曲波变换及全变差最小化技术联合去噪
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摘要
为了更好地发挥曲波变换在地震资料去噪处理方面的优势,同时克服其固有缺陷,在地震资料去噪处理中应用了基于曲波变换和全变差最小化技术的联合衰减随机噪声技术。该技术在应用曲波变换时,对选取的阈值使用非线性阈值法,同时对小系数采用全变差最小化技术。理论模型与实际地震资料的测试结果表明,该技术不仅可以很好地衰减随机噪声,有效地克服单独使用曲波变换带来的伪曲线现象,同时较好地保护了有效信号。
In order to take advantage of curvelet transform in seismic data denosing and overcome its inherent shortcomings,we applied the joint random noise attenuation technique based on curvelet transform and total variation minimization on seismic data.This technique uses the nonlinear-thresholding approach to realize the curvelet transform and adopts total variation minimization for small coefficients.Theoretical model and real data processing results show that this technique can greatly attenuate random noise,effectively overcome aliased curves when merely using curvelet transform,and preserve the significant signal in seismic data as well.
In order to take advantage of curvelet transform in seismic data denosing and overcome its inherent shortcomings,we applied the joint random noise attenuation technique based on curvelet transform and total variation minimization on seismic data.This technique uses the nonlinear-thresholding approach to realize the curvelet transform and adopts total variation minimization for small coefficients.Theoretical model and real data processing results show that this technique can greatly attenuate random noise,effectively overcome aliased curves when merely using curvelet transform,and preserve the significant signal in seismic data as well.
引文
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[13]包乾宗,陈文超,高静怀.基于第二代Curvelet变换的地震资料随机噪声衰减[J].煤田地质与勘探,2010,38(1):66-70Bao Q Z,Chen W C,Gao J H.Seismic data randomnoise attenuation based on the second generationcurvelet transform[J].Coal Geology&Exploration,2010,38(1):66-70
[14]刘国昌,陈小宏,郭志峰,等.基于Curvelet变换的缺失地震数据插值方法[J].石油地球物理勘探,2011,46(2):237-246Liu G C,Chen X H,Guo Z F,et al.Missing seismicdata rebuilding by interpolation based on curvelettransform[J].Oil Geophysical Prospecting,2011,46(2):237-246
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[16]刘冰.基于Curvelet变换的地震数据去噪方法研究[D].长春:吉林大学,2008Liu B.Curvelet-based seismic data denoise[D].Changchun:Jilin University,2008
[17]唐刚.基于压缩感知和稀疏表示的地震数据重建和去噪[D].北京:清华大学,2010Tang G.Seismic data reconstruction and denoisingbased on compressive sensing and sparse Represen-tation[D].Beijing:Tsinghua University,2010
[18]倪雪,李庆武,孟凡,等.基于Curvelet变换和全变差的图像去噪方法[J].光学学报,2009,29(9):2390-2394Ni X,Li Q W,Meng F,et al.Image denoising meth-od based on curvelet transform and total Variation[J].Acta Optica Sinica,2009,29(9):2390-2394
[2]Candès E L,Donoho D L.New tight frames of cur-velets and optimal representations of objects withpiecewise—C2singularities[J].Communications onPure and Applied Mathematics,2004,57(2):219-266
[3]Candès E,Demanet L,Donoho D,et al.Fast discretecurvelet transforms[J].Multiscale Modeling andSimulation,2006,5(3),861-899
[4]Herrmann F J,Verschuur E.Curvelet domain multi-ple elimination with sparseness constraints[J].Ex-panded Abstracts of 74th Annual Internat SEG Mtg,2004,1333-1336
[5]Herrmann F J,Verschuur E.Separation of primariesand multiples by non-linear estimation in the curve-let domain[J].Expanded Abstracts of 66th EAGEAnnual Conference,2004,2883-2886
[6]Hennenfent G,Herrmann F J.Seismic denoisingwith nonuniformly sampled curvelets[J].IEEEComputing in Science and Engineering,2006,8(3):16-25
[7]Herrmann F J,Wang D L,Hennenfent G,et al.Seis-mic data processing with curvelets:A multiscale andnonlinear approach[J].Expanded Abstracts of 77thAnnual Internat SEG Mtg,2007,2220-2224
[8]Neelamani R,Baumstein A I,Gillard D,et al.Coher-ent and random noise attenuation using the curvelettransform[J].The Leading Edge,2008,27(2):240-248
[9]Herrmann F J,Hennenfent G.Non-parametric seis-mic data recovery with frames[J].Geophysical Jour-nal International,2008,173(1):233-248
[10]Hennenfent G,Herrmann F.Simply denoise:wave-field reconstruction via jittered undersampling[J].Geophysics,2008,73(3):V19-V28
[11]单昊,杨慧珠.基于Cuevelet的Stein无偏风险估计图像去噪[J].清华大学学报(自然科学版),2010,50(8):1307-1310Shan H,Yang H Z.Curvelet based stein’s unbiasedrisk estimate for image denoising[J].Journal of Ts-inghua University(Sci&Tech),2010,50(8):1307-1310
[12]仝中飞,王德利,刘冰.基于Curvelet变换阈值法的地震数据去噪方法[J].吉林大学学报(地球科学版),2008,38(增刊):48-52Tong Z F,Wang D L,Liu B.Seismic data denoisebased on curveler transform with the thresholdmethod[J].Journal of Jilin University(Earth ScienceEdition),2008,38(S):48-52
[13]包乾宗,陈文超,高静怀.基于第二代Curvelet变换的地震资料随机噪声衰减[J].煤田地质与勘探,2010,38(1):66-70Bao Q Z,Chen W C,Gao J H.Seismic data randomnoise attenuation based on the second generationcurvelet transform[J].Coal Geology&Exploration,2010,38(1):66-70
[14]刘国昌,陈小宏,郭志峰,等.基于Curvelet变换的缺失地震数据插值方法[J].石油地球物理勘探,2011,46(2):237-246Liu G C,Chen X H,Guo Z F,et al.Missing seismicdata rebuilding by interpolation based on curvelettransform[J].Oil Geophysical Prospecting,2011,46(2):237-246
[15]Rudin L I,Osher S,Fatemi E.Nonlinear total varia-tion based noise removal algorithms[J].Physica D,1992,62(1):63-67
[16]刘冰.基于Curvelet变换的地震数据去噪方法研究[D].长春:吉林大学,2008Liu B.Curvelet-based seismic data denoise[D].Changchun:Jilin University,2008
[17]唐刚.基于压缩感知和稀疏表示的地震数据重建和去噪[D].北京:清华大学,2010Tang G.Seismic data reconstruction and denoisingbased on compressive sensing and sparse Represen-tation[D].Beijing:Tsinghua University,2010
[18]倪雪,李庆武,孟凡,等.基于Curvelet变换和全变差的图像去噪方法[J].光学学报,2009,29(9):2390-2394Ni X,Li Q W,Meng F,et al.Image denoising meth-od based on curvelet transform and total Variation[J].Acta Optica Sinica,2009,29(9):2390-2394
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