模型约束下的在线字典学习地震弱信号去噪方法
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摘要
本文针对噪声成分和噪声结构的复杂性及弱信号的特征,发展了最新的在线字典学习去噪方法.在线字典学习去噪方法是以数据驱动的方式,反复进行学习构建字典方式,求得信号的稀疏性解以实现对信号的去噪,在此基础上,提出了数据驱动与模型驱动联合的模型约束下的在线字典学习去噪方法,先通过模型驱动方式获得一个较优质的学习样本以构建字典再进行去噪处理.通过和传统小波变换进行理论地震合成记录的效果对比,在高噪声比例的弱信号情况下远远优于传统的时频域去噪方法.实际数据去噪处理表明,模型约束下的在线字典学习去噪方法是一种有效的去噪方法,这种联合去噪方式能在高噪声背景下有效地提取出弱信号,具有广阔的推广应用前景.
In this paper,the latest online dictionary learning denoising method is developed for the complexity of noise components and noise structures and the characteristics of weak signals.The online dictionary learning denoising is conducted by means of data-driven and iterative learning to obtain the sparse solution of the signal to realize the denoising of the signal.Based on this,an online dictionary learning denoising method under the combined constraints of datadriven and model-driven models is proposed.A better quality learning sample is obtained in a model driven process to build a dictionary and then to conduct denoising.Compared with the traditional wavelet transform for theoretical seismic synthesis recording,it is far superior to the traditional time-frequency domain denoising method in the case of low-SNR weak signals.The actual data denoising process shows that the online dictionary learning denoising method under model constraints is an effective denoising method.This joint denoising method can effectivelyextract weak signals against high noise and has broad application prospect.
In this paper,the latest online dictionary learning denoising method is developed for the complexity of noise components and noise structures and the characteristics of weak signals.The online dictionary learning denoising is conducted by means of data-driven and iterative learning to obtain the sparse solution of the signal to realize the denoising of the signal.Based on this,an online dictionary learning denoising method under the combined constraints of datadriven and model-driven models is proposed.A better quality learning sample is obtained in a model driven process to build a dictionary and then to conduct denoising.Compared with the traditional wavelet transform for theoretical seismic synthesis recording,it is far superior to the traditional time-frequency domain denoising method in the case of low-SNR weak signals.The actual data denoising process shows that the online dictionary learning denoising method under model constraints is an effective denoising method.This joint denoising method can effectivelyextract weak signals against high noise and has broad application prospect.
引文
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Cheng S J,Han L G,Yu J L,et al.2018.Seismic data denoising based on improved K-SVD dictionary learning method.Global Geology(in Chinese),37(2):627-635.
Deka B,Baishnab D.2012.Removal of random-valued impulse noise using overcomplete DCT dictionary.∥Proceedings of the Cube International Information Technology Conference.New York,NY,USA:ACM:42-46.
Hennenfent G,Herrmann F J.2006.Seismic denoising with nonuniformly sampled curvelets.Computing in Science&Engineering,8(3):16-25.
Jacques L,Duval L,Chaux C,et al.2011.A panorama on multiscale geometric representations,intertwining spatial,directional and frequency selectivity.Signal Processing,91(12):2699-2730.
Jia R S,Zhao T B,Sun H M,et al.2015.Microseismic signal denoising method based on empirical mode decomposition and independent component analysis.Chinese J.Geophys.(in Chinese).58(3):1013-1023.
Kaplan S T,Sacchi M D,Ulrych T J.2009.Sparse coding for datadriven coherent and incoherent noise attenuation.∥79th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
Li L C.2014.Research of seismic signal denoising based on sparse decomposition algorithm[Master′s thesis](in Chinese).Daqing:Northeast Petroleum University.
Ma J W,Plonka G.2011.The curvelet transform.IEEE Signal Processing Magazine,27(2):118-133.
Mairal J,Bach F,Ponce J,et al.2009.Online dictionary learning for sparse coding.∥Proceedings of the 26th Annual International Conference on Machine Learning.New York,NY,USA:ACM,689-696.
Olshausen B A,Millman K J.1997.Learning sparse overcomplete image representations.Proceedings of the SPIE,4119:445-452.
Su J S,Luan X Q.2008.Research of image denoising based on Gabor filter.Journal of Yili Normal University(Natural Science Edition)(in Chinese),(4):15-19.
Tang G,Ma J W,Yang H Z.2012.Seismic data denoising based on learning-type overcomplete dictionaries.Applied Geophysics,9(1):27-32.
