基于交叠组稀疏广义全变分的地震信号随机噪声衰减
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摘要
广义全变分方法能较有效去除地震信号随机噪声。本文将交叠组稀疏收敛技术引入广义全变分模型,提出一种改进的广义全变分去噪方法。该方法更充分地挖掘并利用了图像一阶梯度和二阶梯度的结构稀疏的先验知识,从而获得比常规广义全变分更好的去噪效果。针对构建的改进模型,基于交替乘子迭代法框架,将多约束问题转化为去耦合的若干子问题,并引入傅里叶变换技术以提高算法运行效率。针对地震信号进行的各类全变分去噪方法的对比实验结果显示,本文方法的去噪性能相比于常规广义全变分方法具有较大提升,尤其对重噪声污染像素点具有更好的去噪效果。
The total generalized variation(TGV)denoising is a conventional way to suppress random noise in seismic data.This paper introduces the overlapping group sparsity into the TGV model and proposes an improved TGV denoising model.The proposed model explores the structural property of the first and second orders'image differential information.As a result,the proposed model performs better than the TGV model.We adopt the alternating direction method of multipliers(ADMM)to solve the proposed model.In the framework of ADMM,the multi-constrained problem is divided into several sub-problems that are easier to be solved.Furthermore,to improve the efficiency of the algorithm,we use the fast Fourier transform.Experiments verify that the proposed method outperforms than conventional TGV,especially for removing strong noise.
The total generalized variation(TGV)denoising is a conventional way to suppress random noise in seismic data.This paper introduces the overlapping group sparsity into the TGV model and proposes an improved TGV denoising model.The proposed model explores the structural property of the first and second orders'image differential information.As a result,the proposed model performs better than the TGV model.We adopt the alternating direction method of multipliers(ADMM)to solve the proposed model.In the framework of ADMM,the multi-constrained problem is divided into several sub-problems that are easier to be solved.Furthermore,to improve the efficiency of the algorithm,we use the fast Fourier transform.Experiments verify that the proposed method outperforms than conventional TGV,especially for removing strong noise.
引文
[1] Rudin L I,Osher S,Fatemi E.Nonlinear total variation based noise removal algorithms[J].Physica D:Nonlinear Phenomena,1992,60(1-4):259-268.
[2] 屈勇,曹俊兴,朱海东,等.一种改进的全变分地震图像去噪技术[J].石油学报,2011,32(5):815-819.QU Yong,CAO Junxing,ZHU Haidong,et al.An improved total variation based seismic image denoising techonology[J].Acta Petrolei Sinica,2011,32(5):815-819.
[3] Wu L,Chen Y,Jin J,et al.Four-directional fractional-order total variation regularization for image denoising[J].Journal of Electronic Imaging,2017,26(5):053003.
[4] Chen Y,Wu L,Peng Z,et al.Fast overlapping group sparsity total variation image denoising based on fast Fourier transform and split Bergman iterations[C].The 7th International Workshop on Computer Science and Engineering,Beijing,2017,278-282.
[5] 张岩,任伟建,唐国维.利用多道相似组稀疏表示方法压制随机噪声[J].石油地球物理勘探,2017,52(3):442-450.ZHANG Yan,REN Weijian,TANG Guowei.Random noise suppression based on sparse representation of multi-trace similarity group[J].Oil Geophysical Prospecting,2017,52(3):442-450.
[6] 张广智,常德宽,王一惠,等.基于稀疏冗余表示的三维地震数据随机噪声压制[J].石油地球物理勘探,2015,50(4):600-606.ZHANG Guangzhi,CHANG Dekuan,WANG Yihui,et al.3D seismic random noise suppression with sparse and redundant representation[J].Oil Geophy-sical Prospecting,2015,50(4):600-606.
[7] 周亚同,王丽莉,蒲青山.压缩感知框架下基于K-奇异值分解字典学习的地震数据重建[J].石油地球物理勘探,2014,49(4):652-660.ZHOU Yatong,WANG Lili,PU Qingshan.Seismic data reconstruction based on K-SVD dictionary learning under compressive sensing framework[J].Oil Geophysical Prospecting,2014,49(4):652-660.
[8] 宋炜,邹少峰,欧阳永林,等.快速匹配追踪三参数时频特征滤波[J].石油地球物理勘探,2013,48(4):519-525.SONG Wei,ZOU Shaofeng,OUYANG Yonglin,et al.Three parameter time-frequency characteristics filter based on fast matching pursuit[J].Oil Geophysical Prospecting,2013,48(4):519-525.
