基于离散小波变换的地震资料自适应高频噪声压制
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摘要
针对现有的小波变换阈值去噪方法无法适用于地震资料高频噪声压制的缺点,笔者分别对阈值函数和阈值选取方案进行了改进,提出了连续硬阈值函数与自适应阈值相结合的地震资料高频噪声压制方法。连续硬阈值函数兼具软、硬阈值函数的优点,可提高重构地震信号的保真度,减少人为噪声误差;自适应阈值方案可根据非平稳地震数据中的能量时变、空变分布特点,通过引入不同子带小波系数标准差、代数平均值以及几何平均值等统计参数,使阈值能够随不同子带的小波系数能量变化而自动调整,以适应地震资料高频噪声压制的要求。实际地震数据处理结果表明,笔者提出的方法在提高信噪比的同时,可保护陡倾角反射界面信号,提高噪声压制后地震数据的保真度。
This authors describe a more efficient and adaptive high frequency noise suppression method in which a new adaptive threshold technique is combined with a continuous thresholding function to overcome the shortcoming that existing threshold de-noising technique by wavelet transform is not suitable for seismic data.The continuous hard thresholding function can combine both advantages of soft thresholding function and hard thresholding function,so it can enhance the fidelity of reconstructed signal and reduce the artificial noise.An adaptive threshold scheme is carried out by analyzing the statistical parameters of wavelet subband coefficients like standard deviation,arithmetic mean and geometrical mean in different subbands,which is based on the time-varying and spatial-varying energy distribution feature of nonstationary seismic signal.This threshold can adjust itself automatically with the variation of wavelet coefficient energy in different subbands to meet the requirement of high frequency seismic noise suppression.The actual seismic data processing result indicates that this method can not only raise the signal-to-noise ratio but also protect thoroughly the steep dip angle reflection event and enhance the fidelity of seismic signal after noise elimination.
This authors describe a more efficient and adaptive high frequency noise suppression method in which a new adaptive threshold technique is combined with a continuous thresholding function to overcome the shortcoming that existing threshold de-noising technique by wavelet transform is not suitable for seismic data.The continuous hard thresholding function can combine both advantages of soft thresholding function and hard thresholding function,so it can enhance the fidelity of reconstructed signal and reduce the artificial noise.An adaptive threshold scheme is carried out by analyzing the statistical parameters of wavelet subband coefficients like standard deviation,arithmetic mean and geometrical mean in different subbands,which is based on the time-varying and spatial-varying energy distribution feature of nonstationary seismic signal.This threshold can adjust itself automatically with the variation of wavelet coefficient energy in different subbands to meet the requirement of high frequency seismic noise suppression.The actual seismic data processing result indicates that this method can not only raise the signal-to-noise ratio but also protect thoroughly the steep dip angle reflection event and enhance the fidelity of seismic signal after noise elimination.
引文
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[24]Sendur L,Selesnick I W.Bi-variate shrinkage with local varianceestimation[J].IEEE Signal Processing Letters,2002,9(12):438-441.
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[26]Daubechies I.Ten lectures on wavelet[J].Proceedings CBMS-NSFRegional Conference Series in Applied Mathematics SIAM,1992,61.
[2]Mohideen S K,Perumal S A,Sathik M M.Image de-noising usingdiscrete wavelet transform[J].International Journal of ComputerScience and Network Security,2008,8(1):213-216.
[3]Gnandurai D,Sadasivam V.An efficient adaptive thresholdingtechnique for wavelet based image denoising[J].InternationalJournal of Information and Communication Engineering,2006,2(2):114-119.
[4]Gnanadurai D,Sadasivam V.Image de-noising using double densitywavelet transform based adaptive thresholding technique[J].Inter-national Journal of Wavelets,Multiresolution and Information Pro-cessing,2005,3(1):141-152.