Wang D,Liu C,Liu Y,et al.2006.Study of the noise elimination methods in the reflection seismic exploration.Progress in Geophysics(in Chinese),21(3):957-970.
Xu D X.2016.Research on Seismic Denoising Based on The Sparse Representation and Dictionary Learning[Master′s thesis](in Chinese).Changchun:Jilin University.
程时俊,韩立国,于江龙等.2018.基于改进K-SVD字典学习方法的地震数据去噪.世界地质,37(2):627-635.
李立超.2014.基于稀疏分解算法的地震信号去噪研究[硕士论文].大庆:东北石油大学.
苏金善,栾雪琴.2008.基于Gabor滤波器的图像去噪研究.伊犁师范学院学报(自然科学版),(4):15-19.
王典,刘财,刘洋等.2006.反射法地震勘探噪声消除技术研究.地球物理学进展,21(3):957-970.
许德鑫.2016.基于稀疏表示和字典学习的地震数据去噪研究[硕士论文].长春:吉林大学.
贾瑞生,赵同彬,孙红梅等.2015.基于经验模态分解及独立成分分析的微震信号降噪方法.地球物理学报,58(3):1013-1023.
Beckouche S,Ma J M.2014.Simultaneous dictionary learning and denoising for seismic data.Geophysics,79(3):A27-A31.
Cheng S J,Han L G,Yu J L,et al.2018.Seismic data denoising based on improved K-SVD dictionary learning method.Global Geology(in Chinese),37(2):627-635.
Deka B,Baishnab D.2012.Removal of random-valued impulse noise using overcomplete DCT dictionary.∥Proceedings of the Cube International Information Technology Conference.New York,NY,USA:ACM:42-46.
Hennenfent G,Herrmann F J.2006.Seismic denoising with nonuniformly sampled curvelets.Computing in Science&Engineering,8(3):16-25.
Jacques L,Duval L,Chaux C,et al.2011.A panorama on multiscale geometric representations,intertwining spatial,directional and frequency selectivity.Signal Processing,91(12):2699-2730.
Jia R S,Zhao T B,Sun H M,et al.2015.Microseismic signal denoising method based on empirical mode decomposition and independent component analysis.Chinese J.Geophys.(in Chinese).58(3):1013-1023.
Kaplan S T,Sacchi M D,Ulrych T J.2009.Sparse coding for datadriven coherent and incoherent noise attenuation.∥79th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
Li L C.2014.Research of seismic signal denoising based on sparse decomposition algorithm[Master′s thesis](in Chinese).Daqing:Northeast Petroleum University.
Ma J W,Plonka G.2011.The curvelet transform.IEEE Signal Processing Magazine,27(2):118-133.
Mairal J,Bach F,Ponce J,et al.2009.Online dictionary learning for sparse coding.∥Proceedings of the 26th Annual International Conference on Machine Learning.New York,NY,USA:ACM,689-696.
Olshausen B A,Millman K J.1997.Learning sparse overcomplete image representations.Proceedings of the SPIE,4119:445-452.
Su J S,Luan X Q.2008.Research of image denoising based on Gabor filter.Journal of Yili Normal University(Natural Science Edition)(in Chinese),(4):15-19.
Tang G,Ma J W,Yang H Z.2012.Seismic data denoising based on learning-type overcomplete dictionaries.Applied Geophysics,9(1):27-32.
Wang D,Liu C,Liu Y,et al.2006.Study of the noise elimination methods in the reflection seismic exploration.Progress in Geophysics(in Chinese),21(3):957-970.
Xu D X.2016.Research on Seismic Denoising Based on The Sparse Representation and Dictionary Learning[Master′s thesis](in Chinese).Changchun:Jilin University.
程时俊,韩立国,于江龙等.2018.基于改进K-SVD字典学习方法的地震数据去噪.世界地质,37(2):627-635.
李立超.2014.基于稀疏分解算法的地震信号去噪研究[硕士论文].大庆:东北石油大学.
苏金善,栾雪琴.2008.基于Gabor滤波器的图像去噪研究.伊犁师范学院学报(自然科学版),(4):15-19.
王典,刘财,刘洋等.2006.反射法地震勘探噪声消除技术研究.地球物理学进展,21(3):957-970.
许德鑫.2016.基于稀疏表示和字典学习的地震数据去噪研究[硕士论文].长春:吉林大学.
贾瑞生,赵同彬,孙红梅等.2015.基于经验模态分解及独立成分分析的微震信号降噪方法.地球物理学报,58(3):1013-1023.