[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content

Advertisement

Springer Nature Link
Log in

Time-Varying Weighted Optimal Empirical Mode Decomposition Using Multiple Sets of Basis Functions

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

Empirical mode decomposition (EMD) is a favorite tool for analyzing nonlinear and non-stationary signals. It decomposes any signal into a finite set of oscillation modes consisting of intrinsic mode functions and a residual function. Superimposing all these modes reconstructs the signal without any information loss. In addition to satisfying the perfect reconstruction property, however, there is no implication about the reconstruction optimality of the EMD. The lack of optimality restricts the signal recovery capability of the EMD in the presence of disturbances. Only a few attempts are made to meet this deficiency. In this paper, we propose a new algorithm named as time-varying weighted EMD. By this algorithm, original signal is reconstructed in the minimum mean-square error sense through the EMD followed by time-varying weightings of the oscillation modes. Determining the time-varying weights for the oscillation modes constitutes the backbone of the algorithm. Aiming to determine the time-varying weights of the oscillation modes; we use multiple sets of basis functions. The effectiveness of the proposed algorithm is demonstrated by computer simulations involving real biomedical signals. Simulation results show that the proposed algorithm exhibits better performance than that of its existing counterparts in terms of lower mean-square error and higher signal-to-error ratio.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. M. Blanco-Velasco, B.W. Weng, K.E. Barner, ECG signal denoising and baseline wander correction based on the empirical mode decomposition. Comput. Biol. Med. 38(1), 1–13 (2008)

    Article  Google Scholar 

  2. D. Camarena-Martinez, M. Valtierra-Rodriguez, C.A. Perez-Ramirez, J.P. Amezquita-Sanchez, R.D. Romero-Troncoso, A. Garcia-Perez, Novel downsampling empirical mode decomposition approach for power quality analysis. IEEE Trans. Ind. Electron. 63(4), 2369–2378 (2016)

    Article  Google Scholar 

  3. N. Chatlani, J.J. Soraghan, EMD-based filtering (EMDF) of low-frequency noise for speech enhancement. IEEE Trans. Audio Speech Lang. Process 20(4), 1158–1166 (2012)

    Article  Google Scholar 

  4. R. Dubey, D. Agrawal, A novel approach for diagnosis of noisy component in rolling bearing using improved empirical mode decomposition, in 2nd International Conference on Computer and Communication Technologies (IC3T), Hyderabad, pp. 479–487 (2016)

  5. Y. Gan, L.F. Sui, J.F. Wu, B. Wang, Q.H. Zhang, G.R. Xiao, An EMD threshold de-noising method for inertial sensors. Measurement 49, 34–41 (2014)

    Article  Google Scholar 

  6. A.L. Goldberger, A.N. Amaral, L. Glass, J.M. Hausdorff, P.C. Ivanov, R.G. Mark, J.E. Mietus, G.B. Moody, C.K. Peng, H.E. Stanley, PhysioBank, physiotoolkit, and physionet–components of a new research resource for complex physiologic signals. Circulation 101(23), e215–e220 (2000)

    Article  Google Scholar 

  7. Y.N. Guo, S.H. Huang, Y.T. Li, G.R. Naik, Edge effect elimination in single-mixture blind source separation. Circuits Syst. Signal Process. 32(5), 2317–2334 (2013)

    Article  MathSciNet  Google Scholar 

  8. Y.N. Guo, G.R. Naik, H. Nguyen, Single channel blind source separation based local mean decomposition for biomedical applications, in 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Osaka, pp. 6812–6815 (2013)

  9. T. Hasan, M.K. Hasan, Suppression of residual noise from speech signals using empirical mode decomposition. IEEE Signal Process. Lett. 16(1–3), 2–5 (2009)

    Article  Google Scholar 

  10. A. Hill, B.G. Stewart, S.C. McMeekin, G. Morison, Partial discharge signal denoising using the empirical mode decomposition. Int. J. Signal Process. 1(2), 268–272 (2013)

    Article  Google Scholar 

  11. N.E. Huang, Z. Shen, S.R. Long, M.L.C. Wu, H.H. Shih, Q.N. Zheng, N.C. Yen, C.C. Tung, H.H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. 454(1971), 903–995 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. K. Khaldi, A.O. Boudraa, A. Bouchikhi, M.T.H. Alouane, Speech enhancement via EMD. EURASIP J. Adv. Signal Process. 1–8 (2008). doi:10.1155/2008/873204

