基于字典学习和ADMM的地震数据重建
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摘要
针对压缩感知下与字典学习和交替方向乘子算法(alternating direction method of multipliers,ADMM)密切相关方法存在的问题,研究并提出了一种在压缩感知理论下采用字典学习和ADMM重建地震数据的方法。首先对不完整地震数据进行字典学习,使其稀疏地表示,再根据地震道的缺失情况设计合理的采样矩阵,最后对建立的L1范数约束模型采用ADMM进行求解得到重建后的地震数据。建立了压缩感知下基于字典学习和ADMM的地震数据插值技术流程。正演模拟数据和实际数据的重建实验结果表明:与压缩感知理论下采用固定基的重建方法相比,字典学习能够自适应地对地震数据进行更优的稀疏表示。与常用的curvelet等重建算法相比,采用ADMM能够更加精确地重建地震数据。与固定基和正交匹配追踪(orthogonal matching pursuit,OMP)相比,在压缩感知理论下采用字典学习和ADMM重建的地震数据有更高的信噪比。
This paper proposes a seismic data reconstruction method using dictionary learning and the alternating direction method of multipliers(ADMM) based on compressed sensing.Firstly,a learned dictionary is used to sparsely represent the incomplete seismic data.Then,a reasonable measurement matrix is designed.Finally,the L1-norm constrained model is solved by the ADMM to obtain the reconstructed seismic data.In addition,a seismic data interpolation flow is established,which uses dictionary learning and the ADMM based on compressed sensing.Compared to reconstruction methods using a fixed basis,the dictionary learning is able to sparsely represent seismic data adaptively.Compared to conventional reconstruction algorithms,such as the curvelet,the ADMM can reconstruct seismic data more accurately.Tests on both synthetic and real data indicated that the results of the reconstruction obtained with the proposed method have a higher signal-to-noise ratio(SNR) than those obtained using fixed base and orthogonal matching pursuit(OMP) methods.
This paper proposes a seismic data reconstruction method using dictionary learning and the alternating direction method of multipliers(ADMM) based on compressed sensing.Firstly,a learned dictionary is used to sparsely represent the incomplete seismic data.Then,a reasonable measurement matrix is designed.Finally,the L1-norm constrained model is solved by the ADMM to obtain the reconstructed seismic data.In addition,a seismic data interpolation flow is established,which uses dictionary learning and the ADMM based on compressed sensing.Compared to reconstruction methods using a fixed basis,the dictionary learning is able to sparsely represent seismic data adaptively.Compared to conventional reconstruction algorithms,such as the curvelet,the ADMM can reconstruct seismic data more accurately.Tests on both synthetic and real data indicated that the results of the reconstruction obtained with the proposed method have a higher signal-to-noise ratio(SNR) than those obtained using fixed base and orthogonal matching pursuit(OMP) methods.
引文
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[13] ZHANG H,CHEN X H,WU X M.Seismic data reconstruction based on CS and Fourier theory[J].Applied Geophysics,2013,10(2):170-180
[14] LIANG J,MA J,ZHANG X.Seismic data restoration via data-driven tight frame[J].Geophysics,2014,79(3):V65-V74
[15] 马继涛,王建花,刘国昌.基于频率域奇异值分解的地震数据插值去噪方法研究[J].石油物探,2016,55(2):205-213MA J T,WANG J H,LIU G C.Seismic data noise attenuation and interpolation using singular value decomposition in frequency domain[J].Geophysical Prospectiong for Petroleum,2016,55(2):205-213
[16] ZHU L,LIU E,MCCLELLAN J H.Seismic data denoising through multiscale and sparsity-promoting dictionary learning[J].Geophysics,2015,80(6):WD45-WD57
[17] BOYD S,PARIKH N,CHU E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations and Trends? in Machine Learning,2011,3(1):1-122
[18] STERNFELS R,VIGUIER G,GONDOIN R,et al.Multidimensional simultaneous random plus erratic noise attenuation and interpolation for seismic data by joint low-rank and sparse inversion[J].Geophysics,2015,80(6):WD129-WD141
[19] HARIKUMAR K,ATHIRA S,NAIR Y C,et al.ADMM based algorithm for spike and smooth signal separation using over-complete dictionary[C]//Communications and Signal Processing (ICCSP).2015 International Conference on Communications and Signal Processing (ICCSP).India:Melmaruvathur,2015:1617-1622
[20] ZHOU Y,GAO J,CHEN W,et al.Seismic simultaneous source separation via patchwise sparse representation[J].IEEE Transactions on Geoscience and Remote Sensing,2016,54(9):5271-5284