[9] 魏海涛,陆文凯,郑晓东.基于F-X域预测和全变分的串行滤波器[J].石油地球物理勘探,2011,46(5):700-704.WEI Haitao,LU Wenkai,ZHENG Xiaodong.Cascaded filter based on F-X prediction and total variation filter[J].Oil Geophysical Prospecting,2011,46(5):700-704.
[10] Kong D,Peng Z,Fan H,et al.Seismic random noise attenuation using directional total variation in the shearlet domain[J].Journal of Seismic Exploration,2016,25(4):321-338.
[11] Kong D,Peng Z.Seismic random noise attenuation using shearlet and total generalized variation[J].Journal of Geophysics and Engineering,2015,12(6):1024-1035.
[12] Li S,Peng Z.Seismic acoustic impedance inversion with multi-parameter regularization[J].Journal of Geophysics and Engineering,2017,14(3):520-532.
[13] 王治强,曹思远,陈红灵,等.基于TV约束和Toeplitz矩阵分解的波阻抗反演[J].石油地球物理勘探,2017,52(6):1193-1199.WANG Zhiqiang,CAO Siyuan,CHEN Hongling,et al.Wave impedance inversion based on TV regularization and Toeplitz-sparse matrix factorization[J].Oil Geophysical Prospecting,2017,52(6):1193-1199.
[14] 张盼,韩立国,巩向博,等.基于各向异性全变分约束的多震源弹性波全波形反演[J].地球物理学报,2018,61(2):716-732.ZHANG Pan,HAN Liguo,GONG Xiangbo,et al.Multi-source elastic full waveform inversion based on the anisotropic total variation constraint[J].Chinese Journal of Geophysics,2018,61(2):716-732.
[15] Wang X,Peng Z,Kong D,et al.Infrared dim target detection based on total variation regularization andprincipal component pursuit[J].Image and Vision Computing,2017,63:1-9.
[16] Huang L L,Xiao L,Wei Z H.Efficient and effective total variation image super-resolution:A preconditioned operator splitting approach[J].Mathematical Problems in Engineering,2011,44-48.
[17] Bredies K,Kunisch K,Pock T.Total generalized variation[J].SIAM Journal on Imaging Sciences,2010,3(3):492-526.
[18] Knoll F,Bredies K,Pock T,et al.Second order total generalized variation(TGV) for MRI[J].Magnetic Resonance in Medicine,2011,65(2):480-491.
[19] Guo W,Qin J,Yin W.A new detail-preserving regularization scheme[J]. SIAM Journal on Imaging Sciences,2014,7(2):1309-1334.
[20] Qin J,Yi X,Weiss S,et al.Shearlet-TGV based fluorescence microscopy image deconvolution[R].CAM Report,University of California,Los Angeles (UCLA),2014,14-32.
[21] Liu J,Huang T Z,Selesnick I W,et al.Image restoration using total variation with overlapping group sparsity[J].Information Sciences,2015,295:232-246.
[22] Chen P Y,Selesnick I W.Group-sparse signal denoising: non-convex regularization,convex optimization[J].IEEE Transactions on Signal Processing,2014,62(13):3464-3478.
[23] Chen P Y,Selesnick I W.Translation-invariant shrinka-ge/thresholding of group sparse signals[J].Signal Processing,2014,94:476-489.
[24] Selesnick I,Farshchian M.Sparse signal approximation via nonseparable regularization[J].IEEE Tran-sactions on Signal Processing,2017,65(10):2561-2575.
[25] Liu G,Huang T Z,Liu J,et al.Total variation with overlapping group sparsity for image deblurring under impulse noise[J].Plos One,2015,10(4):e0122562.
[26] Liu J,Huang T Z,Liu G,et al.Total variation with overlapping group sparsity for speckle noise reduction [J].Neurocomputing,2016,216:502-513.
[27] Boyd S.Distributed optimization and statistical learning via the alternating direction method of multipliers [J].Foundations and Trends in Machine Learning,2010,3(1):1-122.
[28] Gabay D,Mercier B.A dual algorithm for the solution of nonlinear variational problems via finite element approximation[J].Computers & Mathematics with Applications,1976,2(1):17-40.
[29] Wang Y,Yang J,Yin W,et al.A new alternating mini-mization algorithm for total variation image reconstruction[J].SIAM Journal on Imaging Sciences,2008,1(3):248-272.
[30] Yang J,Zhang Y,Yin W.An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise[J].SIAM Journal on Scientific Computing,2009,31(4):2842-2865.
[31] Yang J,Yin W,Zhang Y,et al.A fast algorithm for edge-preserving variational multichannel image restoration[J].SIAM Journal on Imaging Sciences,2009,2(2):569-592.
[32] Goldstein T,Osher S.The split Bregman method for L1-regularized problems[J].SIAM Journal on Imaging Sciences,2009,2(2):323-343.
