地震信号随机噪声压制的双树复小波域双变量方法
|
摘要
有效地压制地震信号中的噪声是地震信号解释和后续处理的重要环节之一.本文建立两种双树复小波域双变量模型对地震信号中的随机噪声进行压制.地震信号经双树复小波变换后,同一方向实部与虚部系数、实部(或虚部)系数与对应的模之间存在较强的相关性.鉴于此,对同一方向实部与虚部小波系数建立双变量模型,从含噪地震信号小波系数中估计原始信号的小波系数,再基于双树复小波逆变换重构得到降噪后的地震信号.进一步对同一方向实部(或虚部)系数与对应的模建立双变量模型,得到地震信号随机噪声压制的第二种双树复小波域双变量方法.最后对合成地震记录和实际地震资料中的随机噪声进行压制的实验结果证实本文两种方法都能够有效地压制地震信号中的随机噪声.
Seismic signal noise attenuation is important in processing and interpreting seismic signal subsequently.Two dual-tree complex wavelet domain bivariate methods for seismic signal random noise attenuation are proposed.After the dual-tree complex discrete wavelet transform,the real and imaginary parts of the wavelet coefficients have dependency in the same direction.The real or imaginary parts and the corresponding magnitudes of the wavelet coefficients have dependency in the same direction.So we construct the bivariate model for the real and imaginary parts in the same direction.Using the model the wavelet coefficients of the original seismic signal are estimated.The denoised seismic signal is achieved based on the dual-tree complex wavelet inverse transform.The proposed algorithm is also extended to the real or imaginary parts and the corresponding magnitudes of dual-tree complex wavelet coefficients in the same direction.Through experiments on the synthetic seismic record and the field seismic data,the results demonstrate that the proposed two methods can attenuate random noise effectively.
Seismic signal noise attenuation is important in processing and interpreting seismic signal subsequently.Two dual-tree complex wavelet domain bivariate methods for seismic signal random noise attenuation are proposed.After the dual-tree complex discrete wavelet transform,the real and imaginary parts of the wavelet coefficients have dependency in the same direction.The real or imaginary parts and the corresponding magnitudes of the wavelet coefficients have dependency in the same direction.So we construct the bivariate model for the real and imaginary parts in the same direction.Using the model the wavelet coefficients of the original seismic signal are estimated.The denoised seismic signal is achieved based on the dual-tree complex wavelet inverse transform.The proposed algorithm is also extended to the real or imaginary parts and the corresponding magnitudes of dual-tree complex wavelet coefficients in the same direction.Through experiments on the synthetic seismic record and the field seismic data,the results demonstrate that the proposed two methods can attenuate random noise effectively.
引文
Abdelnour A F,Selesnick I W.2001.Nearly symmetric orthogonal wavelet bases.∥Proceedings of the IEEE International Conference on Acoustics,Speech,Signal Processing(ICASSP).IEEE.
Berkner K,Wells R O Jr.2002.Smoothness estimates for softthreshold denoising via translation-invariant wavelet transforms.Applied and Computational Harmonic Analysis,12(1):1-24,doi:10.1006/acha.2001.0366.
Coifman P R,Donoho D L.1995.Translation-invariant de-noising.∥Wavelets and Statistics.New York:Springer,125-150.
Donoho D L,Johnstone J M.1994.Ideal spatial adaptation by wavelet shrinkage.Biometrika,81(3):425-455.
Hill P,Achim A,Bull D.2012.The Undecimated dual Tree Complex Wavelet Transform and its application to bivariate image denoising using a Cauchy model.∥2012 19th IEEEInternational Conference on Image Processing(ICIP).Orlando,FL:IEEE,1205-1208.
Kingsbury N.1998.The dual-tree complex wavelet transform:Anew technique for shift invariance and directional filters.∥Proceedings of European signal processing Conference.Rhodes,319-322.
Kingsbury N.2001.Complex wavelets for shift invariant analysis and filtering of signals.Applied and Computational Harmonic Analysis,10(3):234-253,doi:10.1006/acha.2000.0343.