[5]Durga M K,Sukanesh R.Resolution enhancement of low dose CT-images using wavelet transform method[C]//Chennai:Proceedingsof the Int.Conf.on Information Science and Applications,ICISA,2010.
[6]Sambasiva R G,NagaRaju C L,Reddy L S,et al.A novel threshol-ding technique for adaptive noise reduction[J].International Jour-nal of Computer Science and Network Security,2008,8(12):315-320.
[7]Kozowski B.Time series denoising with wavelet transform[J].Journal of telecommunications and information technology,2005,3(1):91-95.
[8]Donoho D L,Johnstone I M.Adapting to unknown smoothness viawavelet shrinkage[J].Journal of American Statistical Association,1995,90(432):1200-1224.
[9]夏洪瑞,葛川庆,彭涛.小波时空变阈值去噪方法在可控震源资料处理中的应用[J].石油地球物理勘探,2010,45(1):23-27.
[10]Faghih F,Smith M.Combining spatial and scale-space techniquesfor edge detection to provide a spatially adaptive wavelet-basednoise filtering algorithm[J].IEEE Trans.Image Process.,2002,11(9):1062-1071.
[11]Donoho D L.De-nosing soft thresholding[J].IEEE Transactions onInformation Theory,1995,41(3):613-627.
[12]Grace C S,Bin Y,Vattereli M.Adaptive wavelet thresholding forimage denoising and compression[J].IEEE Transaction ImageProcessing,2000,9(9):1532-15460.
[13]Grace C S,Bin Y,Vattereli M.Spatially adaptive wavelet threshol-ding with context modeling for imaged noising[J].IEEE Transac-tion Image Processing,2000,9(9):1522-1530.
[14]Abramovich F,Sapatinas T,Silverman B W.Wavelet thresholdingvia a Bayesian approach[J].J.Roy.Statist.Soc.B,1998,60(4):725-749.
[15]Elyasi I,Zarmehi S.Elimination noise by adaptive wavelet threshold[J].World Academy of Science,Engineering and Technology,2009,56:462-466.
[16]Zhang X P,Desai M.Adaptive denoising based on SURE risk[J].IEEE Signal Processing Letter,1998,10(5):265-267.
[17]Chen G Y,Bui T D.Multi-wavelet de-noising using neighboring co-efficients[J].IEEE Signal Processing Letters,2003,10(7):211-214.
[18]Terzija N,Repges M,Luck K,et al.Digital image watermarking u-sing discrete wavelet transform:performance comparison of errorcorrection codes[J].Proceeding of Visualization,Imaging,and Im-age Processing,2002,364:803.
[19]Matz V,Kreidl M,Sˇmíd R.Signal-to-noise ratio improvement basedon the discrete wavelet transform in ultrasonic defectoscopy[J].Acta polytechnica,2004,44(4):61-66.
[20]Lang M,Guo H,Odegard J E,et al.Noise reduction using an un-decimated discrete wavelet transform[J].IEEE Signal ProcessingLett.,1996,3(1):10-12.
[21]Bui T D,Chen G Y.Translation invariant de-noising using multi-wavelets[J].IEEE Transactions on Signal Processing,1998,46(12):3414-3420.
[22]刘洋,Sergey F,刘财,等.高阶seislet变换及其在随机噪声消除中的应用[J].地球物理学报,2009,52(8):2142-2151.
[23]Zhang X P.Thresholding neural network for adaptive noise reduc-tion[J].IEEE Transactions on Neural Networks,2001,12(3):567-584.
[24]Sendur L,Selesnick I W.Bi-variate shrinkage with local varianceestimation[J].IEEE Signal Processing Letters,2002,9(12):438-441.
[25]Aidi W,Xiu L Z.Seismic denosing with curvelet shrinkage[J].Journal of Communication and Computer,2010,7(9):13-17.
[26]Daubechies I.Ten lectures on wavelet[J].Proceedings CBMS-NSFRegional Conference Series in Applied Mathematics SIAM,1992,61.
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