基于贝叶斯阈值估计的曲波域自适应随机噪声衰减
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摘要
与小波变换相比,曲波变换可以更好地表达曲线奇异函数的异向性。根据曲波变换对于光滑且二阶连续可微函数所具有的最优逼近性能,结合贝叶斯理论,给出了基于曲波域的自适应阈值去噪方法。通过对合成地震记录及实际地震数据的处理,验证了该方法的有效性。结果表明,与传统小波阈值法相比,基于贝叶斯阈值估计的曲波域自适应去噪方法不仅可以很好地衰减随机噪声,有效提高地震资料的信噪比,而且能够较好地保持有效信号。
The curvelet transform can represent anisotropy of curved singular function better than wavelet transform.According to the optimal approximation property of the curvelet transform for smoothing and second-order continuous differentiable singular functions,an adaptive thresholding denoising method for combining the improved curvelet transform with Bayesian theory is proposed.The processing results of seismogram and real seismic data verify that curvelet transform for self-adaptive random noise attenuation based on Bayes estimation can not only attenuate random noise and effectively improve S/N in seismic data but also well preserve effective signal compared with conventional wavelet transform threshold method.
The curvelet transform can represent anisotropy of curved singular function better than wavelet transform.According to the optimal approximation property of the curvelet transform for smoothing and second-order continuous differentiable singular functions,an adaptive thresholding denoising method for combining the improved curvelet transform with Bayesian theory is proposed.The processing results of seismogram and real seismic data verify that curvelet transform for self-adaptive random noise attenuation based on Bayes estimation can not only attenuate random noise and effectively improve S/N in seismic data but also well preserve effective signal compared with conventional wavelet transform threshold method.
引文
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[10]姜宇东,杨勤勇,何柯,等.基于曲波变换的地面微地震资料去噪方法研究[J].石油物探,2012,51(6):620-624Jiang Y D,Yang Q Y,He K.Surface microseismicdate denoising method based on curvelet transform[J].Geophysical Prospecting for Petroleum,2012,51(6):620-624
[11]Pennec E L,Mallat S.Sparse geometric image repre-sentation with bandelets[J].IEEE Transactions onImage Processing,2005,14(4):423-438
[12]Candès E J,Guo F.New multiscale transform,mini-mum total variation synthesis:applications to edge-preserving image reconstruction[J].Signal Process-ing,2002,82:1519-1543
[13]Candès E J,Donoho D L.New tight frames of curve-lets and optimal representations of objects withpiecewise-C2singularities[J].Communications onPure and Applied Mathematics,2004,57(2):219-266
[14]Candès E J,Demannet S L,Donoho D L,et al.Fastdiscrete curvelet transforms[J].Multiscale ModelingSimulation,2006,5(3):861-899
[15]Grace C,Yu B,Vetterli M.Adaptive wavelet thresh-olding for image denoising and compression[J].IEEE Transactions on Image Porcessing,2000,9(9):1532-1546
[2]杨立强,宋海斌,郝天珧,等.基于二维小波变换的随机噪音压制方法研究[J].石油物探,2005,44(1):4-6Yang L Q,Song H B,Hao T Y,et al.Method of 2-Dwavelet transform in attenuating random noise[J].Geophysical Prospecting for Petroleum,2005,44(1):4-6
[3]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):112-114Peng C,Zhu S J,Song J K,et al.K-L transformationin wavelet conversion domain and the analysis of de-noise effect[J].Geophysical Prospecting for Petrole-um,2007,46(2):112-114
[4]焦李成,谭山.图像的多尺度几何分析:回顾和展望[J].电子学报,2003,31(12A):1975-1981Jiao L C,Tan S.Development and prospect of imagemultiscale geometric analysis[J].Acta ElectronicaSinica,2003,31(12A):1975-1981
[5]王振国,汪恩华.小波包相关阈值去噪[J].石油物探,2002,41(4):400-405Wang Z G,Wang E H.Noise elimination with cor-relative threshold plus wavelet packet transforma-tion[J].Geophysical Prospecting for Petroleum,2002,41(4):400-405
[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):1331-1337Long G,Xiao L,Chen X Q.Overview of the applica-tions of curvelet transform in image processing[J].Journal of Computer Research and Development,2005,42(8):1331-1337
[7]Do M M,Vetterli M.The finite ridgelet transformfor image representation[J].IEEE Transactions onImage Processing,2003,12(1):16-28
[8]Starck J L,Candès E J,Donoho D L.The curvelettransform for image denoising[J].IEEE Transac-tions on Image Porcessing,2002,11(6):670-684
[9]俞华,薛永安,王勇,等.曲波变换及全变差最小化技术联合去噪[J].石油物探,2012,51(4):350-355Yu H,Xue Y A,Wang Y,et al.Joint noise attenua-tion technique based on curvelet transform and totalvariation minimization[J].Geophysical Prospectingfor Petroleum,2012,51(4):350-355
[10]姜宇东,杨勤勇,何柯,等.基于曲波变换的地面微地震资料去噪方法研究[J].石油物探,2012,51(6):620-624Jiang Y D,Yang Q Y,He K.Surface microseismicdate denoising method based on curvelet transform[J].Geophysical Prospecting for Petroleum,2012,51(6):620-624
[11]Pennec E L,Mallat S.Sparse geometric image repre-sentation with bandelets[J].IEEE Transactions onImage Processing,2005,14(4):423-438
[12]Candès E J,Guo F.New multiscale transform,mini-mum total variation synthesis:applications to edge-preserving image reconstruction[J].Signal Process-ing,2002,82:1519-1543
[13]Candès E J,Donoho D L.New tight frames of curve-lets and optimal representations of objects withpiecewise-C2singularities[J].Communications onPure and Applied Mathematics,2004,57(2):219-266
[14]Candès E J,Demannet S L,Donoho D L,et al.Fastdiscrete curvelet transforms[J].Multiscale ModelingSimulation,2006,5(3):861-899
[15]Grace C,Yu B,Vetterli M.Adaptive wavelet thresh-olding for image denoising and compression[J].IEEE Transactions on Image Porcessing,2000,9(9):1532-1546
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