1.College of Geo-Exploration Science and Technology,Jilin University,Changchun 130026,China; 2.China Water Northeastern Investigation,Design & Research Co. Ltd.,Changchun 130062,China;
Abstract：In seismic exploration,the random noise severely distorts and interferes with seismic signals,and hence the denoising process is very important.In order to meet the high-precision requirement,the authors,based on the sparse and redundant representation theory,improve the dictionary update stage and the sparse coding stage in the conventional dictionary learning algorithm.While keeping the supports intact,the dictionary atoms are recurrently updated to adapt them to the specific seismic data.In the dictionary domain,large coefficients represent effective signals.Taking full advantage of this characteristic,the authors use several large coefficients from the last round of iteration as initial coefficients.In this way,the computational efficiency of the learning algorithm can be improved.The new algorithm is applied to synthetic and field seismic records and compared with the conventional K-SVD algorithm.The denoising results are satisfactory.It is shown that the new method can remove the random noise and protect the effective information at the same time.It is competitive in improving the signal-to-noise ratio of seismic records.
[1] 孙晶明.压缩感知中观测矩阵的研究[D].武汉:华中科技大学,2013. [2] Yu L L.EEG de-noising based on wavelet transformation[C]//Proceedings of the 3 rd International Conference on—Bioinformatics and Biomedical Engineering.Beijing,China:IEEE,2009:1 4. [3] 李雪英,张晶,孔祥琦,等.基于离散小波变换的地震资料自适应高频噪声压制[J].物探与化探,2013,37(1):165-170. [4] 何柯,周丽萍,于宝利,等.基于补偿阈值的曲波变换地面微地震弱信号检测方法[J].物探与化探,2016,40(1):55-60. [5] 刘国昌,陈小宏,郭志峰,等.基于Curvelet变换的缺失地震数据插值方法[J].石油地球物理勘探,2011,46(2):237-246. [6] 薛永安,王勇,李红彩,等.改进的曲波变换及全变差联合去噪技术[J].物探与化探,2014,38(1):81-86. [7] 刘成明,王德利,王通,等.基于Shearlet变换的地震随机噪声压制[J].石油学报,2014,35(4):692-699. [8] 王德营,李振春,董烈乾.Shearlet域和TT域联合压制面波方法[J].石油地球物理勘探,2014,49(1):53-60. [9] 路交通,曹思远,董建华,等.基于稀疏变换的地震数据重构方法[J].物探与化探,2013,37(1):175-179. [10] Kelly S E.Gibbs phenomenon for wavelets[J].Applied and Computational Harmonic Analysis,1996,3(1):72-81. [11] Elad M,Aharon M.Image denoising via learned dictionaries and sparse representation[C]//Proceedings of IEEE Computer Society Conference on Computer Vision & Pattern Recognition.New York,NY,USA:IEEE,2006,:895-900. [12] Protter M,Elad M.Image sequence denoising via sparse and redundant representations[J].IEEE Transactions on Image Processing,2009,18(1):27-35. [13] 蔡泽民,赖剑煌.一种基于超完备字典学习的图像去噪方法[J].电子学报,2009,37(2):347-350. [14] Zhou Z,Luo L M.Research on image denoising algorithm based on adaptive overcomplete sparse representation theories[J].Journal of Convergence Information Technology,2012,7(16):315-321. [15] 刘钢.基于压缩感知和稀疏表示理论的图像去噪研究[D].成都:电子科技大学,2013. [16] Li M,Zhou G,Zhao B,et al.Radar HRRP adaptive denoising via sparse and redundant representations[C]//Proceedings of the International Symposium on Antennas & Propagation,Nanjing,China:IEEE,2013:1094-1097. [17] Deka B,Bora P K.Removal of correlated speckle noise using sparse and overcomplete representations[J].Biomedical Signal Processing and Control,2013,8(6):520-533. [18] 银壮辰.基于稀疏表示和字典学习的图像去噪研究[D].武汉:武汉理工大学,2014. [19] Tang G,Ma J W,Yang H Z.Seismic data denoising based on learning-type over-complete dictionaries[J].Applied Geophysics,2012,9(1):27-32. [20] 唐刚.基于压缩感知和稀疏表示的地震数据重建与去噪[D].清华大学,2010. [21] Aharon M,Elad M,Bruckstein A. rmK -SVD:An algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Transactions on Signal Processing,2006,54(11):4311-4322. [22] Bryt O,Elad M.Compression of facial images using the K-SVD algorithm[J].Journal of Visual Communication and Image Representation,2008,19(4):270-282. [23] 沈鸿雁.SVD地震波场分离与去噪技术在鄂尔多斯盆地地震资料处理中的应用[J].地球物理学进展,2012,27(5):2051-2058. [24] 邵婕,孙成禹,唐杰,等.基于字典训练的小波域稀疏表示微地震去噪方法[J].石油地球物理勘探,2016,51(2):254-260. [25] Pati Y C,Rezaiifar R,Krishnaprasad P S.Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition[C]//Proceedings of the Twenty-Seventh Asilomar—Conference on Signals,Systems and Computers,Pacific Grove,CA:IEEE,1993:40-44. [26] Mallat S G,Zhang Z.Matching pursuits with time-frequency dictionaries[J].IEEE Transactions on Signal Processing,1994,41(12):3397-3415. [27] Smith L N,Elad M.Improving dictionary learning:uultiple dictionary updates and coefficient reuse[J].IEEE Signal Processing Letters,2013,20(1):79-82.
