基于Curvelet变换阈值法的地震数据插值和去噪
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摘要
成功的信号分离和去噪依赖于所用的变换能否足够稀疏地表达该类信号。事实上,信号在某变换域的系数越稀疏,阈值去噪的效果也就越好。Curvelet变换是一种非自适应的多尺度、多方向性变换,地震数据在Curvelet域有着几乎最优的稀疏表达。最近的研究表明,Curvelet阈值能够得到比小波阈值更好的随机噪声抑制效果,更高的提高信噪比。同时,这种去噪方法还克服了传统滤波法对有效地震信号损失较大这一缺点。针对含有随机噪声的地震数据缺失道插值问题,本文提出了一种基于Curvelet阈值迭代的插值方法。实验结果表明,该方法不仅可以得到较好的插值重构效果,而且几乎可以达到和没有地震数据丢失情况下同样的信噪比。
The success of signal denoising and separating depends largely on the ability of a transform to sparsely represent a particular type of a signal.In fact,the sparser the transformation is,the better denoising result will be achieved from the coefficient shrinkage.Curvelet transform is a multi-scale directional transform,which allows an almost optimal non-adaptive sparse representation for seismic data.Recent research has shown that the method of curvelet thresholding could suppress the random noise more effectively and achieve a higher ratio of signal to noise than the traditional methods,such as wavelet denoising.At the same time,it overcame the drawback that the conventional filtering approach might affect the effective wave when suppressing noise.In this paper,we proposed a new iterative interpolation idea based on curvelet thresholding to reconstruct seismic data with missing traces.Application of this method to interpolation and noise removal problems on incomplete seismic data demonstrated that the proposed mothod could obtain a fine reconstructed result and effectively attenuate the random noise for the case without seismic data missing.
The success of signal denoising and separating depends largely on the ability of a transform to sparsely represent a particular type of a signal.In fact,the sparser the transformation is,the better denoising result will be achieved from the coefficient shrinkage.Curvelet transform is a multi-scale directional transform,which allows an almost optimal non-adaptive sparse representation for seismic data.Recent research has shown that the method of curvelet thresholding could suppress the random noise more effectively and achieve a higher ratio of signal to noise than the traditional methods,such as wavelet denoising.At the same time,it overcame the drawback that the conventional filtering approach might affect the effective wave when suppressing noise.In this paper,we proposed a new iterative interpolation idea based on curvelet thresholding to reconstruct seismic data with missing traces.Application of this method to interpolation and noise removal problems on incomplete seismic data demonstrated that the proposed mothod could obtain a fine reconstructed result and effectively attenuate the random noise for the case without seismic data missing.
引文
[1]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,2008.
[2]Hennenfent G.and Herrmann F.J.Seismic denoisingwith nonuniformly sampled curvelets[J].IEEEComputing in Science and Engineering,2006,(8):16-25.
[3]Mallat S.A wavelet tour of signal processing[M].SanDiego,CA:Academic Press,1998.
[4]Candes E.J.,Demanet L.,Donoho D.L.,et al.Fastdiscrete curvelet transforms[R].Applied andcomputational mathematics,California Institute ofTechnology,2005:1-43.
[5]Herrmann F.J.,Wang Deli,Hennenfent G.,et al.Seismic data processing with curvelets:a multiscaleand nonlinear approach[C].in Society of ExplorationGeophysicists,Expanded Abstracts,2007:2220-2224.
[6]Candes E.J.,Donoho D.L.Curvelets——a surprisinglyeffective non-adaptive representation for objects withedges[M].Nashville,TN:Vanderbilt University Press,2000.
[7]Herrmann F.J.and Hennenfent G.Non-parametricseismic data recovery with curvelet frames[J].Geophysical Journal International,2008,173(1):233-248.
[2]Hennenfent G.and Herrmann F.J.Seismic denoisingwith nonuniformly sampled curvelets[J].IEEEComputing in Science and Engineering,2006,(8):16-25.
[3]Mallat S.A wavelet tour of signal processing[M].SanDiego,CA:Academic Press,1998.
[4]Candes E.J.,Demanet L.,Donoho D.L.,et al.Fastdiscrete curvelet transforms[R].Applied andcomputational mathematics,California Institute ofTechnology,2005:1-43.
[5]Herrmann F.J.,Wang Deli,Hennenfent G.,et al.Seismic data processing with curvelets:a multiscaleand nonlinear approach[C].in Society of ExplorationGeophysicists,Expanded Abstracts,2007:2220-2224.
[6]Candes E.J.,Donoho D.L.Curvelets——a surprisinglyeffective non-adaptive representation for objects withedges[M].Nashville,TN:Vanderbilt University Press,2000.
[7]Herrmann F.J.and Hennenfent G.Non-parametricseismic data recovery with curvelet frames[J].Geophysical Journal International,2008,173(1):233-248.
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