[21] BARANIUK R G.Compressive sensing[J].IEEE Signal Processing Magazine,2007,24(4):118-121
[22] GLEICHMAN S,ELDAR Y C.Blind compressed sensing[J].IEEE Transactions on Information Theory,2011,57(10):6958-6975
[23] AHARON M,ELAD M,BRUCKSTEIN A.K-SVD:An algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Transactions on Signal Processing,2006,54(11):4311-4322
[2] SPITZ S.Seismic trace interpolation in the f-x domain[J].Geophysics,1991,56(6):785-794
[3] ZWARTJES P,GISOLF A.Fourier reconstruction with sparse inversion[J].Geophysical Prospecting,2007,55(2):199-221
[4] 王本锋,陆文凯,陈小宏,等.基于3D Curvelet变换的频率域高效地震数据插值方法研究[J].石油物探,2018,57(1):65-71WANG B F,LU W K,CHEN X H,et al.Efficient seismic data interpolation using three-dimensional Curvelet transform in the frequency domain[J].Geophysical Prospectiong for Petroleum,2018,57(1):65-71
[5] 周艳辉,陈文超.基于稀疏反演的同步震源地震数据分离方法[J].石油物探,2018,57(1):33-38ZHOU Y H,CHEN W C.Separation of simultaneous source data based on sparse inversion[J].Geophysical Prospectiong for Petroleum,2018,57(1):33-38
[6] 张良,韩立国,刘争光.基于压缩感知和Contourlet变换的地震数据重建方法[J].石油物探,2017,56(6):804-811ZHANG L,HAN L G,LIU Z G.Seismic data reconstruction based on compressed sensing and Contourlet transform[J].Geophysical Prospectiong for Petroleum,2017,56(6):804-811
[7] ZHOU Y H,CHEN W C,GAO J H,et al.Seismic deblending by sparse inversion over dictionary learning[J].Expanded Abstracts of 83rd Annual Internat SEG Mtg,2013:273-278
[8] ZHOU Y H,CHEN W C,GAO J H,et al.Separation of seismic blended data by sparse inversion over dictionary learning[J].Journal of Applied Geophysics,2014,106(1):146-153
[9] 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):652-662ZHOU Y T,WANG L L,PU Q S.K-SVD and Dictionary learning of seismic data recovery based on compressed sensing[J].Oil Geophysical Prospecting,2014,49(4):652-662
[10] CANDèS E J,ROMBERG J,TAO T.Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information[J].IEEE Transactions on Information Theory,2006,52(2):489-509
[11] DONOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306
[12] HERRMANN F J,HENNENFENT G.Non-parametric seismic data recovery with curvelet frames[J].Geophysical Journal International,2008,173(1):233-248
[13] ZHANG H,CHEN X H,WU X M.Seismic data reconstruction based on CS and Fourier theory[J].Applied Geophysics,2013,10(2):170-180
[14] LIANG J,MA J,ZHANG X.Seismic data restoration via data-driven tight frame[J].Geophysics,2014,79(3):V65-V74
[15] 马继涛,王建花,刘国昌.基于频率域奇异值分解的地震数据插值去噪方法研究[J].石油物探,2016,55(2):205-213MA J T,WANG J H,LIU G C.Seismic data noise attenuation and interpolation using singular value decomposition in frequency domain[J].Geophysical Prospectiong for Petroleum,2016,55(2):205-213
[16] ZHU L,LIU E,MCCLELLAN J H.Seismic data denoising through multiscale and sparsity-promoting dictionary learning[J].Geophysics,2015,80(6):WD45-WD57
[17] BOYD S,PARIKH N,CHU E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations and Trends? in Machine Learning,2011,3(1):1-122
[18] STERNFELS R,VIGUIER G,GONDOIN R,et al.Multidimensional simultaneous random plus erratic noise attenuation and interpolation for seismic data by joint low-rank and sparse inversion[J].Geophysics,2015,80(6):WD129-WD141
[19] HARIKUMAR K,ATHIRA S,NAIR Y C,et al.ADMM based algorithm for spike and smooth signal separation using over-complete dictionary[C]//Communications and Signal Processing (ICCSP).2015 International Conference on Communications and Signal Processing (ICCSP).India:Melmaruvathur,2015:1617-1622
[20] ZHOU Y,GAO J,CHEN W,et al.Seismic simultaneous source separation via patchwise sparse representation[J].IEEE Transactions on Geoscience and Remote Sensing,2016,54(9):5271-5284
[21] BARANIUK R G.Compressive sensing[J].IEEE Signal Processing Magazine,2007,24(4):118-121
[22] GLEICHMAN S,ELDAR Y C.Blind compressed sensing[J].IEEE Transactions on Information Theory,2011,57(10):6958-6975
[23] AHARON M,ELAD M,BRUCKSTEIN A.K-SVD:An algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Transactions on Signal Processing,2006,54(11):4311-4322