[33] Wang Z,Bovik A C,Sheikh H R,et al.Image quality assessment:from error visibility to structural similarity[J].IEEE Transactions on Image Processing,2004,13(4):600-612.
[34] 彭真明,陈颖频,蒲恬,等.基于稀疏表示及正则约束的图像去噪方法综述[J].数据采集与处理,2018,33(1):1-11.PENG Zhenming,CHEN Yingpin,PU Tian,et al.Ima-ge denoising based on sparse representation and re-gularization constraint:A review[J].Journal of Data Acquisition and Processing,2018,33(1):1-11.
[35] 林凡,程祝媛,陈颖频,等.基于交叠组合稀疏全变分的图像去噪方法.科学技术与工程,2018,18(18):67-73.LIN Fan,CHENG Zhuyuan,CHEN Yingpin,et al.Animage denoising method based on overlapping groupsparsity total variation[J].Sceience Technology andEngineering,2018,18(18):67-73.
[36] Sun Y,Babu P,Palomar D P.Majorization-minimization algorithms in signal processing,communications,and machine learning[J].IEEE Transactions on Signal Processing,2016,65(3):794-816.
[2] 屈勇,曹俊兴,朱海东,等.一种改进的全变分地震图像去噪技术[J].石油学报,2011,32(5):815-819.QU Yong,CAO Junxing,ZHU Haidong,et al.An improved total variation based seismic image denoising techonology[J].Acta Petrolei Sinica,2011,32(5):815-819.
[3] Wu L,Chen Y,Jin J,et al.Four-directional fractional-order total variation regularization for image denoising[J].Journal of Electronic Imaging,2017,26(5):053003.
[4] Chen Y,Wu L,Peng Z,et al.Fast overlapping group sparsity total variation image denoising based on fast Fourier transform and split Bergman iterations[C].The 7th International Workshop on Computer Science and Engineering,Beijing,2017,278-282.
[5] 张岩,任伟建,唐国维.利用多道相似组稀疏表示方法压制随机噪声[J].石油地球物理勘探,2017,52(3):442-450.ZHANG Yan,REN Weijian,TANG Guowei.Random noise suppression based on sparse representation of multi-trace similarity group[J].Oil Geophysical Prospecting,2017,52(3):442-450.
[6] 张广智,常德宽,王一惠,等.基于稀疏冗余表示的三维地震数据随机噪声压制[J].石油地球物理勘探,2015,50(4):600-606.ZHANG Guangzhi,CHANG Dekuan,WANG Yihui,et al.3D seismic random noise suppression with sparse and redundant representation[J].Oil Geophy-sical Prospecting,2015,50(4):600-606.
[7] 周亚同,王丽莉,蒲青山.压缩感知框架下基于K-奇异值分解字典学习的地震数据重建[J].石油地球物理勘探,2014,49(4):652-660.ZHOU Yatong,WANG Lili,PU Qingshan.Seismic data reconstruction based on K-SVD dictionary learning under compressive sensing framework[J].Oil Geophysical Prospecting,2014,49(4):652-660.
[8] 宋炜,邹少峰,欧阳永林,等.快速匹配追踪三参数时频特征滤波[J].石油地球物理勘探,2013,48(4):519-525.SONG Wei,ZOU Shaofeng,OUYANG Yonglin,et al.Three parameter time-frequency characteristics filter based on fast matching pursuit[J].Oil Geophysical Prospecting,2013,48(4):519-525.
[9] 魏海涛,陆文凯,郑晓东.基于F-X域预测和全变分的串行滤波器[J].石油地球物理勘探,2011,46(5):700-704.WEI Haitao,LU Wenkai,ZHENG Xiaodong.Cascaded filter based on F-X prediction and total variation filter[J].Oil Geophysical Prospecting,2011,46(5):700-704.
[10] Kong D,Peng Z,Fan H,et al.Seismic random noise attenuation using directional total variation in the shearlet domain[J].Journal of Seismic Exploration,2016,25(4):321-338.
[11] Kong D,Peng Z.Seismic random noise attenuation using shearlet and total generalized variation[J].Journal of Geophysics and Engineering,2015,12(6):1024-1035.
[12] Li S,Peng Z.Seismic acoustic impedance inversion with multi-parameter regularization[J].Journal of Geophysics and Engineering,2017,14(3):520-532.
[13] 王治强,曹思远,陈红灵,等.基于TV约束和Toeplitz矩阵分解的波阻抗反演[J].石油地球物理勘探,2017,52(6):1193-1199.WANG Zhiqiang,CAO Siyuan,CHEN Hongling,et al.Wave impedance inversion based on TV regularization and Toeplitz-sparse matrix factorization[J].Oil Geophysical Prospecting,2017,52(6):1193-1199.
