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Signal Denoising Based on the Adaptive Shrinkage Function and Neighborhood characteristics

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Abstract

In order to provide more accurate and better denoising results, a novel denoising method based on an adaptive shrinkage function and neighborhood characteristics is proposed in this paper for one-dimensional signal. According to the number of large coefficients in neighborhoods of small coefficients, the small coefficients are shrunk term by term so as to preserve more useful information in detail coefficients. Several denoising experiments are performed in this paper. The optimal neighborhood size is selected to perform the more effective signal denoising. The visual perception of denoising signals shows that the proposed method can preserve information of original signal very well. Numerical results indicate that the proposed method is very effective and superior to hard thresholding, NeighShrink scheme and neighboring coefficients preservation scheme for almost all noise levels.

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References

  1. M.J. Alam, D.O’. Shaughnessy, Perceptual improvement of Wiener filtering employing a post-filter. Digital Signal Process. 21, 54–65 (2011)

    Article  Google Scholar 

  2. S. Beheshti, M. Hashemi, X.P. Zhang, N. Nikvand, Noise invalidation denoising. IEEE Trans. Signal Process. 58(12), 6007–6016 (2010)

    Article  MathSciNet  Google Scholar 

  3. R.R. Coifman, D.L. Donoho, Translation invariant de-noising, in Wavelets and Statistics, ed. by A. Antoniadis, G. Oppenheim. Springer Lecture Notes in Statistics, vol. 103 (Springer-Verlag, New York, 1995), pp. 125–150

  4. G.Y. Chen, T.D. Bui, Multiwavelets denoising using neighboring coefficients. IEEE Signal Process. Lett. 10(7), 211–214 (2003)

    Article  Google Scholar 

  5. T.T. Cai, B.W. Silverman, Incorporating information on neighboring coefficients into wavelet estimation. Sankhya 63(2), 127–148 (2001)

    MATH  MathSciNet  Google Scholar 

  6. X. Chen, H. Sun, C.Z. Deng, Image denoising algorithm using adaptive shrinkage threshold based on shearlet transform, in Fourth International Conference on Frontiers of Computer Science and Technology, IEEE Computer society, pp. 254–257 (2009)

  7. B. Droge, Minimax regret comparison of hard and soft thresholding for estimating a bounded normal mean. Stat. Probab. Lett. 76, 83–92 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. D.L. Dohono, De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41(3), 613–627 (1995)

    Article  Google Scholar 

  9. D.L. Dohono, I.M. Johnstone, Adapting to unknown smoothness via wavelet shrinkage. J. Am. Stat. Assoc. 90, 1200–1224 (1995)

    Article  Google Scholar 

  10. K. Deng, L. Zhang, M.K. Luo, A denoising algorithm for noisy chaotic signals based on the higher order threshold function in wavelet-packet. Chin. Phys. Lett. 28(2), 020502 (2011)

    Article  Google Scholar 

  11. Y.M. Fang, H.L. Feng, J. Li, G.H. Li, Stress wave signal denoising using ensemble empirical mode decomposition and an instantaneous half period model. Sensors 11, 7554–7567 (2011)

    Article  Google Scholar 

  12. B. Goossens, A. Pižurica, W. Philips, Removal of correlated noise by modeling the signal of interest in the wavelet domain. IEEE Trans. Image Process. 18(6), 1153–1165 (2009)

    Article  MathSciNet  Google Scholar 

  13. D. Giaouris, J.W. Finch, Denoising using wavelets on electric drive applications. Electric Power Syst. Res. 78, 559–565 (2008)

    Article  Google Scholar 

  14. S. Ghael, A. Sayeed, R. Baraniuk, Improved wavelet denoising via empirical wiener filtering. in Proceedings of SPIE, vol. 3169, San Diego, pp. 389–399 (1997)

  15. N.E. Huang, Z. Shen, S.R. Long et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. 454, 903–995 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  16. M. Kazubek, Wavelet domain image denoising by thresholding and Wiener filtering. IEEE Signal Process. Lett. 10(11), 324–326 (2003)

    Article  Google Scholar 

  17. M. Raphan, E.P. Simoncelli, Optimal denoising in redundant representations. IEEE Trans. Image Process. 17(8), 1342–1352 (2008)

    Article  MathSciNet  Google Scholar 

  18. W. Shengqian, Z. Yuanhua, Z. Daowen, Adaptive shrinkage de-noising using neighborhood characteristic. Electron. Lett. 38(17), 502–503 (2002)

    Article  Google Scholar 

  19. L. Sendur, I.W. Selesnick, Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Trans. Signal Process. 50(11), 2744–2756 (2002)

    Article  Google Scholar 

  20. M.B. Velascoa, B. Wengb, K.E. Barnerc, ECG signal denoising and baselinewander correction based on the empirical mode decomposition. Comput. Biol. Med. 38, 1–13 (2008)

    Article  Google Scholar 

  21. S.F. Yin, L.C. Cao, Y.S. Ling, G.F. Jin, Image denoising with anisotropic bivariate shrinkage. Signal Process. 91, 2078–2090 (2011)

    Article  MATH  Google Scholar 

  22. Y. Yang, Y. Wei, Neighboring coefficients preservation for signal denoising. Circuits Syst. Signal Process. 31(2), 827–832 (2012)

    Article  MathSciNet  Google Scholar 

  23. Y. Yang, Y. Wei, Random interpolation average for signal denoising. Signal Process. IET 4(6), 708–719 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This project was supported by the National Natural Science Foundation of China (Grant No. 51207128) and Research Foundation of Education Bureau of Shaanxi Province, (Grant No. 00K1310). We would like to express our appreciation to the anonymous referees and the Associate Editor for their valuable comments and suggestions.

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Correspondence to Yusen Wei.

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Yang, Y., Wei, Y. & Yang, M. Signal Denoising Based on the Adaptive Shrinkage Function and Neighborhood characteristics. Circuits Syst Signal Process 33, 3921–3930 (2014). https://doi.org/10.1007/s00034-014-9834-1

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  • DOI: https://doi.org/10.1007/s00034-014-9834-1

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