双稀疏字典和FISTA的地震数据去噪
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摘要
地震数据的随机噪声去除是地震数据处理中的一项重要步骤,双稀疏字典提供了两层稀疏模型,比单层稀疏模型可以更好地去除噪声.该方法首先利用contourlet变换对地震数据进行稀疏表示,然后在contourlet域中使用快速迭代收缩阈值算法(fast iterative shrinkage-thresholding algorithm,FISTA)对初始字典系数进行更新,接着采用数据驱动紧标架(data-driven tight frame,DDTF)在contourlet域中得到DDTF字典并通过FISTA得到更新后的字典系数,最后通过DDTF字典和更新后的字典系数获得新的contourlet系数,并对新的contourlet系数进行硬阈值和contourlet反变换得到去噪后的数据.通过模拟数据和实际数据的实验证明:与固定基变换去噪方法相比,该方法可以自适应地对地震数据进行稀疏表示,在地震数据较为复杂时得到更高的信噪比;与字典学习去噪方法相比,该方法不仅拥有较快的去噪速度,而且克服了字典学习因为缺少先验约束造成瑕疵的缺点.
Seismic data denoising acts as one of the important roles in seismic data processing.Double sparse dictionary can provide the two-level sparsity for model,which has higher anti-noise ability than single sparsity transform denoising.In this paper,we developed a seismic data denoising workflow based on the double sparse transform and fast iterative shrinkage-thresholding algorithm(FISTA).We firstly represent data by contourlet transform and obtain a primary coefficient dictionary via FISTA.Then we obtain the learned dictionary through the data-driven tight frame(DDTF)and update the learned dictionary via FISTA.Finally,the new contourlet coefficients are reconstructed by DDTF dictionary and updated dictionary coefficients.Moreover,the hard thresholding and inverse contourlet transform are applied in new contourlet coefficients.Consequently,it achieves denoising.The synthetic data and field data experiments illustrated that compared with fixed-base transform,the proposed method obtains sparse representation ofseismic data adaptively,and it performances well in the complexity seismic data.Compared with dictionary learning,the proposed method has less computational time-consuming.What is more,the proposed method overcomes the disadvantage that dictionary learning often produces artifacts due to no prior-constraint structural information in seismic data denoising.
Seismic data denoising acts as one of the important roles in seismic data processing.Double sparse dictionary can provide the two-level sparsity for model,which has higher anti-noise ability than single sparsity transform denoising.In this paper,we developed a seismic data denoising workflow based on the double sparse transform and fast iterative shrinkage-thresholding algorithm(FISTA).We firstly represent data by contourlet transform and obtain a primary coefficient dictionary via FISTA.Then we obtain the learned dictionary through the data-driven tight frame(DDTF)and update the learned dictionary via FISTA.Finally,the new contourlet coefficients are reconstructed by DDTF dictionary and updated dictionary coefficients.Moreover,the hard thresholding and inverse contourlet transform are applied in new contourlet coefficients.Consequently,it achieves denoising.The synthetic data and field data experiments illustrated that compared with fixed-base transform,the proposed method obtains sparse representation ofseismic data adaptively,and it performances well in the complexity seismic data.Compared with dictionary learning,the proposed method has less computational time-consuming.What is more,the proposed method overcomes the disadvantage that dictionary learning often produces artifacts due to no prior-constraint structural information in seismic data denoising.
引文
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Beck A,Teboulle M.2009.A fast iterative shrinkage-thresholding algorithm for linear inverse problems.SIAM Journal on Imaging Sciences,2(1):183-202.
Cai J F,Ji H,Shen Z W,et al.2014.Data-driven tight frame construction and image denoising.Applied and Computational Harmonic Analysis,37(1):89-105.
Chen Y K,Ma J W,Fomel S.2016.Double sparsity dictionary for seismic noise attenuation.Geophysics,81(2):V17-V30.
Chen Y K.2017.Fast dictionary learning for noise attenuation of multidimensional seismic data.Geophysical Journal International,209(1):21-31.