Liu J,Moulin P.2001.Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients.IEEE Transactions on Image Processing,10(11):1647-1658,doi:10.1109/83.967393.
Liu X,He Z H,Huang D J.2006.Seismic data denoising research based on wavelet transform.Petroleum Geophysics(in Chinese),4(4):15-18.
Luisier F,Blu T,Unser M.2007.A new SURE approach to image denoising:Interscale orthonormal wavelet thresholding.IEEETransactions on Image Processing,16(3):593-606,doi:10.1109/TIP.2007.891064.
Peng H C,Long F H,Ding C.2005.Feature selection based on mutual information criteria of max-dependency,max-relevance,and min-redundancy.IEEE Transactions on Pattern Analysis and Machine Intelligence,27(8):1226-1238,doi:10.1109/TPAMI.2005.159.
Sendur L,Selesnick I W.2002.Bivariate shrinkage with local variance estimation.IEEE Signal Processing Letters,9(12):438-441,doi:10.1109/LSP.2002.806054
Shi F,Selesnick I W.2007.An elliptically contoured exponential mixture model for wavelet based image denoising.Applied and Computational Harmonic Analysis,23(1):131-151,doi:10.1016/j.acha.2007.01.007.
Wang Z G,Zhou X X,Li J.2002.Noise attenuation using minimum smooth filter based on wavelet transform.Oil Geophysical Prospecting(in Chinese),37(6):594-600.
Yin M,Liu W.2012.Image denoising using mixed statistical model in nonsubsampled Contourlet transform domain.Acta Photonica Sinica,41(6):751-756,doi:10.3788/gzxb20124106.0751.
Yin M,Bai R F,Xing Y,et al.2014.Denoising algorithm by Nonsubsampled Dual-tree Complex Wavelet domain bivariate model.Acta Photonica Sinica(in Chinese),43(10):1010004,doi:10.3788/gzxb20144310.1010004.
Zhang B,Yin X Y,Wu G C,et al.1999.Random noise elimination using wavelet analysis and inversion.Oil Geophysical Prospecting(in Chinese),34(6):635-641.
Zhang K,Liu G Z,Zou D W,et al.1996.Seismic data timefrequency Domain Denoising based on dyadic wavelet transform.Acta Geophysica Sinica(in Chinese),39(2):265-271.
Zong T,Meng H Y,Jia Y L,et al.1998.Denoising method based on wavelet packet and forward-backward prediction in F-Xdomain.Acta Geophysica Sinica(in Chinese),41(S1):337-346.
刘鑫,贺振华,黄德济.2006.基于小波变换的地震资料去噪处理研究.油气地球物理,4(4):15-18.
王振国,周熙襄,李晶.2002.基于小波变换的最小光滑滤波去噪.石油地球物理勘探,37(6):594-600.
殷明,白瑞峰,邢燕等.2014.基于非下采样双树复小波域的双变量模型去噪算法.光子学报,43(10):1010004,doi:10.3788/gzxb20144310.1010004.
张波,印兴耀,吴国忱等.1999.用小波分析和反演方法联合去除随机噪声的研究.石油地球物理勘探,34(6):635-641.
章珂,刘贵忠,邹大文等.1996.二进小波变换方法的地震信号分时分频去噪处理.地球物理学报,39(2):265-271.
宗涛,孟鸿鹰,贾玉兰等.1998.小波包F-X域前后向预测去噪.地球物理学报,41(S1):337-346.
Berkner K,Wells R O Jr.2002.Smoothness estimates for softthreshold denoising via translation-invariant wavelet transforms.Applied and Computational Harmonic Analysis,12(1):1-24,doi:10.1006/acha.2001.0366.
Coifman P R,Donoho D L.1995.Translation-invariant de-noising.∥Wavelets and Statistics.New York:Springer,125-150.
Donoho D L,Johnstone J M.1994.Ideal spatial adaptation by wavelet shrinkage.Biometrika,81(3):425-455.
