2D地震数据规则化中随机稀疏采样方案(英文)
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摘要
地震数据规则化是地震信号处理中一个重要步骤,近年来受到广泛关注的压缩感知技术已经被应用到地震数据规则化中。压缩感知技术突破了传统的Shannon-Nyqiust采样定理的限制,可以用采集的少量地震数据重构完整数据。基于压缩感知技术的地震数据规则化质量主要受三个因素影响,除了受地震信号在不同变换域的稀疏表达和11范数重构算法的影响外,极大地取决于地震道随机稀疏采样方式。尽管已有学者开展了2D地震数据离散均匀分布随机采样方式研究,但设计新的稀疏采样方案仍然很有必要。在本文中,我们提出满足Bernoulli分布规律的Bernoulli随机稀疏采样方式和它的抖动形式。对2D数值模拟数据进行四种随机稀疏采样方案和两种变换(Fourier变换和Curvelet变换)实验,对获取的不完整数据应用11范数谱投影梯度算法(SPGL1)进行重构。考虑到不同随机种子点产生不同约束矩阵R会有不同的规则化质量,对每种方案和每个稀疏采样因子进行10次规则化实验,并计算出相应信噪比(SNR)的平均值和标准偏差。实验结果表明,我们提出的新方案好于或等于已有的离散均匀分布采样方案。
Seismic data regularization is an important preprocessing step in seismic signal processing. Traditional seismic acquisition methods follow the Shannon–Nyquist sampling theorem, whereas compressive sensing(CS) provides a fundamentally new paradigm to overcome limitations in data acquisition. Besides the sparse representation of seismic signal in some transform domain and the 1-norm reconstruction algorithm, the seismic data regularization quality of CS-based techniques strongly depends on random undersampling schemes. For 2D seismic data, discrete uniform-based methods have been investigated, where some seismic traces are randomly sampled with an equal probability. However, in theory and practice, some seismic traces with different probability are required to be sampled for satisfying the assumptions in CS. Therefore, designing new undersampling schemes is imperative. We propose a Bernoulli-based random undersampling scheme and its jittered version to determine the regular traces that are randomly sampled with different probability, while both schemes comply with the Bernoulli process distribution. We performed experiments using the Fourier and curvelet transforms and the spectral projected gradient reconstruction algorithm for 1-norm(SPGL1), and ten different random seeds. According to the signal-to-noise ratio(SNR) between the original and reconstructed seismic data, the detailed experimental results from 2D numerical and physical simulation data show that the proposed novel schemes perform overall better than the discrete uniform schemes.
Seismic data regularization is an important preprocessing step in seismic signal processing. Traditional seismic acquisition methods follow the Shannon–Nyquist sampling theorem, whereas compressive sensing(CS) provides a fundamentally new paradigm to overcome limitations in data acquisition. Besides the sparse representation of seismic signal in some transform domain and the 1-norm reconstruction algorithm, the seismic data regularization quality of CS-based techniques strongly depends on random undersampling schemes. For 2D seismic data, discrete uniform-based methods have been investigated, where some seismic traces are randomly sampled with an equal probability. However, in theory and practice, some seismic traces with different probability are required to be sampled for satisfying the assumptions in CS. Therefore, designing new undersampling schemes is imperative. We propose a Bernoulli-based random undersampling scheme and its jittered version to determine the regular traces that are randomly sampled with different probability, while both schemes comply with the Bernoulli process distribution. We performed experiments using the Fourier and curvelet transforms and the spectral projected gradient reconstruction algorithm for 1-norm(SPGL1), and ten different random seeds. According to the signal-to-noise ratio(SNR) between the original and reconstructed seismic data, the detailed experimental results from 2D numerical and physical simulation data show that the proposed novel schemes perform overall better than the discrete uniform schemes.
引文
Baraniuk,R.G.,2007,Compressive sensing:IEEESignal Processing Magazine,24(4),118–121.
Baraniuk,R.G.,2011,More is less:signal processingand the data deluge:Science,331(6018),717–719.
Berg,E.V.D.,and Friedlander,M.P.,2008,Probingthe Pareto frontier for basis pursuit solutions:SIAMJournal on Scientifi c Computing,31(2),890–912.
Berg,E.V.D.,Friedlander,M.P.,Hennenfent,G.,Herrmann,F.J.,Saab,R.,and Yilmaz,O.,2009,Algorithm 890:Sparco:a testing framework for sparsereconstruction:ACM Transactions on MathematicalSoftware,35(4),1–16.
Billingsley,P.,1986,Probability and measure(2ndEdition):Wiley press.
Candes,E.J.,2006,Compressive sampling:InternationalCongress of Mathematics,3,1433–1452.
Davenport,M.,Duarte,M.,Eldar,Y.C.,and Kutyniok,G.,2012,Introduction to compressed sensing,InEldar,Y.C.,and Kutyniol,G.,Eds.,CompressedSensing:Theory and Applications:CambridgeUniversity Press.
Donoho,D.,2006,Compressed sensing:IEEETransactions on Information Theory,52(4),1289–1306.
Fornasier,M.,2010,Theoretical foundations andnumerical methods for sparse recovery:de GruyterPress.
Hennenfent,G.,and Herrmann,F.J.,2008,Simplydenoise:wavefield reconstruction via jitteredundersampling:Geophysics,73(3),V19–V28.
