消减地震勘探随机噪声:导数算子约束下的维纳滤波
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摘要
为使传统的维纳滤波方法在最小均方准则下的解更准确、稳定,采用正则化思想,提出导数算子约束下的最小均方准则;在这种准则下,推导了维纳滤波因子及其频率响应。通过在不同频段取不同的正则化函数值,控制滤波结果。理论及实际地震勘探资料的分析表明:正则化维纳滤波去噪效果比传统维纳滤波好,且对有效波的损失较小,表明了文中所取正则项的可行性及有效性。最后讨论了通过建立正则化函数关系式,方便地提供正则化函数值以及圆滑振幅谱对改进滤波效果的可能性。
To make the solution of the traditional Wiener filtering method with the least mean square criterion more accurate and stable,we proposed a least mean square criterion with regularization idea based on the derivative operator constrains in this paper.Under this criterion,Wiener filter coefficients and its frequency response were derived.The filter result can be controlled by different regularization function values in different frequencies.The analyses of theoretical and practical seismic data show that this method is better than the traditional Wiener filter in the denoising.And the method can reduce the losing of the energy of effective signal.In view of the foregoing it shows that the regular terms is reasonable and effective.Finally,the expression of the regularization function is built;and its purpose is convenient to compute the regularization function value.And the possibility of improved filtering is discussed by smoothing amplitude spectrum.
To make the solution of the traditional Wiener filtering method with the least mean square criterion more accurate and stable,we proposed a least mean square criterion with regularization idea based on the derivative operator constrains in this paper.Under this criterion,Wiener filter coefficients and its frequency response were derived.The filter result can be controlled by different regularization function values in different frequencies.The analyses of theoretical and practical seismic data show that this method is better than the traditional Wiener filter in the denoising.And the method can reduce the losing of the energy of effective signal.In view of the foregoing it shows that the regular terms is reasonable and effective.Finally,the expression of the regularization function is built;and its purpose is convenient to compute the regularization function value.And the possibility of improved filtering is discussed by smoothing amplitude spectrum.
引文
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[10]Murli A,D’Amore L,De Simone V.The Wiener filter and regularization methods for image restoration problems[C]//Image analysis and processing.Washington D C:IEEE Computer Society,1999:394-399.
[11]Sekko E,Thomas G,Boukrouche A.A disconsola-tion technique using optimal Wiener filtering and regularization[J].Signal Processing,2009,72(2):23-32.
[12]Rugini L,Banelli P,Cacopardi S.A full-rank re-gularization technique for MMSE detection in multiuser CDMA systems[J].IEEE Communications Letters,2005,9(1):34-36.
[13]Feigin M,Sochen N.Anisotropic regularization for inverse problems with application to the Wiener filter with Gaussion and impulse noise[J].Lecture Notes in Computer Science,2009,5567(1):319-330.
[14]杨宝俊,李勤学,唐建人,等.松辽盆地反射地震莫霍面的形态、三瞬处理结果及其地质解释[J].地球物理学报,2003,46(3):398-402.YANG Bao-jun,LI Qin-xue,TANGJian-ren,et al.The form and three-instantaneous information of the seismic reflection Moho in Songliao basin and geological[J].Chinese Journal of Geophysics,2003,46(3):398-402.
[2]杨宝俊,李月,刘晓华,等.改善地震勘探记录的4项技术[J].吉林大学学报:地球科学版,2006,36(5):856-862.YANG Bao-jun,LI Yue,LI U Xiao-hua,et al.Four processing techniques for improving the seismic prospecting records[J].Journal of Jilin University:Earth Science Edition,2006,36(5):856-862.
[3]杨德宽,郑泽继,胡立新,等.对深层地震勘探中随机噪声的一点认识[J].石油物探,2000,39(3):50-61.YANG De-kuan,ZHENG Ze-ji,HU Li-xin,et al.Some cognitions on randomnoise in deep-layer seismic exploration[J].Geophysical Prospecting for Petroleum,2000,39(3):50-61.
[4]何樵登.地震勘探原理和方法[M].北京:地质出版社,1989.HE Qiao-deng.Principles and methods of seismic exploration[M].Beijing:Geological Publishing House,1989.
[5]Vaseghi S V.现代信号处理与噪声降低[M].邱天爽,刘文红,郭莹,等译.北京:电子工业出版社,2007.Vaseghi S V.Advanced digital signal processing and noise reduction[M].Translated by QI U Tian-shuang,LI U Wen-hong,GUO Ying,et al.Beijing:Publishing House of Electronics Industry,2007.
[6]Simon D,Marc M.GSVD-based optimal filter for single and multi-microphone speech enhancement[J].IEEE Transctions on Signal Processing,2002,50(9):2230-2244.
[7]Nikolas P,Aggelos K.Methods for choosing the regu-larization parameter and estimating the noise variance in image restoration and their relation[J].IEEE Transactions on Image Processing,1992,1(3):322-336.
[8]Zhang Z J,Wang G J,Harris J M.Multi-component wavefield simulation in viscous extensively dilatancy anisotropic media[J].Phys Earth planet Inter,1999,114:25-28.
[9]王岩,梁甸农,郭汉伟.基于改进正则化方法的SAR图像增强技术[J].电子学报,2003,31(9),1307-1309.WANG Yan,LIANG Dian-nong,GUO Han-wei.SARimage enhancement using modified regularization method[J].Acta Electronica Sinica,2003,31(9):1307-1309.
[10]Murli A,D’Amore L,De Simone V.The Wiener filter and regularization methods for image restoration problems[C]//Image analysis and processing.Washington D C:IEEE Computer Society,1999:394-399.
[11]Sekko E,Thomas G,Boukrouche A.A disconsola-tion technique using optimal Wiener filtering and regularization[J].Signal Processing,2009,72(2):23-32.
[12]Rugini L,Banelli P,Cacopardi S.A full-rank re-gularization technique for MMSE detection in multiuser CDMA systems[J].IEEE Communications Letters,2005,9(1):34-36.
[13]Feigin M,Sochen N.Anisotropic regularization for inverse problems with application to the Wiener filter with Gaussion and impulse noise[J].Lecture Notes in Computer Science,2009,5567(1):319-330.
[14]杨宝俊,李勤学,唐建人,等.松辽盆地反射地震莫霍面的形态、三瞬处理结果及其地质解释[J].地球物理学报,2003,46(3):398-402.YANG Bao-jun,LI Qin-xue,TANGJian-ren,et al.The form and three-instantaneous information of the seismic reflection Moho in Songliao basin and geological[J].Chinese Journal of Geophysics,2003,46(3):398-402.
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