  13. A. Kizilkaya, M.D. Elbi, Different scenarios on denoising of signals in the intrinsic mode function selection framework. IETE J. Res. 62(5), 605–614 (2016)

    Article  Google Scholar 

  14. A. Kizilkaya, A. Ukte, M.D. Elbi, Statistical multirate high-resolution signal reconstruction using the EMD-IT based denoising approach. Radioengineering 24(1), 226–232 (2015)

    Article  Google Scholar 

  15. M.S. Koh, E. Rodriguez-Marek, Speech enhancement of color noise using empirical mode decomposition, in 46th Asilomar Conference on Signals, Systems and Computers (ASILOMAR), Pacific Grove, pp. 1688–1692 (2012)

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

    Google Scholar 

  17. G.J. Li, X.P. Zeng, X.N. Zhou, Y. Zhou, G.J. Liu, X.C. Zhou, Robust suppression of nonstationary power-line interference in electrocardiogram signals. Physiol. Meas. 33(7), 1151–1169 (2012)

    Article  Google Scholar 

  18. Y.P. Liu, Y. Li, H.B. Lin, H.T. Ma, An amplitude-preserved time-frequency peak filtering based on empirical mode decomposition for seismic random noise reduction. IEEE Trans. Geosci. Remote Sens. Lett. 11(5), 896–900 (2014)

    Article  Google Scholar 

  19. Y. Mao, P. Que, Noise suppression and flaw detection of ultrasonic signals via empirical mode decomposition. Russ. J. Nondestr. Test. 43(3), 196–203 (2007)

    Article  Google Scholar 

  20. A. Mert, A. Akan, EEG denoising based on empirical mode decomposition and mutual information, in Proceedings on IFMBE XIII Mediterranean Conference on Medical and Biological Engineering and Computing (MEDICON), Seville, pp. 631–634 (2013)

  21. G.R. Naik, S.E. Selvan, H.T. Nguyen, Single-channel EMG classification with ensemble-empirical-mode-decomposition-based ICA for diagnosing neuromuscular disorders. IEEE Trans. Neural Syst. Rehabil. Eng. 24(7), 734–743 (2016)

    Article  Google Scholar 

  22. O.A. Omitaomu, V.A. Protopopescu, A.R. Ganguly, Empirical mode decomposition technique with conditional mutual information for denoising operational sensor data. IEEE Sens. J. 11(10), 2565–2575 (2011)

    Article  Google Scholar 

  23. T.S. Rao, The fitting of non-stationary time-series models with time-dependent parameters. J. R. Stat. Soc. Ser. B 32(2), 312–322 (1970)

    MathSciNet  MATH  Google Scholar 

  24. G. Rilling, P. Flandrin, P. Gonçalves, On empirical mode decomposition and its algorithms, in IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing (NSIP, Grado, 2003)

    Google Scholar 

  25. S. Shukla, S. Mishra, B. Singh, Power quality event classification under noisy conditions using EMD-based de-noising techniques. IEEE Trans. Ind. Inform. 10(2), 1044–1054 (2014)

    Article  Google Scholar 

  26. G. Strang, Linear Algebra and Its Applications (Brooks/Cole, New Delhi, 2005)

    MATH  Google Scholar 

  27. S.K. Subhani, B. Suresh, V.S. Ghali, Empirical mode decomposition approach for defect detection in non-stationary thermal wave imaging. NDT & E Int. 81, 39–45 (2016)

    Article  Google Scholar 

  28. M. Suchetha, N. Kumaravel, Empirical mode decomposition-based subtraction techniques for 50 Hz interference reduction from electrocardiogram. IETE J. Res. 59(1), 55–62 (2013)

    Article  Google Scholar 

  29. M. Suchetha, N. Kumaravel, Empirical mode decomposition based filtering techniques for power line interference reduction in electrocardiogram using various adaptive structures and subtraction methods. Biomed. Signal Process. Control 8(6), 575–585 (2013)

    Article  Google Scholar 

  30. L. Tan, J. Jiang, Digital Signal Processing-Fundamentals and Applications (Academic Press, San Diego, 2013)

    Google Scholar 

  31. Y.W. Tang, C.C. Tai, C.C. Su, C.Y. Chen, J.F. Chen, A correlated empirical mode decomposition method for partial discharge signal denoising. Meas. Sci. Technol. 21(8), 1–11 (2010). doi:10.1088/0957-0233/21/8/085106

