自适应小波阈值去噪方法Adaptive Denoising by Soft-thresholding with Wavelets
刘静,张道明,田华,崔连成
摘要(Abstract)：
针对未知含噪信号的小波去噪理论,提出了一种新的阈值方程,并基于斯坦恩无偏估计(SURE)优化算法和阈值方程寻找最优门限值,以确保去噪后的信号是对未知原信号的最优估计。同时,注意到使用正交小波去噪,容易在信号奇异点处产生Gibbs振荡。为解决该问题,在信号分解和重构时使用了平稳小波变换算法。最后,应用以上方法与基于SURE的正交小波去噪方法对2种含噪信号进行去噪分析,结果令人满意。
关键词(KeyWords)： 小波变换;SURE;自适应算法;信号去噪
基金项目(Foundation):
作者(Author): 刘静,张道明,田华,崔连成
参考文献(References)：
- [1]Albert Boggess,Francis J.Narcowich.A First Course inWavelets with Fourier Analysis[M].Publishing House ofElectronics Industry,2002.
- [2]Mallat S.A Theory for Multi resolution Approximation:the Wavelet Approximation.IEEE Trans.PAMI 11(1989).674 693.
- [3]Mallat S,Hwang W L.Singularity Detection and Processingwith Wavelets[J].IEEE Transaction on InformationTheory,1992,38(2):617 643.
- [4]Donoho D L.De noising by Soft thresholding[J].IEEETransactions on Information Theory,1995,41(3):13 627.
- [5]Donoho D L.Adapting to Unknown Smoothness via WaveletShrinkage[J].Journal of the American Statistical Associa-tion,1995,90:1 200 1 224.
- [6]Coifman R R,Donoho D L.Translation invariant Denois-ing,Wavelets and Statistics[M].New York:Springer Ver-lag,1995.125 150.
- [7]Goodman T N T,Lee S L.Wavelets of Multiplicity[J].Trans.of American Math Society,1994,342(1):307 324.
- [8]Charles C Stein.Estimation of the Mean of a MultivariateNormal Distribution[J].Annals of Stattistics.1981,9(6):1 135 1 151.
- [9]李士心,刘鲁源,杨晔,等.基于平稳小波变换的陀螺仪信号去噪方法.天津大学学报,2003,36(2):165 168.
- [10]Li Shi Xin.Gyro Signal Denoising Using Stationary Wave-let Transform.Journal of Tianjin University,2003,36(2):165 168.
- [11]Donoho D L,Johnstone I M.Threshold Selection for Wave-let Shrinkage of Noisy Data.Proceedings of the 16th Annu-al International Conference of the IEEE 3 6 Nov.1994,1:A24 A25.
- [12]Xiao Ping Zhang,Desai M D.Adaptive Denoising Based onSURE Risk.Signal Processing Letters,IEEE 1998,5(10):265 267.
- [13]陈峰,成新民.基于小波变换的信号去噪技术及实现[J].现代电子技术,2005,28(3):11 13.