[14] 张盼,韩立国,巩向博,等.基于各向异性全变分约束的多震源弹性波全波形反演[J].地球物理学报,2018,61(2):716-732.ZHANG Pan,HAN Liguo,GONG Xiangbo,et al.Multi-source elastic full waveform inversion based on the anisotropic total variation constraint[J].Chinese Journal of Geophysics,2018,61(2):716-732.
[15] Wang X,Peng Z,Kong D,et al.Infrared dim target detection based on total variation regularization andprincipal component pursuit[J].Image and Vision Computing,2017,63:1-9.
[16] Huang L L,Xiao L,Wei Z H.Efficient and effective total variation image super-resolution:A preconditioned operator splitting approach[J].Mathematical Problems in Engineering,2011,44-48.
[17] Bredies K,Kunisch K,Pock T.Total generalized variation[J].SIAM Journal on Imaging Sciences,2010,3(3):492-526.
[18] Knoll F,Bredies K,Pock T,et al.Second order total generalized variation(TGV) for MRI[J].Magnetic Resonance in Medicine,2011,65(2):480-491.
[19] Guo W,Qin J,Yin W.A new detail-preserving regularization scheme[J]. SIAM Journal on Imaging Sciences,2014,7(2):1309-1334.
[20] Qin J,Yi X,Weiss S,et al.Shearlet-TGV based fluorescence microscopy image deconvolution[R].CAM Report,University of California,Los Angeles (UCLA),2014,14-32.
[21] Liu J,Huang T Z,Selesnick I W,et al.Image restoration using total variation with overlapping group sparsity[J].Information Sciences,2015,295:232-246.
[22] Chen P Y,Selesnick I W.Group-sparse signal denoising: non-convex regularization,convex optimization[J].IEEE Transactions on Signal Processing,2014,62(13):3464-3478.
[23] Chen P Y,Selesnick I W.Translation-invariant shrinka-ge/thresholding of group sparse signals[J].Signal Processing,2014,94:476-489.
[24] Selesnick I,Farshchian M.Sparse signal approximation via nonseparable regularization[J].IEEE Tran-sactions on Signal Processing,2017,65(10):2561-2575.
[25] Liu G,Huang T Z,Liu J,et al.Total variation with overlapping group sparsity for image deblurring under impulse noise[J].Plos One,2015,10(4):e0122562.
[26] Liu J,Huang T Z,Liu G,et al.Total variation with overlapping group sparsity for speckle noise reduction [J].Neurocomputing,2016,216:502-513.
[27] Boyd S.Distributed optimization and statistical learning via the alternating direction method of multipliers [J].Foundations and Trends in Machine Learning,2010,3(1):1-122.
[28] Gabay D,Mercier B.A dual algorithm for the solution of nonlinear variational problems via finite element approximation[J].Computers & Mathematics with Applications,1976,2(1):17-40.
[29] Wang Y,Yang J,Yin W,et al.A new alternating mini-mization algorithm for total variation image reconstruction[J].SIAM Journal on Imaging Sciences,2008,1(3):248-272.
[30] Yang J,Zhang Y,Yin W.An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise[J].SIAM Journal on Scientific Computing,2009,31(4):2842-2865.
[31] Yang J,Yin W,Zhang Y,et al.A fast algorithm for edge-preserving variational multichannel image restoration[J].SIAM Journal on Imaging Sciences,2009,2(2):569-592.
[32] Goldstein T,Osher S.The split Bregman method for L1-regularized problems[J].SIAM Journal on Imaging Sciences,2009,2(2):323-343.
[33] Wang Z,Bovik A C,Sheikh H R,et al.Image quality assessment:from error visibility to structural similarity[J].IEEE Transactions on Image Processing,2004,13(4):600-612.
[34] 彭真明,陈颖频,蒲恬,等.基于稀疏表示及正则约束的图像去噪方法综述[J].数据采集与处理,2018,33(1):1-11.PENG Zhenming,CHEN Yingpin,PU Tian,et al.Ima-ge denoising based on sparse representation and re-gularization constraint:A review[J].Journal of Data Acquisition and Processing,2018,33(1):1-11.
[35] 林凡,程祝媛,陈颖频,等.基于交叠组合稀疏全变分的图像去噪方法.科学技术与工程,2018,18(18):67-73.LIN Fan,CHENG Zhuyuan,CHEN Yingpin,et al.Animage denoising method based on overlapping groupsparsity total variation[J].Sceience Technology andEngineering,2018,18(18):67-73.
[36] Sun Y,Babu P,Palomar D P.Majorization-minimization algorithms in signal processing,communications,and machine learning[J].IEEE Transactions on Signal Processing,2016,65(3):794-816.
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