Hill P,Achim A,Bull D.2012.The Undecimated dual Tree Complex Wavelet Transform and its application to bivariate image denoising using a Cauchy model.∥2012 19th IEEEInternational Conference on Image Processing(ICIP).Orlando,FL:IEEE,1205-1208.
Kingsbury N.1998.The dual-tree complex wavelet transform:Anew technique for shift invariance and directional filters.∥Proceedings of European signal processing Conference.Rhodes,319-322.
Kingsbury N.2001.Complex wavelets for shift invariant analysis and filtering of signals.Applied and Computational Harmonic Analysis,10(3):234-253,doi:10.1006/acha.2000.0343.
Liu J,Moulin P.2001.Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients.IEEE Transactions on Image Processing,10(11):1647-1658,doi:10.1109/83.967393.
Liu X,He Z H,Huang D J.2006.Seismic data denoising research based on wavelet transform.Petroleum Geophysics(in Chinese),4(4):15-18.
Luisier F,Blu T,Unser M.2007.A new SURE approach to image denoising:Interscale orthonormal wavelet thresholding.IEEETransactions on Image Processing,16(3):593-606,doi:10.1109/TIP.2007.891064.
Peng H C,Long F H,Ding C.2005.Feature selection based on mutual information criteria of max-dependency,max-relevance,and min-redundancy.IEEE Transactions on Pattern Analysis and Machine Intelligence,27(8):1226-1238,doi:10.1109/TPAMI.2005.159.
Sendur L,Selesnick I W.2002.Bivariate shrinkage with local variance estimation.IEEE Signal Processing Letters,9(12):438-441,doi:10.1109/LSP.2002.806054
Shi F,Selesnick I W.2007.An elliptically contoured exponential mixture model for wavelet based image denoising.Applied and Computational Harmonic Analysis,23(1):131-151,doi:10.1016/j.acha.2007.01.007.
Wang Z G,Zhou X X,Li J.2002.Noise attenuation using minimum smooth filter based on wavelet transform.Oil Geophysical Prospecting(in Chinese),37(6):594-600.
Yin M,Liu W.2012.Image denoising using mixed statistical model in nonsubsampled Contourlet transform domain.Acta Photonica Sinica,41(6):751-756,doi:10.3788/gzxb20124106.0751.
Yin M,Bai R F,Xing Y,et al.2014.Denoising algorithm by Nonsubsampled Dual-tree Complex Wavelet domain bivariate model.Acta Photonica Sinica(in Chinese),43(10):1010004,doi:10.3788/gzxb20144310.1010004.
Zhang B,Yin X Y,Wu G C,et al.1999.Random noise elimination using wavelet analysis and inversion.Oil Geophysical Prospecting(in Chinese),34(6):635-641.
Zhang K,Liu G Z,Zou D W,et al.1996.Seismic data timefrequency Domain Denoising based on dyadic wavelet transform.Acta Geophysica Sinica(in Chinese),39(2):265-271.
Zong T,Meng H Y,Jia Y L,et al.1998.Denoising method based on wavelet packet and forward-backward prediction in F-Xdomain.Acta Geophysica Sinica(in Chinese),41(S1):337-346.
刘鑫,贺振华,黄德济.2006.基于小波变换的地震资料去噪处理研究.油气地球物理,4(4):15-18.
王振国,周熙襄,李晶.2002.基于小波变换的最小光滑滤波去噪.石油地球物理勘探,37(6):594-600.
殷明,白瑞峰,邢燕等.2014.基于非下采样双树复小波域的双变量模型去噪算法.光子学报,43(10):1010004,doi:10.3788/gzxb20144310.1010004.
张波,印兴耀,吴国忱等.1999.用小波分析和反演方法联合去除随机噪声的研究.石油地球物理勘探,34(6):635-641.
章珂,刘贵忠,邹大文等.1996.二进小波变换方法的地震信号分时分频去噪处理.地球物理学报,39(2):265-271.
宗涛,孟鸿鹰,贾玉兰等.1998.小波包F-X域前后向预测去噪.地球物理学报,41(S1):337-346.