基于学习型超完备字典的地震数据去噪(英文)
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摘要
基于变换基函数的方法,是地震去噪处理中最常用的技术之一,它利用地震数据在某种基函数变换域内的稀疏性和可分离性来达到剔除噪声的目的。但传统的做法是事先选定一组固定的变换基并在对应域内进行处理,其效果往往并不十分令人满意。为了探索新的改进方法,我们引入学习型超完备冗余字典,即根据地震模型数据进行学习和训练,以寻求最优的稀疏表示字典,而不是只选用固定的变换基。本文在字典学习中融入全变差最小化策略以压制伪吉布斯现象。我们选用离散傅里叶变换作为初始变换,并以随机噪声为例,对单一的全局变换、未经学习的超完备冗余字典和学习型超完备冗余字典做了比较。结果表明,利用经过训练的超完备冗余字典,在对地震数据进行稀疏表示的同时,也达到了有效去除噪声的目的,可视性和信噪比都得到了明显提高。我们也比较了均匀和不均匀字典子块的效果,结果表明,不均匀的字典子块更利于地震数据去噪。
The transform base function method is one of the most commonly used techniques for seismic denoising, which achieves the purpose of removing noise by utilizing the sparseness and separateness of seismic data in the transform base function domain. However, the effect is not satisfactory because it needs to pre-select a set of fixed transform-base functions and process the corresponding transform. In order to find a new approach, we introduce learning-type overcomplete dictionaries, i.e., optimally sparse data representation is achieved through learning and training driven by seismic modeling data, instead of using a single set of f ixed transform bases. In this paper, we combine dictionary learning with total variation (TV) minimization to suppress pseudo-Gibbs artifacts and describe the effects of non-uniform dictionary sub-block scale on removing noises. Taking the discrete cosine transform and random noise as an example, we made comparisons between a single transform base, non-learning-type, overcomplete dictionary and a learning-type overcomplete dictionary and also compare the results with uniform and nonuniform size dictionary atoms. The results show that, when seismic data is represented sparsely using the learning-type overcomplete dictionary, noise is also removed and visibility and signal to noise ratio is markedly increased. We also compare the results with uniform and nonuniform size dictionary atoms, which demonstrate that a nonuniform dictionary atom is more suitable for seismic denoising.
The transform base function method is one of the most commonly used techniques for seismic denoising, which achieves the purpose of removing noise by utilizing the sparseness and separateness of seismic data in the transform base function domain. However, the effect is not satisfactory because it needs to pre-select a set of fixed transform-base functions and process the corresponding transform. In order to find a new approach, we introduce learning-type overcomplete dictionaries, i.e., optimally sparse data representation is achieved through learning and training driven by seismic modeling data, instead of using a single set of f ixed transform bases. In this paper, we combine dictionary learning with total variation (TV) minimization to suppress pseudo-Gibbs artifacts and describe the effects of non-uniform dictionary sub-block scale on removing noises. Taking the discrete cosine transform and random noise as an example, we made comparisons between a single transform base, non-learning-type, overcomplete dictionary and a learning-type overcomplete dictionary and also compare the results with uniform and nonuniform size dictionary atoms. The results show that, when seismic data is represented sparsely using the learning-type overcomplete dictionary, noise is also removed and visibility and signal to noise ratio is markedly increased. We also compare the results with uniform and nonuniform size dictionary atoms, which demonstrate that a nonuniform dictionary atom is more suitable for seismic denoising.
引文
Broadhead, M., 2008, The impact of random noise on seismic wavelet estimation: The Leading Edge, 27(2), 226 – 230.
Candes, E., and Donoho, D., 2002, New tight frames of curvelets and optimal representations of objects with smooth singularities: Technical Report, Stanford University.
Deng, C. Z., 2008, Research on image sparse representation theory and its applications: PhD Thesis, Huazhong University of Science and Technology.
Elad, M., and Aharon, M., 2006, Image denoising via sparse and redundant representations over learned dictionaries: IEEE Trans. Image Process, 15(12), 3736 – 3745.
Herrmann, F., and Hennenfent, G., 2008, Non-parametricseismic data recovery with curvelet frames: Geophys. J.Int., 173, 233 – 248.