    Article  Google Scholar 

  32. A. Ukte, A. Kizilkaya, M.D. Elbi, An hybrid method for statistical multirate high-resolution signal reconstruction, in 22nd IEEE Signal Processing and Communications Applications Conference (SIU), Trabzon, pp. 1287–1290 (2014)

  33. A. Ukte, A. Kizilkaya, M.D. Elbi, Statistical multirate high-resolution signal reconstruction using the empirical mode decomposition based denoising approach, in 19th International Conference on Applied Electronics (AE), Pilsen, pp. 303–306 (2014)

  34. A. Ukte, A. Kizilkaya, M.D. Elbi, Two empirical methods for improving the performance of statistical multirate high-resolution signal reconstruction. Digital Signal Process. 26(3), 36–49 (2014)

    Article  Google Scholar 

  35. B.W. Weng, K.E. Barner, Optimal and bidirectional optimal empirical mode decomposition, in 32th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Honolulu, pp. iii/1501–iii/1504 (2007)

  36. B.W. Weng, K.E. Barner, Optimal signal reconstruction using the empirical mode decomposition. EURASIP J. Adv. Signal Process. 1–12 (2008). doi:10.1155/2008/845294

  37. L. Zao, R. Coelho, P. Flandrin, Speech enhancement with EMD and hurst-based mode selection. IEEE/ACM Trans. Audio Speech Lang. Process. 22(5), 899–911 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Associate Editor and anonymous reviewers for their valuable comments and suggestions that have greatly helped to improve the manuscript.

Author information

Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Engineering Faculty, Pamukkale University, 20070, Kinikli, Denizli, Turkey

    Aydin Kizilkaya

  2. Department of Electrical and Electronics Engineering, Institute of Science, Pamukkale University, 20070, Kinikli, Denizli, Turkey

    Mehmet D. Elbi

Authors
  1. Aydin Kizilkaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mehmet D. Elbi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aydin Kizilkaya.

Appendix: Description of the Sub-blocks in Matrix \({\varvec{\Delta }}\)

Appendix: Description of the Sub-blocks in Matrix \({\varvec{\Delta }}\)

Sub-blocks in the matrix (23) are described as follows:

$$\begin{aligned} {\varvec{\Delta }}^{\alpha \alpha }= & {} \left[ {{\begin{array}{lll} {{\varvec{\Delta }}_{1,1}^{\alpha \alpha } }&{} \quad \cdots &{} \quad {{\varvec{\Delta }}_{1,N}^{\alpha \alpha } } \\ \vdots &{} \quad \ddots &{} \quad \vdots \\ {{\varvec{\Delta }}_{N,1}^{\alpha \alpha } }&{} \quad \cdots &{} \quad {{\varvec{\Delta }}_{N,N}^{\alpha \alpha } } \\ \end{array} }} \right] , \end{aligned}$$
(24)
$$\begin{aligned} {\varvec{\Delta }}^{\alpha \beta }= & {} \left[ {{\begin{array}{lll} {{\varvec{\Delta }}_{1,N+1}^{\alpha \beta } }&{} \quad \cdots &{} \quad {{\varvec{\Delta }}_{1,M+1}^{\alpha \beta } } \\ \vdots &{} \quad \ddots &{} \quad \vdots \\ {{\varvec{\Delta }}_{N,N+1}^{\alpha \beta } }&{} \quad \cdots &{} \quad {{\varvec{\Delta }}_{N,M+1}^{\alpha \beta } } \\ \end{array} }} \right] , \end{aligned}$$
(25)
$$\begin{aligned} {\varvec{\Delta }}^{\beta \alpha }= & {} \left[ {{\begin{array}{lll} {{\varvec{\Delta }}_{N+1,1}^{\beta \alpha } }&{} \quad \cdots &{} \quad {{\varvec{\Delta }}_{N+1,N}^{\beta \alpha } } \\ \vdots &{} \quad \ddots &{} \quad \vdots \\ {{\varvec{\Delta }}_{M+1,1}^{\beta \alpha } }&{} \quad \cdots &{} \quad {{\varvec{\Delta }}_{M+1,N}^{\beta \alpha } } \\ \end{array} }} \right] , \end{aligned}$$
(26)
$$\begin{aligned} {\varvec{\Delta }}^{\beta \beta }= & {} \left[ {{\begin{array}{lll} {{\varvec{\Delta }}_{N+1,N+1}^{\beta \beta } }&{} \quad \cdots &{} \quad {{\varvec{\Delta }}_{N+1,M+1}^{\beta \beta } } \\ \vdots &{} \quad \ddots &{} \quad \vdots \\ {{\varvec{\Delta }}_{M+1,N+1}^{\beta \beta } }&{} \quad \cdots &{} \quad {{\varvec{\Delta }}_{M+1,M+1}^{\beta \beta } } \\ \end{array} }} \right] , \end{aligned}$$
(27)

