随机噪声的多尺度多方向域压制方法研究
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摘要
介绍了信号的多尺度多方向特性和具有此功能的第2代curvelet变换的基本原理,阐述了对于光滑且二阶连续可微的函数,第2代curvelet变换所具有的最优逼近性能。给出了地震资料随机噪声衰减的阈值方法。基于理论模型讨论了多尺度多方向域(curvelet域)的去噪特性,并将其与传统小波变换的去噪效果进行了对比。最后,将该方法应用于实际地震资料处理,结果表明,与传统小波变换相比,多尺度多方向域阈值法充分利用了信号与噪声在方向上的差异,使随机噪声得到了较好的衰减,有效提高了地震资料的信噪比,较好地保留了地震记录的有效信号。
We introduced the multi-scale & multi-direction characteristic of signal and the principles of the second generation of curvelet transform which has the multi-scale & multi-direction characteristic. According to the optimal approximation property of the second curvelet transform about smooth and second-order continuous differentiable singular function,a threshold method of random noise attenuation was proposed based on the second generation of curvelet transform.On basis of theoretical model,the suppressing effect in multi-direction domain(curvelet domain) was discussed,and was compared to that of traditional wavelet transform.Finally,our method was applied on actual data.The result shows that our method sufficiently utilized the difference of directions for signal and noise,which obtained better attenuation result for random noise,efficiently improved the S/N of seismic data,and preserved the effective signal in seismic record.
We introduced the multi-scale & multi-direction characteristic of signal and the principles of the second generation of curvelet transform which has the multi-scale & multi-direction characteristic. According to the optimal approximation property of the second curvelet transform about smooth and second-order continuous differentiable singular function,a threshold method of random noise attenuation was proposed based on the second generation of curvelet transform.On basis of theoretical model,the suppressing effect in multi-direction domain(curvelet domain) was discussed,and was compared to that of traditional wavelet transform.Finally,our method was applied on actual data.The result shows that our method sufficiently utilized the difference of directions for signal and noise,which obtained better attenuation result for random noise,efficiently improved the S/N of seismic data,and preserved the effective signal in seismic record.
引文
[1]陈香朋,曹思远.第二代小波变换及其在地震信号去噪中的应用[J].石油物探,2004,43(6):547-550
[2]彭才,朱仕军,孙建库,等.小波变换域K-L变换及其去噪效果分析[J].石油物探,2007,46(2): 112-114
[3]王振国,汪恩华.小波包相关阈值去噪[J].石油物探,2002,41(4):400-405
[4]杨立强,宋海斌,郝天珧,等.基于二维小波变换的随机噪声压制方法研究[J].石油物探,2005,44(1): 4-6
[5]何劲,李宏伟,张帆.基于curvelet变换与小波包变换联合的图像去噪算法[J].通信技术,2008,41(1): 140-142
[6]隆刚,肖磊,陈学佺.Curvelet变换在图像处理中的应用综述[J].计算机研究与发展,2005,42(8): 1331-1337
[7]焦李成,谭山,刘芳.脊波理论:从脊波变换到curvelet变换[J].工程数学学报,2005,22(5):761-762
[8]吴芳平,狄红卫.基于curvelet变换的软硬阈值折中图像去噪[J].光学技术,2007,33(5):688-690
[9]Candes E J,Donoho D L.Curvelets:a surprisingly effective nonadaptive representation for objects with ??edges[M].Tennessee,USA:Vanderbilt University Press,1999:1-16
[10]张志禹,毕杨.基于曲波变换和独立分量分析的有噪图像盲分离[J].计算机应用,2007,27(2):438-441
[11]Herrmann F J,Hennenfent G.Non-parametric seismic data recovery with curvelet frames[J].Geophysical Journal International,2008,173(1):233-248
[12]Starck J L,Candes E J,Donoho D L.The curvelet transform for image denoising[J].IEEE Transactions On Image Processing,2002,11(6):670-684
[13]Candes E J,Guo F.New multiscale transform,minimum total variation synthesis:applications to edge-preserving image reconstruction[J].Signal Processing, 2002,82(11):1519-1543
[14]Candes E J,Donoho D L.New tight frames of curvelets and optimal representation of objects with piecewise -singularities[J].Communications on Pure and Applied Mathematics,2004,57(2):219-266
[15]Candes E J,Donoho D L.Continuous curvelet transformⅡ:discretization and frames[J].Applied and Computational Harmonic Analysis,2005,19(2): 198-222
[16]Candes E J,Demannet S L,Donoho D L,et al.Fast discrete curvelet transforms[J].Multiscale Modeling and Simulation,2006,5(3):861-899
[2]彭才,朱仕军,孙建库,等.小波变换域K-L变换及其去噪效果分析[J].石油物探,2007,46(2): 112-114
[3]王振国,汪恩华.小波包相关阈值去噪[J].石油物探,2002,41(4):400-405
[4]杨立强,宋海斌,郝天珧,等.基于二维小波变换的随机噪声压制方法研究[J].石油物探,2005,44(1): 4-6
[5]何劲,李宏伟,张帆.基于curvelet变换与小波包变换联合的图像去噪算法[J].通信技术,2008,41(1): 140-142
[6]隆刚,肖磊,陈学佺.Curvelet变换在图像处理中的应用综述[J].计算机研究与发展,2005,42(8): 1331-1337
[7]焦李成,谭山,刘芳.脊波理论:从脊波变换到curvelet变换[J].工程数学学报,2005,22(5):761-762
[8]吴芳平,狄红卫.基于curvelet变换的软硬阈值折中图像去噪[J].光学技术,2007,33(5):688-690
[9]Candes E J,Donoho D L.Curvelets:a surprisingly effective nonadaptive representation for objects with ??edges[M].Tennessee,USA:Vanderbilt University Press,1999:1-16
[10]张志禹,毕杨.基于曲波变换和独立分量分析的有噪图像盲分离[J].计算机应用,2007,27(2):438-441
[11]Herrmann F J,Hennenfent G.Non-parametric seismic data recovery with curvelet frames[J].Geophysical Journal International,2008,173(1):233-248
[12]Starck J L,Candes E J,Donoho D L.The curvelet transform for image denoising[J].IEEE Transactions On Image Processing,2002,11(6):670-684
[13]Candes E J,Guo F.New multiscale transform,minimum total variation synthesis:applications to edge-preserving image reconstruction[J].Signal Processing, 2002,82(11):1519-1543
[14]Candes E J,Donoho D L.New tight frames of curvelets and optimal representation of objects with piecewise -singularities[J].Communications on Pure and Applied Mathematics,2004,57(2):219-266
[15]Candes E J,Donoho D L.Continuous curvelet transformⅡ:discretization and frames[J].Applied and Computational Harmonic Analysis,2005,19(2): 198-222
[16]Candes E J,Demannet S L,Donoho D L,et al.Fast discrete curvelet transforms[J].Multiscale Modeling and Simulation,2006,5(3):861-899
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