Meyer, F. G., 1999, Fast compression of seismic data with local trigonometric bases, in Aldroubi, A., Laine, A., and Unser, M., Eds., Wavelet VII: Proc. SPIE 3813, 648 – 658.
Protter, M., and Elad, M., 2009, Image sequence denoising via sparse and redundant representations: IEEE Trans. Image Process, 18(1), 27 – 35.
Shan, H., Ma, J. W., and Yang, H. Z., 2009, Comparisons of wavelets, contourlets and curvelets in seismic denoising: Journal of Applied Geophysics, 69, 103 – 115.
Tang, G., and Ma, J. W., 2009, Application of total variation based curvelet shrinkage for three-dimensional seismic data denoising: IEEE Geosci. Remote Sensing Lett.,8(1), 103 – 107. van den Berg, E., and Friedlander, M., 2008, Probing the Pareto frontier for basis pursuit solutions: SIAM J. Scientifi c Computing, 31(2), 890 – 912.
Wang, Y., and Wu, R., 2000, Seismic data compression by an adaptive local cosine/sine transform and its effects on migration: Geophysical Prospecting, 48, 1009 – 1031.
Xiao, Q., Deng, X. H., Wang, S. J., et al., 2009, Image denoising based on adaptive over-complete sparse representation: Chinese Journal of Scientifi c Instrument, 30(9), 1886 – 1890.
Zhang, C. M., Yin, Z. K., and Xiao, M. X., 2006, Overcomplete representation and sparse decomposition of signals based on redundant dictionary: Chinese Science Bulletin, 51(6), 628 – 632.
Zheludev, A. V. A., Koslo, B., Dan, D., and Ragoza, E. Y., 2004, On compression of segmented 3D seismic data: International Journal of Wavelets, Multiresolution and Information Processing, 2(3), 269 – 281.
Candes, E., and Donoho, D., 2002, New tight frames of curvelets and optimal representations of objects with smooth singularities: Technical Report, Stanford University.
Deng, C. Z., 2008, Research on image sparse representation theory and its applications: PhD Thesis, Huazhong University of Science and Technology.
Elad, M., and Aharon, M., 2006, Image denoising via sparse and redundant representations over learned dictionaries: IEEE Trans. Image Process, 15(12), 3736 – 3745.
Herrmann, F., and Hennenfent, G., 2008, Non-parametricseismic data recovery with curvelet frames: Geophys. J.Int., 173, 233 – 248.
Meyer, F. G., 1999, Fast compression of seismic data with local trigonometric bases, in Aldroubi, A., Laine, A., and Unser, M., Eds., Wavelet VII: Proc. SPIE 3813, 648 – 658.
Protter, M., and Elad, M., 2009, Image sequence denoising via sparse and redundant representations: IEEE Trans. Image Process, 18(1), 27 – 35.
Shan, H., Ma, J. W., and Yang, H. Z., 2009, Comparisons of wavelets, contourlets and curvelets in seismic denoising: Journal of Applied Geophysics, 69, 103 – 115.
Tang, G., and Ma, J. W., 2009, Application of total variation based curvelet shrinkage for three-dimensional seismic data denoising: IEEE Geosci. Remote Sensing Lett.,8(1), 103 – 107. van den Berg, E., and Friedlander, M., 2008, Probing the Pareto frontier for basis pursuit solutions: SIAM J. Scientifi c Computing, 31(2), 890 – 912.
Wang, Y., and Wu, R., 2000, Seismic data compression by an adaptive local cosine/sine transform and its effects on migration: Geophysical Prospecting, 48, 1009 – 1031.
Xiao, Q., Deng, X. H., Wang, S. J., et al., 2009, Image denoising based on adaptive over-complete sparse representation: Chinese Journal of Scientifi c Instrument, 30(9), 1886 – 1890.
Zhang, C. M., Yin, Z. K., and Xiao, M. X., 2006, Overcomplete representation and sparse decomposition of signals based on redundant dictionary: Chinese Science Bulletin, 51(6), 628 – 632.
Zheludev, A. V. A., Koslo, B., Dan, D., and Ragoza, E. Y., 2004, On compression of segmented 3D seismic data: International Journal of Wavelets, Multiresolution and Information Processing, 2(3), 269 – 281.
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