Herrmann,F.J.,Wang,D.,Hennenfent,G.,andMoghaddam,P.P.,2008,Curvelet-based seismic dataprocessing:a multiscale and nonlinear approach:Geophysics,73(1),A1–A5.
H e r r m a n n,F.J.,a n d H e n n e n f e n t,G.,2 0 0 8,Nonparametric seismic data recovery with curveletframes:Geophysical Journal International,173(1),233–248.
Herrmann,F.J.,2010,Randomized sampling andsparsity:getting more information from fewersamples:Geophysics,75(6),WB172–WB187.
Li,C.,Mosher C.C.,Shan,S.,and Brewer,J.D.,2013,Marine towed streamer data reconstruction based oncompressive sensing:83th Ann.Soc.Expl.Geophys.Mtg.,Expanded Abstracts,3597–3602.
Mansour,H.,Herrmann,F.J.,and Yilmaz,O,2013,Improved wavefield reconstruction from randomizedsampling via weighted one-norm minimization:Geophysics,78(5),V193–V206
Patel,V.M.,and Chellappa,R.,2013,Sparserepresentations and compressive sensing for imagingand vision,Springer press.
Shao,J.,2003,Mathematical statistics(2nd Edition):Springer press.
Wang,S.,Li,J.,Chiu,S.K.,and Anno,P.D.,2010,Seismic data compression and regularization viawave packets:80th Ann.Soc.Expl.Geophys.Mtg.,Expanded Abstracts,3650–3655.
Wang,Y.,Cao,J.,and Yang,C.,2011,Recovery ofseismic wavefield-based on compressive sensing byan l1-norm constrained trust region method and thepiecewise random subsampling:Geophysical JournalInternational,187(1),199–213.
Wu,R.-S.,Geng,Y.and Ye,L.,2013,Preliminary studyon dreamlet-based compressive sensing data recovery:83th Ann.Soc.Expl.Geophys.Mtg.,ExpandedAbstracts,3585–3590.
Baraniuk,R.G.,2011,More is less:signal processingand the data deluge:Science,331(6018),717–719.
Berg,E.V.D.,and Friedlander,M.P.,2008,Probingthe Pareto frontier for basis pursuit solutions:SIAMJournal on Scientifi c Computing,31(2),890–912.
Berg,E.V.D.,Friedlander,M.P.,Hennenfent,G.,Herrmann,F.J.,Saab,R.,and Yilmaz,O.,2009,Algorithm 890:Sparco:a testing framework for sparsereconstruction:ACM Transactions on MathematicalSoftware,35(4),1–16.
Billingsley,P.,1986,Probability and measure(2ndEdition):Wiley press.
Candes,E.J.,2006,Compressive sampling:InternationalCongress of Mathematics,3,1433–1452.
Davenport,M.,Duarte,M.,Eldar,Y.C.,and Kutyniok,G.,2012,Introduction to compressed sensing,InEldar,Y.C.,and Kutyniol,G.,Eds.,CompressedSensing:Theory and Applications:CambridgeUniversity Press.
Donoho,D.,2006,Compressed sensing:IEEETransactions on Information Theory,52(4),1289–1306.
Fornasier,M.,2010,Theoretical foundations andnumerical methods for sparse recovery:de GruyterPress.
Hennenfent,G.,and Herrmann,F.J.,2008,Simplydenoise:wavefield reconstruction via jitteredundersampling:Geophysics,73(3),V19–V28.
Herrmann,F.J.,Wang,D.,Hennenfent,G.,andMoghaddam,P.P.,2008,Curvelet-based seismic dataprocessing:a multiscale and nonlinear approach:Geophysics,73(1),A1–A5.
H e r r m a n n,F.J.,a n d H e n n e n f e n t,G.,2 0 0 8,Nonparametric seismic data recovery with curveletframes:Geophysical Journal International,173(1),233–248.
Herrmann,F.J.,2010,Randomized sampling andsparsity:getting more information from fewersamples:Geophysics,75(6),WB172–WB187.
Li,C.,Mosher C.C.,Shan,S.,and Brewer,J.D.,2013,Marine towed streamer data reconstruction based oncompressive sensing:83th Ann.Soc.Expl.Geophys.Mtg.,Expanded Abstracts,3597–3602.
Mansour,H.,Herrmann,F.J.,and Yilmaz,O,2013,Improved wavefield reconstruction from randomizedsampling via weighted one-norm minimization:Geophysics,78(5),V193–V206
Patel,V.M.,and Chellappa,R.,2013,Sparserepresentations and compressive sensing for imagingand vision,Springer press.
Shao,J.,2003,Mathematical statistics(2nd Edition):Springer press.
Wang,S.,Li,J.,Chiu,S.K.,and Anno,P.D.,2010,Seismic data compression and regularization viawave packets:80th Ann.Soc.Expl.Geophys.Mtg.,Expanded Abstracts,3650–3655.
Wang,Y.,Cao,J.,and Yang,C.,2011,Recovery ofseismic wavefield-based on compressive sensing byan l1-norm constrained trust region method and thepiecewise random subsampling:Geophysical JournalInternational,187(1),199–213.
Wu,R.-S.,Geng,Y.and Ye,L.,2013,Preliminary studyon dreamlet-based compressive sensing data recovery:83th Ann.Soc.Expl.Geophys.Mtg.,ExpandedAbstracts,3585–3590.