each of which is \(N\left( {M-N+1} \right) \times N\left( {M-N+1} \right) \) matrix.

From (12) to (14) and (16) to (18), the entries of matrices defined by (24)–(27) are defined as in the following forms:

$$\begin{aligned} {\varvec{\Delta }}_{l,m}^{\alpha \alpha }= & {} \left[ {{\begin{array}{lll} {\varDelta _{l,0,m,0}^{\alpha \alpha } }&{} \quad \cdots &{} \quad {\varDelta _{l,0,m,M-N}^{\alpha \alpha } } \\ \vdots &{} \quad \ddots &{} \quad \vdots \\ {\varDelta _{l,M-N,m,0}^{\alpha \alpha } }&{} \quad \cdots &{} \quad {\varDelta _{l,M-N,m,M-N}^{\alpha \alpha } } \\ \end{array} }} \right] , \end{aligned}$$
(28)
$$\begin{aligned} {\varvec{\Delta }}_{l,z}^{\alpha \beta }= & {} \left[ {{\begin{array}{lll} {\varDelta _{l,0,z,0}^{\alpha \beta } }&{} \quad \cdots &{} \quad {\Delta _{l,0,z,N-1}^{\alpha \beta } } \\ \vdots &{} \ddots &{} \vdots \\ {\varDelta _{l,M-N,z,0}^{\alpha \beta } }&{} \quad \cdots &{} \quad {\varDelta _{l,M-N,z,N-1}^{\alpha \beta } } \\ \end{array} }} \right] , \end{aligned}$$
(29)
$$\begin{aligned} {\varvec{\Delta }}_{y,m}^{\beta \alpha }= & {} \left[ {{\begin{array}{lll} {\varDelta _{y,0,m,0}^{\beta \alpha } }&{} \quad \cdots &{} \quad {\varDelta _{y,0,m,M-N}^{\beta \alpha } } \\ \vdots &{} \quad \ddots &{} \quad \vdots \\ {\varDelta _{y,N-1,m,0}^{\beta \alpha } }&{} \quad \cdots &{} \quad {\varDelta _{y,N-1,m,M-N}^{\beta \alpha } } \\ \end{array} }} \right] , \end{aligned}$$
(30)
$$\begin{aligned} {\varvec{\Delta }}_{y,z}^{\beta \beta }= & {} \left[ {{\begin{array}{lll} {\varDelta _{y,0,z,0}^{\beta \beta } }&{} \quad \cdots &{} \quad {\varDelta _{y,0,z,N-1}^{\beta \beta } } \\ \vdots &{} \ddots &{} \vdots \\ {\varDelta _{y,N-1,z,0}^{\beta \beta } }&{} \quad \cdots &{} \quad {\varDelta _{y,N-1,z,N-1}^{\beta \beta } } \\ \end{array} }} \right] , \end{aligned}$$
(31)

where \(1\le \left( {l,m} \right) \le N\) and \(N+1\le \left( {y,z} \right) \le M+1\). Matrices in (28)–(31) have a size of \(\left( {M-N+1} \right) \times \left( {M-N+1} \right) \), \(\left( {M-N+1} \right) \times N\), \(N\times \left( {M-N+1} \right) \), and \(N\times N\), respectively.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kizilkaya, A., Elbi, M.D. Time-Varying Weighted Optimal Empirical Mode Decomposition Using Multiple Sets of Basis Functions. Circuits Syst Signal Process 36, 3919–3943 (2017). https://doi.org/10.1007/s00034-017-0501-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-017-0501-1

Keywords

Search

Navigation