doi.org/10.1190/geo2014-0442.1 [Google Scholar]
  29. Wu Z. Huang N. E. 2009 Ensemble empirical mode decomposition: a noise-assisted data analysis method: Advances in Adaptive Data Analysis 1 1 41 10.1142/S1793536909000047
    https://doi.org/10.1142/S1793536909000047 [Google Scholar]
/content/journals/10.1071/EG17004
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Seismic signal denoising using thresholded variational mode decomposition
Exploration Geophysics 49, 450 (2018); https://doi.org/10.1071/EG17004
/content/journals/10.1071/EG17004
/content/journals/10.1071/EG17004
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  • Article Type: Research Article
Keyword(s): adaptive filtering; detrended fluctuation analysis (DFA); empirical mode decomposition (EMD); seismic signal denoising; variational mode decomposition (VMD)

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