Daubechies I,Defrise M,De Mol C.2004.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint.Communications on Pure and Applied Mathematics,57(11):1413-1457.
Donoho D L.2006.For most large underdetermined systems of linear equations the minimal L1-norm solution is also the sparsest solution.Communications on Pure and Applied Mathematics,59(6):797-829.
Gaci S.2014.The use of wavelet-based denoising techniques to enhance the first-arrival picking on seismic traces.IEEETransactions on Geoscience and Remote Sensing,52(8):4558-4563.
Gomes V M,Santos H B,Schleicher J,et al.2017.Seismic data inversion with curvelet denoising preconditioning.∥Aquino F,Faria E eds.15th International Congress of the Brazilian Geophysical Society&EXPOGEF.Rio de Janeiro,Brazil:Society of Exploration Geophysicists,1556-1561.
Hou S A,Zhang F,Li X Y,et al.2018.Simultaneous multicomponent seismic denoising and reconstruction via K-SVD.Journal of Geophysics and Engineering,15(3):681,doi:10.1088/1742-2140/aa953a.
Kong D H,Peng Z M.2015.Seismic random noise attenuation using shearlet and total generalized variation.Journal of Geophysics and Engineering,12(6):1024-1035.
Li Q,Gao J H.2013.Contourlet based seismic reflection data nonlocal noise suppression.Journal of Applied Geophysics,95:16-22.
Liang J W,Ma J W,Zhang X Q.2014.Seismic data restoration via data-driven tight frame.Geophysics,79(3):V65-V74.
Liu C M,Wang D L,Wang T,et al.2014.Random seismic noise attenuation based on the Shearlet transform.Acta Petrolei Sinica(in Chinese),35(4):692-699.
Liu Y,Fomel S,Liu C,et al.2009.High-order seislet transform and its application of random noise attenuation.Chinese Journal of Geophysics(in Chinese),52(8):2142-2151,doi:10.3969/j.issn.0001-5733.2009.08.024.
Liu Y,Fomel S.2013.Seismic data analysis using local time-frequency decomposition.Geophysical Prospecting,61(3):516-525.
Liu Y,Fomel S,Liu C.2015.Signal and noise separation in prestack seismic data using velocity-dependent seislet transform.Geophysics,80(6):WD117-WD128.
Nazari Siahsar M A,Gholtashi S,Roshandel Kahoo A,et al.2017.Data-driven multitask sparse dictionary learning for noise attenuation of 3Dseismic data.Geophysics,82(6):V385-V396.
Qu Z D,Wu W,He R Z,et al.2015.Soft threshold filter based on S transform and its application to data processing of deep seismic reflection.Chinese Journal of Geophysics(in Chinese),58(9):3157-3168,doi:10.6038/cjg20150912.
Shan H,Ma J W,Yang H Z.2009.Comparisons of wavelets,contourlets and curvelets in seismic denoising.Journal of Applied Geophysics,69(2):103-115.
Tang G,Ma J W.2011.Application of total-variation-based curvelet shrinkage for three-dimensional seismic data denoising.IEEEGeoscience and Remote Sensing Letters,8(1):103-107.
Tian X,Zhang K,Li Z C.2017.Seismic data denoising based on modified K-singular value decomposition algorithm.∥Wang YH,Wang Z J eds.International Geophysical Conference.Qingdao:Society of Exploration Geophysicists,158-161.
Tong Q B,Sun Z L,Nie Z W,et al.2016.Sparse decomposition based on ADMM dictionary learning for fault feature extraction of rolling element bearing.Journal of Vibroengineering,18(8):5204-5216.
Vassiliou A A,Garossino P.1998-12-15.Time-frequency processing and analysis of seismic data using very short-time Fourier transforms:US,5850622.
Wang J J,Yuan L,Liu W R,et al.2016.Dual-tree complex wavelet domain bivariate method for seismic signal random noise attenuation.Chinese Journal of Geophysics(in Chinese),59(8):3046-3055,doi:10.6038/cjg20160827.
