基于主成分分析的经验模态分解消噪方法
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摘要
针对非线性非平稳信号的去噪问题,提出一种基于主成分分析(PCA)的经验模态分解(EMD)消噪方法.该方法根据EMD的分解特性,利用PCA对噪声信号经EMD分解后的内蕴模态函数(IMF)进行去噪处理:首先利用"3σ法则"对第一层IMF进行细节信息提取,并估计每层IMF中所含噪声的能量;然后对IMF进行PCA变换,根据IMF中所含噪声的能量选择合适数目的主成分分量进行重构,以去除IMF中的噪声.为验证本文方法的有效性,进行了数字仿真与实例应用实验.实验结果均表明,所提方法的消噪效果整体上优于Bayesian小波阈值消噪方法和基于模态单元的EMD阈值消噪方法,是一种有效的信号消噪新方法.
In order to solve the problem of nonlinear and nonstationary signal de-noising,a novel de-noising method is proposed by combining the principal component analysis(PCA) and empirical mode decomposition(EMD).The method removes noise of intrinsic mode functions(IMFs) using PCA,after the noisy signal is decomposed by EMD.Firstly,the signal details of the first IMF are extracted by using 3σ criterion,and the noise energy of each level IMF is estimated.Secondly,the PCA is implemented on each IMF,and the part of principle components are selected to reconstruct the IMF according to noise energy of IMFs,then the noise of IMF is removed efficiently.Numerical simulation and real data test were carried out to evaluate the performance of the proposed method.The experimental results showed that the proposed method outperformed the Bayesian wavelet threshold de-noising algorithm and mode cell EMD de-noising algorithm.So it is an effective signal de-noising method.
In order to solve the problem of nonlinear and nonstationary signal de-noising,a novel de-noising method is proposed by combining the principal component analysis(PCA) and empirical mode decomposition(EMD).The method removes noise of intrinsic mode functions(IMFs) using PCA,after the noisy signal is decomposed by EMD.Firstly,the signal details of the first IMF are extracted by using 3σ criterion,and the noise energy of each level IMF is estimated.Secondly,the PCA is implemented on each IMF,and the part of principle components are selected to reconstruct the IMF according to noise energy of IMFs,then the noise of IMF is removed efficiently.Numerical simulation and real data test were carried out to evaluate the performance of the proposed method.The experimental results showed that the proposed method outperformed the Bayesian wavelet threshold de-noising algorithm and mode cell EMD de-noising algorithm.So it is an effective signal de-noising method.
引文
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[18]Flandrin P,Riling G,Goncalves P.Empirical mode decompo-sition as a filter bank[J].IEEE Signal Processing Letters,2004,11(2):112-114.
[2]A Pizurica,W Philips.Estimating the probability of the pres-ence of a signal of interest in multiresolution single and mult-iband image denoising[J].IEEE Transaction on Image Process-ing,2006,15(3):654-665.
[3]J Portilla,V Strela,M J Wainwright,E P Simoncelli.Image de-noising using scale mixtures of gaussians in the wavelet domain[J].IEEE Transaction on Image Processing,2003,12(11):1338-1351.
[4]L Zhang,P Bao,X Wu.Multiscale LMMSE-based image de-noising with optimal wavelet selection[J].IEEE Transaction onCircuits System Video Technology,2005,15(4):469-481.
[5]张华,陈小宏,杨海燕.地震信号去噪的最优小波基选取方法[J].石油地球物理勘探,2011,46(1):70-75.Zhang Hua,Chen Xiaohong,Yang Haiyan.Optimistic waveletbasis selection in seismic signal noise elimination[J].OGP,2011,46(1):70-75.(in Chinese)
[6]Huang N E,Shen Z,Long S R,et al.The empirical mode de-composition and the Hilbert spectrum for nonlinear and nonsta-tionary time series analysis[J].Proceedings of the Royal Soc-iety of London,1998,A454(1971):903-995.
[7]徐晓刚,徐冠雷,王孝通,秦绪佳.经验模态分解及其应用[J].电子学报,2009,37(3):581-585.Xu Xiaogang,Xu Guanlei,Wang Xiaotong,et al.Empiricalmode decomposition and its application[J].Acta ElectronicaSinica,2009,37(3):581-585.(in Chinese)
[8]陈东方,吴先良.采用EMD方法消除瞬态散射回波中的高斯白噪声干扰[J].电子学报,2004,32(3):496-498.Chen Dong-fang,WuXian-liang.Recovery of signal from tran-sient scattered response contaminated by gaussian white noisebased on EMD method[J].Acta Electronica Sinica,2004,32(3):496-498.(in Chinese)
[9]杨向林,严洪,许志,等.基于Hilber-t Huang变换的ECG消噪[J].电子学报,2011,39(4):819-824.Yang Xiang-lin,Yan Hong,Xu Zhi,etc.ECG de-noising basedon Hilber-t Huang transform[J].Acta Eletronica Sinica,2011,39(4):819-824.(in Chinese)
[10]Olufemi A,Vladimir A,Auroop R.Empirical mode decompo-sition technique with conditional mutual information for de-noising operational sensor data[J].IEEE Sensors Journal,2011,11(10):2565-2575.
[11]赵志宏,杨绍普,申永军.一种改进的EMD降噪方法[J].振动与冲击,2009,28(12):35-37.Zhao Zhihong,Yang Shaopu,Shen Yongjun.Improved EMDbased on de-noising method[J].Journal of Vibration andShock,2009,28(12):35-37.(in Chinese)
[12]曲从善,路延镇,谭营.一种改进型经验模态分解及其在信号消噪中的应用[J].自动化学报,2010,36(1):67-73.Qu Congshan,Lu Tingzhen,Tan Ying.A modified empiricalmode decomposition method with applications to signal de-noising[J].Acta Automatica Sinica,2010,36(1):67-73.(inChinese)
[13]Y Kopsinis,S Mclaughli.Development ofEMD-based denois-ing methods inspired by wavelet thresholding[J].IEEE Trans-actions on Signal Processing,2009,57(4):1351-1362.
[14]Zhaohua Wu,Norden E H.A study of the characteristics ofwhite noise using the empirical mode decomposition method[J].Proceedings of the Royal Society of London A8,2004,460(2046):1597-1611.
[15]Lei Zhang,Rastislav L,Wu Xiaolin.PCA-based spatiallyadaptive denoising of CFA images for single-sensor digitalcameras[J].IEEE Transaction on Image Processing,2009,18(4):797-812.
[16]王宏宝.电子测量[M].北京:科学出版社,2005.Wang Hongbao.Electronic Measuring[M].Beijing:SciencePress,2005.(in Chinese)
[17]Johnstone I,Wilverman B.Wavelet threshold estimators fordata with correlated noise[J].Journal of the Royal StatisticalSociety,Series B(Methodological),1997,59(2):319-351.
[18]Flandrin P,Riling G,Goncalves P.Empirical mode decompo-sition as a filter bank[J].IEEE Signal Processing Letters,2004,11(2):112-114.
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