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基于二進(jìn)小波變換的信號(hào)去噪

張宗平,  劉貴忠,  董恩清

張宗平, 劉貴忠, 董恩清. 基于二進(jìn)小波變換的信號(hào)去噪[J]. 電子與信息學(xué)報(bào), 2001, 23(11): 1083-1090.
引用本文: 張宗平, 劉貴忠, 董恩清. 基于二進(jìn)小波變換的信號(hào)去噪[J]. 電子與信息學(xué)報(bào), 2001, 23(11): 1083-1090.
Zhang Zongping, Liu Guizhong, Dong Enqing. DENOISING VIA DYADIC WAVELET TRANSFORM[J]. Journal of Electronics & Information Technology, 2001, 23(11): 1083-1090.
Citation: Zhang Zongping, Liu Guizhong, Dong Enqing. DENOISING VIA DYADIC WAVELET TRANSFORM[J]. Journal of Electronics & Information Technology, 2001, 23(11): 1083-1090.

基于二進(jìn)小波變換的信號(hào)去噪

DENOISING VIA DYADIC WAVELET TRANSFORM

  • 摘要: 由于信號(hào)在二進(jìn)小波變換空間的表示是冗余的,同小波級(jí)數(shù)相比,基于二進(jìn)小波變換的信號(hào)重建效果對(duì)信號(hào)的小波變換系數(shù)的誤差靈敏度將會(huì)下降,因此可以期望在相同的誤判概率下基于二進(jìn)小波變換的去噪效果將優(yōu)于基于小波級(jí)數(shù)變換的去噪效果?；谶@個(gè)思想,該文將已有的基于小波級(jí)數(shù)的去噪方法推廣到基于二進(jìn)小波變換去噪上去,比較了基于二進(jìn)小波去噪同基于小波級(jí)數(shù)去噪的效果。數(shù)值實(shí)驗(yàn)表明,對(duì)于各種檢驗(yàn)信號(hào),較之小波級(jí)數(shù)去噪,二進(jìn)小波變換去噪效果有明顯改善。
    Abstract: Signals representation in dyadic wavelet domain is very redundant. Compared with wavelet series reconstruction, signals dyadic wavelet reconstruction dependency on the individual coefficients in transform domain will be decreased. Therefore, with the same error decision probability, the better reconstruction can be expected. Based on this idea, this paper extends the existing wavelet-based denoising approaches to the dyadic wavelet-based denoising. Numerical experiments show that the dyadic wavelet-based denoising can significantly improve the signal-to-noise rate (SNR).
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  • D.L. Donoho, I. M. Johnstone, Ideal spatial adaptation by wavelet shrinkage, Biometrika 1994,81 (2), 425-455.[2]D.L. Donoho, I. M. Johnstone, Wavelets and optimal nonparametric function estimation, Tech-nical Report. Dept. of Statistics, U. C. Berkeley, 1990.[3]S. Mallat, A theory for multiresolution decomposition: the wavelet representation, IEEE Trans.on Pattn. Anal. Mach. Intell., 1989, 11(7), 674-693.[4]S. Mallat, S. Zhong, Characterization of signals from multiscale edges, IEEE Trans. on Pattn.Anal. Mach. Intell., 1992, 14(7), 709-732.[5]S. Mallat, W. L. Hwang, Singularity detection and processing with wavelets, Technical ReportNo. 549, Robotics Report, No. 245, New York University, Courant Institute of MathematicalSciences. March. [6]S[J].Saitoh, Theory of reproducing kernels and its applications, Longman Scientific TechnicalPress.1991,1988:1-15[6]D.L. Donoho, De-noising via soft-thresholding, IEEE Trans. on Info. Theo., 1992, 41(3), 613627.[7]F. Abramovich, et al., Wavelet thresholding via a Bayesian approach. J. R. Statistc. Soc., 1998,B60, Part 4, 725-749.
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出版歷程
  • 收稿日期:  1999-11-30
  • 修回日期:  2000-09-14
  • 刊出日期:  2001-11-19

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