Xing H F,Li F,Liu Y L.2007.Wavelet denoising and feature extraction of seismic signal for footstep detection.∥Proceedings of2007International Conference on Wavelet Analysis and Pattern Recognition.Beijing:IEEE,218-223.
Yu S W,Ma J W,Osher S.2016.Monte Carlo data-driven tight frame for seismic data recovery.Geophysics,2016,81(4):V327-V340.
Zhan R H,Dong B.2016.CT image reconstruction by spatial-radon domain data-driven tight frame regularization.SIAM Journal on Imaging Sciences,9(3):1063-1083.
Zhao X,Li Y,Zhuang G H,et al.2016.2-D TFPF based on Contourlet transform for seismic random noise attenuation.Journal of Applied Geophysics,129:158-166.
Zhu L C,Liu E T,McClellan J H.2015.Seismic data denoising through multiscale and sparsity-promoting dictionary learning.Geophysics,80(6):WD45-WD57.
刘成明,王德利,王通等.2014.基于Shearlet变换的地震随机噪声压制.石油学报,35(4):692-699.
刘洋,Fomel S,刘财等.2009.高阶seislet变换及其在随机噪声消除中的应用.地球物理学报,52(8):2142-2151,doi:10.3969/j.issn.0001-5733.2009.08.024.
曲中党,吴蔚,贺日政等.2015.基于S变换的软阈值滤波在深地震反射数据处理中的应用.地球物理学报,58(9):3157-3168,doi:10.6038/cjg20150912.
汪金菊,袁力,刘婉如等.2016.地震信号随机噪声压制的双树复小波域双变量方法.地球物理学报,59(8):3046-3055,doi:10.6038/cjg20160827.
Beck A,Teboulle M.2009.A fast iterative shrinkage-thresholding algorithm for linear inverse problems.SIAM Journal on Imaging Sciences,2(1):183-202.
Cai J F,Ji H,Shen Z W,et al.2014.Data-driven tight frame construction and image denoising.Applied and Computational Harmonic Analysis,37(1):89-105.
Chen Y K,Ma J W,Fomel S.2016.Double sparsity dictionary for seismic noise attenuation.Geophysics,81(2):V17-V30.
Chen Y K.2017.Fast dictionary learning for noise attenuation of multidimensional seismic data.Geophysical Journal International,209(1):21-31.
Daubechies I,Defrise M,De Mol C.2004.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint.Communications on Pure and Applied Mathematics,57(11):1413-1457.
Donoho D L.2006.For most large underdetermined systems of linear equations the minimal L1-norm solution is also the sparsest solution.Communications on Pure and Applied Mathematics,59(6):797-829.
Gaci S.2014.The use of wavelet-based denoising techniques to enhance the first-arrival picking on seismic traces.IEEETransactions on Geoscience and Remote Sensing,52(8):4558-4563.
Gomes V M,Santos H B,Schleicher J,et al.2017.Seismic data inversion with curvelet denoising preconditioning.∥Aquino F,Faria E eds.15th International Congress of the Brazilian Geophysical Society&EXPOGEF.Rio de Janeiro,Brazil:Society of Exploration Geophysicists,1556-1561.
Hou S A,Zhang F,Li X Y,et al.2018.Simultaneous multicomponent seismic denoising and reconstruction via K-SVD.Journal of Geophysics and Engineering,15(3):681,doi:10.1088/1742-2140/aa953a.
Kong D H,Peng Z M.2015.Seismic random noise attenuation using shearlet and total generalized variation.Journal of Geophysics and Engineering,12(6):1024-1035.
Li Q,Gao J H.2013.Contourlet based seismic reflection data nonlocal noise suppression.Journal of Applied Geophysics,95:16-22.
Liang J W,Ma J W,Zhang X Q.2014.Seismic data restoration via data-driven tight frame.Geophysics,79(3):V65-V74.
Liu C M,Wang D L,Wang T,et al.2014.Random seismic noise attenuation based on the Shearlet transform.Acta Petrolei Sinica(in Chinese),35(4):692-699.
