1. School of Geosciences, China University of Petroleum(East China), Qingdao, Shandong 266580, China; 2. Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao, Shandong 266071, China
Abstract:Compared to a single transformation,the morphological component analysis (MCA) is a more efficient method of sparse representation of signals.In this paper,we propose a seismic data reconstruction method with the discrete cosine transform (DCT) and Shearlet dictionaries under the MCA framework.Firstly,we select the DCT dictionary and the Shearlet dictionary to represent local singular components and smooth linear components of seismic data respectively.Then we reconstruct all the components by the block coordinate relaxation (BCR) algorithm with an exponential threshold model and exponential threshold function.Finally,we merge the components to get a reconstructed result.Experiments on synthetic and real data show that the proposed method can effectively reconstruct missing seismic data and the accuracy of reconstruction is higher than the single Shearlet dictionary,the Curvelet + the DCT dictionaries,the Shearlet + the Curvelet dictionaries.
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.
[2]
Donoho D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[3]
温睿,刘国昌,冉扬.压缩感知地震数据重建中的三个关键因素分析[J].石油地球物理勘探,2018,53(4):682-693.WEN Rui,LIU Guochang and RAN Yang.Three key factors in seismic data reconstruction based on compressive sensing[J].Oil Geophysical Prospecting,2018,53(4):682-693.
[4]
Zwartjes P,Gisolf A.Fourier reconstruction with sparse inversion[J].Geophysical Prospecting,2007,5(2):199-221.
[5]
Herrmann F J,Hennenfent G.Non-parametric seismic data recovery with curvelet frames[J].Geophysical Journal International,2008,173(1):233-248.
[6]
Hennenfent G,Herrmann F J.Simply denoise:Wave-field reconstruction via jittered under sampling[J].Geophysics,2008,73(3):V19-V28.
[7]
陈祖斌,王丽芝,宋扬,等.基于压缩感知的小波域地震数据实时压缩与高精度重建[J].石油地球物理勘探,2018,53(4):674-681,693.CHEN Zubin,WANG Lizhi,SONG Yang,et al.Seismic data real-time compression and high-precision reconstruction in the wavelet domain based on the compressed sensing[J].Oil Geophysical Prospecting,2018,53(4):674-681,693.
[8]
Wu R S,Geng Y,Ye L.Preliminary study on Dreamlet based compressive sensing data recovery[C].SEG Technical Program Expanded Abstracts,2013,32:3585-3590.
[9]
Guo K,Kutyniok G,Labate D.Sparse multidimensional representations using anisotropic dilation and shear operators[C].International Conference on the Interaction Between Wavelets and Splines,2005.
[10]
Labate D,Lim W Q,Kutyniok G,et al.Sparse multidimensional representation using shearlets[J].Optics & Photonics,2005,5914:254-262.
[11]
张良,韩立国,刘争光,等.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):804-811.ZHANG Liang,HAN Liguo,LIU Zhengguang,et al.Seismic data reconstruction based on compressed sensing and Contourlet transform[J].Geophysical Prospecting for Petroleum,2017,56(6):804-811.
[12]
王新全,耿瑜,Wu Ru-Shan,等.基于压缩感知的Drea-mlet域数据重构方法及应用[J].石油地球物理勘探,2015,53(3):399-404.WANG Xinquan,GENG Yu,WU Ru-Shan,et al.Seismic data reconstruction in Dreamlet domain based on compressive sensing[J].Oil Geophysical Prospecting,2015,53(3):399-404.
[13]
郭念民,李海山,冯雪梅,等.非抽样离散小波叠前地震数据重建方法[J].石油地球物理勘探,2014,49(3):508-516.GUO Nianmin,LI Haishan,FENG Xuemei,et al.Pre-stack seismic data reconstruction based on the undecimated wavelet transform[J].Oil Geophysical Prospecting,2014,49(3):508-516.
[14]
Liang J W,Ma J W,Zhang X Q.Seismic data restoration via data-driven tightframe[J].Geophysics,2014,79(3):V65-V74.
[15]
Starck J L,Elad M,Donoho D L.Redundant multiscale transforms and their application for morphological component separation[J].Advances in Imaging & Electron Physics,2004,132(4):287-348.
[16]
李海山,吴国忱,印兴耀.形态分量分析在地震数据重建中的应用[J].石油地球物理勘探,2012,47(2):236-243.LI Haishan,WU Guochen,YIN Xingyao.Morphological component analysis in seismic data reconstruction[J].Oil Geophysical Prospecting,2012,47(2):236-243.
[17]
周亚同,刘志峰,张志伟.形态分量分析框架下基于DCT与曲波字典组合的地震信号重建[J].石油物探,2015, 54(5):560-568.ZHOU Yatong,LIU Zhifeng,ZHANG Zhiwei.Seismic signal reconstruction under the morphological component analysis framework combined with discrete cosine transform (DCT) and curvelet dictionary[J].Geophysical Prospecting for Petroleum,2015,54(5):560-568.
[18]
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.LIU Chengming,WANG Deli,WANG Tong,et al.Random seismic noise attenuation based on the Shearlet transform[J].Acta Petrolei Sinica,2014,35(4):692-699.
[19]
张良,韩立国,许德鑫,等.基于压缩感知技术的Shearlet变换重建地震数据[J].石油地球物理勘探,2017,52(2):220-225.ZHANG Liang,HAN Liguo,XU Dexin,et al.Seismic data reconstruction with Shearlet transform based on compressed sensing technology[J].Oil Geophysical Prospecting,2017,52(2):220-225.
[20]
舒国旭,吕公河,吕尧,等.基于压缩感知的地震数据重建[J].石油物探,2018,57(4):549-554.SHU Guoxu,LYU Gonghe,LYU Yao,et al. Seismic data reconstruction based on compressive sensing[J].Geophysical Prospecting for Petroleum, 2018,57(4):549-554.
[21]
Sardy S,Bruce A G,Tseng P.Block coordinate relaxation methods for nonparametric wavelet denoising[J].Journal of Computational and Graphical Statistics,2000,9(2):361-379.
[22]
Yang P,Fomel S.Seislet-based morphological component analysis using scale-dependent exponential shrinkage[J]. Journal of Applied Geophysics,2015,118:66-74.