基于核函数主分量的维纳滤波方法研究
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摘要
针对强随机噪声地震资料背景下经典维纳滤波方法在信号的保幅及高维数据空间求解过程中产生病态矩阵的问题,提出利用核函数主分量维纳滤波压制强地震勘探随机噪声.首先利用线性核函数将地震信号映射到特征空间,再通过主分量分析方法提取地震数据主分量进行数据降维,并得到核主分量维纳滤波因子,从而进行核主分量维纳滤波(K-WPC).正演仿真及对实际地震资料处理表明,该方法对随机噪声有较好的压制作用,保幅效果也令人满意.
Focusing on the deficiencies in keeping amplitude of signal and generating ill-conditioned matrix when determining the solution of high-dimensional data space by the classical Wiener filtering,this paper proposed to utilize kernel-principal-component Wiener filter(K-WPC) to process seismic data disturbed by the strong random noise.The method tansforms the seismic data to the feature space by kernel function firstly,and reduces the dimension of the transformed seismic data by principal component analysis.The filtering factors of K-WPC are then solved based on kernel matrix to execute K-WPC.The result of the simulation experiments and the application in the practical seismic data processing indicate that it can suppress the random noise and preserve the amplitude of the signal satisfactorily.
Focusing on the deficiencies in keeping amplitude of signal and generating ill-conditioned matrix when determining the solution of high-dimensional data space by the classical Wiener filtering,this paper proposed to utilize kernel-principal-component Wiener filter(K-WPC) to process seismic data disturbed by the strong random noise.The method tansforms the seismic data to the feature space by kernel function firstly,and reduces the dimension of the transformed seismic data by principal component analysis.The filtering factors of K-WPC are then solved based on kernel matrix to execute K-WPC.The result of the simulation experiments and the application in the practical seismic data processing indicate that it can suppress the random noise and preserve the amplitude of the signal satisfactorily.
引文
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[14] 丛瑜,肖怀铁,付强.基于核主分量分析的高分辨雷达目标特征提取与识别.电光与控制,2008,15(2) :31～38 Cong Y,Xiao H T,Fu Q.Target feature extraction and recognition for high-range recognition radar based on the KPCA method.Electronics Optics & Control (in Chinese) , 2008,18(2) :31～38
[15] M(u|¨)ller K-R,Mika S,R(a|¨)tsch G,Tsuda K,Sch(o|¨)lkopf B.An introduction to kernel-based learning algorithms.IEEE Trans.Neural Networks,2001,12:181 ～ 201
[16] Sch(o|¨)lkopf B,SmolaAJ,M(u|¨)ller K-R.Nonlinear component analysis as a kernel eigen value problem.Neural Comput,1998,10:1299 ～ 1319
[17] Zhang Z J,Lin Y H,Liu E R.Large static correction using a hybrid optimization method in complex terrain:some experience learnt from China.Journal of Seismic Exploration,2005,13(4) :337 ～ 352
[18] Li Y,Yang B J,Bada J,et al.Chaotic system detection of weak seismic signals.Geophys.J.Int.,2009,178:1493 ～ 1522
[2] 胡天跃.地震资料叠前去噪技术的现状与未来.地球物理学进展,2002,17(2) :218～223 Hu T Y.The current situation and future of seismic data prestack noise attenuation techniques.Progress in Geophysics (in Chinese) ,2002 ,17(2) :218～223
[3] 崔若飞,王 辉.多项式拟合技术在煤田地震勘探中的应 用.地球物理学进展,2000,15(2) :47～54 Cui R F,Wang H.Application of polynomial fitting technique on coal seismic surveying.Progress in Geophysics (in Chinese),2000,15(2) :47～54
[4] 董恩清,刘贵忠,张宗平.自适应Kalman滤波反褶积的快速实现方法.地球物理学报,2001,44(2) :255～262 Dong E Q,Liu G Z,Zhang Z P.Fast implementation technique of adaptive Kalman filtering deconvplution via dyadic wavelet transform.ChineseJ.Geophys.(in Chinese),2001,44(2) :255 ～262
[5] Wang Y.Quantifying the effectiveness of stabilized inverse Q filtering.Geophysics,2003,68:337 ～345
[6] 刘沈衡.维纳滤波法在重力资料解释中的应用.有色金属矿产与勘查,1995,4(1) :48～51 Liu S H.Application of the Wiener-filtration to the interpretation of gravity data.Geological Exploration for Non-Ferrous Metals (in Chinese) ,1995 ,4(1) :48 ～ 51
[7] 崔晓杰.维纳滤波的应用研究[硕士论文].西安:长安大学,2006 Cui X J.The application of Wiener filtering[Master s thesis] (in Chinese).Xi'an:Chang An University,2006
[8] Sadasivan P K,Dutt D N.SVD based technique for noise reduction in electroencephalographic signals.Signal Process ,1996,55:179～189
[9] Hyv(a|¨)rinen A,Karhunen J,Oja E.独立成分分析.周宗潭,董国华,徐昕等译.北京:电子工业出版社,2007 Hyv(a|¨)rinen A,Karhunen J,Oja E.Independent Component Analysis.Zhou Z T,Dong G H,Hu D W,translation.Beijing:Publishing House of Electronics Industry,2007
[10] Xu Q S,Liang Y Z.Monte Carlo cross validation.Chemometrics and Intelligent Laboratory Systems,2001,56:1～11
[11] Stordrange L,Libnau F O,Malthe-S(o|¨)renssen D,Kvalheim O M.Feasibility study of NIR for surveillance of a pharmaceutical process,including a study of different preprocessing techniques.Chemometrics,2002,16:529～541
[12] 范羚.独立分量分析及其在图像特征提取和消噪中的应用[硕士论文].合肥:安徽大学,2003 Fang L.Independent component analysis and its applications of image feature extraction and denoising[Master s thesis](in Chinese).Hefei:University of Anhui,2003
[13] 姜晓东.主成分分析法在纳米KF/Al_2O_3催化剂制备中的应用[硕士论文].南京:南京工业大学,2007 Jiang X D.Application of principal component analysis in preparation of Nano-KF/Al_2O_3 Catalyst[Master's thesis] (in Chinese).Nanjing:Nanjing University of Technology,2007
[14] 丛瑜,肖怀铁,付强.基于核主分量分析的高分辨雷达目标特征提取与识别.电光与控制,2008,15(2) :31～38 Cong Y,Xiao H T,Fu Q.Target feature extraction and recognition for high-range recognition radar based on the KPCA method.Electronics Optics & Control (in Chinese) , 2008,18(2) :31～38
[15] M(u|¨)ller K-R,Mika S,R(a|¨)tsch G,Tsuda K,Sch(o|¨)lkopf B.An introduction to kernel-based learning algorithms.IEEE Trans.Neural Networks,2001,12:181 ～ 201
[16] Sch(o|¨)lkopf B,SmolaAJ,M(u|¨)ller K-R.Nonlinear component analysis as a kernel eigen value problem.Neural Comput,1998,10:1299 ～ 1319
[17] Zhang Z J,Lin Y H,Liu E R.Large static correction using a hybrid optimization method in complex terrain:some experience learnt from China.Journal of Seismic Exploration,2005,13(4) :337 ～ 352
[18] Li Y,Yang B J,Bada J,et al.Chaotic system detection of weak seismic signals.Geophys.J.Int.,2009,178:1493 ～ 1522
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