小波域中用多尺度滤波器提取探地雷达信号
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摘要
针对实际中观测到的探地雷达信号时常会被噪声污染的情况,根据小波分析和分形理论在多尺度分析和自相似本质上的一致性,将多尺度维纳滤波器理论引入探地雷达信号处理中,提出基于双正交小波变换与维纳滤波的多尺度滤波算法,提取探地雷达1/f类分形有用信号。首先,利用双正交小波变换将带有加性白噪的探地雷达信号分解成多尺度的子带信号,通过小波变换对1/f类分形信号的白化作用,消除了1/f类分形信号的非平稳性、自相似性和长程相关性。然后,在多尺度小波域中利用维纳滤波,实现噪声和有用信号的分离,估计出各子带中探地雷达1/f类分形有用信号。最后,利用双正交小波的精确重构性,恢复加性白噪背景下的探地雷达1/f类分形信号。实验表明,该滤波器能有效提取探地雷达有用信号,显著地提高信噪比。
In terms of the identical properties of the wavelet analysis and fractal theory in multi-scale analysis and self similarity, the authors introduce the theory of multi-scale wiener filter into the treatment of ground penetrating radar signals,extract available 1/f fractal signal from ground penetrating radar based on biorthogonal wavelet transformation and calculation of multi-scale wiener filter.First,the signal with white noise is transformed into multi-scale subsystems through biorthogonal wavelet transformation.Unsteadiness,self-similarity,long-range correlation of 1/f fractal signal can be eliminated through whitening activity.Then,the Wiener filter can be applied to estimate the available signal from each sub-band.Finally,the 1/f fractional signal interfered by white noise is resumed through reconstruction of biorthogonal wavelet.The simulation experiment shows the wiener filter can extract signal from ground penetrating radar effectively,and improve signal to noise ratio remarkably.
In terms of the identical properties of the wavelet analysis and fractal theory in multi-scale analysis and self similarity, the authors introduce the theory of multi-scale wiener filter into the treatment of ground penetrating radar signals,extract available 1/f fractal signal from ground penetrating radar based on biorthogonal wavelet transformation and calculation of multi-scale wiener filter.First,the signal with white noise is transformed into multi-scale subsystems through biorthogonal wavelet transformation.Unsteadiness,self-similarity,long-range correlation of 1/f fractal signal can be eliminated through whitening activity.Then,the Wiener filter can be applied to estimate the available signal from each sub-band.Finally,the 1/f fractional signal interfered by white noise is resumed through reconstruction of biorthogonal wavelet.The simulation experiment shows the wiener filter can extract signal from ground penetrating radar effectively,and improve signal to noise ratio remarkably.
引文
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[2]Scholz C H,Aviles C A.The fractal geometry of faults and faulting[J].5th Sympon Earth quake Source Mechanisms,1986:147-156.
[3]刘刚,胡远来,贾?.随机分形插值法在地震数据处理中的应用[J].物探与化探计算技术,2002,24(4):304-308.
[4]B.B.Mandellbrot,J.W.Van Ness.Fractional Brownian motion,Frac-tional motion,and Fractional noises and applications[J].SLAMRev,1968,10(4):422-437.
[5]P.Frandrin.Wavelet analysis and synthesis of fractional Brownian mo-tions[J].IEEE Trans.Information theory,1992,38(2):910-917.
[6]G.W.Wornell,A.V.Oppenheim.Estimation of fractal signals fromnoise measurements using wavelets[J].IEEE Trans.Signal Process-ing,1992,40(3):611-623.
[7]G.W.Wornell.Wavelet-based represents for the 1/f family of fractalprocess[J].Proc IEEE,1993,81:1 428-1 450.
[8]B.S.Chen,G.W.Lin.Multiscale Wiener filter for the restoration offractal signals:Wavelet bank approach[J].IEEE Trans.Signal Pro-cessing,1994,42(11):2 972-2 982.
[9]B.S.Chen,W.S.Hou.Deconvoluation filter bank approach[J].IEEETrans.Signal Processing,1997,45:1 395-1 364.
[10]Cao Kunyong,Yu Shenglin.Restoration of noisy1/f family fractal sig-nal based on Haar wavelets and Wiener filter[J].Journal of Electron-ic Science and Technology of China,2003,1(1):69-73.
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