Liu Y,Fomel S,Liu C,et al.2009.High-order seislet transform and its application of random noise attenuation.Chinese Journal of Geophysics(in Chinese),52(8):2142-2151,doi:10.3969/j.issn.0001-5733.2009.08.024.
Liu Y,Fomel S.2013.Seismic data analysis using local time-frequency decomposition.Geophysical Prospecting,61(3):516-525.
Liu Y,Fomel S,Liu C.2015.Signal and noise separation in prestack seismic data using velocity-dependent seislet transform.Geophysics,80(6):WD117-WD128.
Nazari Siahsar M A,Gholtashi S,Roshandel Kahoo A,et al.2017.Data-driven multitask sparse dictionary learning for noise attenuation of 3Dseismic data.Geophysics,82(6):V385-V396.
Qu Z D,Wu W,He R Z,et al.2015.Soft threshold filter based on S transform and its application to data processing of deep seismic reflection.Chinese Journal of Geophysics(in Chinese),58(9):3157-3168,doi:10.6038/cjg20150912.
Shan H,Ma J W,Yang H Z.2009.Comparisons of wavelets,contourlets and curvelets in seismic denoising.Journal of Applied Geophysics,69(2):103-115.
Tang G,Ma J W.2011.Application of total-variation-based curvelet shrinkage for three-dimensional seismic data denoising.IEEEGeoscience and Remote Sensing Letters,8(1):103-107.
Tian X,Zhang K,Li Z C.2017.Seismic data denoising based on modified K-singular value decomposition algorithm.∥Wang YH,Wang Z J eds.International Geophysical Conference.Qingdao:Society of Exploration Geophysicists,158-161.
Tong Q B,Sun Z L,Nie Z W,et al.2016.Sparse decomposition based on ADMM dictionary learning for fault feature extraction of rolling element bearing.Journal of Vibroengineering,18(8):5204-5216.
Vassiliou A A,Garossino P.1998-12-15.Time-frequency processing and analysis of seismic data using very short-time Fourier transforms:US,5850622.
Wang J J,Yuan L,Liu W R,et al.2016.Dual-tree complex wavelet domain bivariate method for seismic signal random noise attenuation.Chinese Journal of Geophysics(in Chinese),59(8):3046-3055,doi:10.6038/cjg20160827.
Xing H F,Li F,Liu Y L.2007.Wavelet denoising and feature extraction of seismic signal for footstep detection.∥Proceedings of2007International Conference on Wavelet Analysis and Pattern Recognition.Beijing:IEEE,218-223.
Yu S W,Ma J W,Osher S.2016.Monte Carlo data-driven tight frame for seismic data recovery.Geophysics,2016,81(4):V327-V340.
Zhan R H,Dong B.2016.CT image reconstruction by spatial-radon domain data-driven tight frame regularization.SIAM Journal on Imaging Sciences,9(3):1063-1083.
Zhao X,Li Y,Zhuang G H,et al.2016.2-D TFPF based on Contourlet transform for seismic random noise attenuation.Journal of Applied Geophysics,129:158-166.
Zhu L C,Liu E T,McClellan J H.2015.Seismic data denoising through multiscale and sparsity-promoting dictionary learning.Geophysics,80(6):WD45-WD57.
刘成明,王德利,王通等.2014.基于Shearlet变换的地震随机噪声压制.石油学报,35(4):692-699.
刘洋,Fomel S,刘财等.2009.高阶seislet变换及其在随机噪声消除中的应用.地球物理学报,52(8):2142-2151,doi:10.3969/j.issn.0001-5733.2009.08.024.
曲中党,吴蔚,贺日政等.2015.基于S变换的软阈值滤波在深地震反射数据处理中的应用.地球物理学报,58(9):3157-3168,doi:10.6038/cjg20150912.
汪金菊,袁力,刘婉如等.2016.地震信号随机噪声压制的双树复小波域双变量方法.地球物理学报,59(8):3046-3055,doi:10.6038/cjg20160827.