基于泊松碟采样的地震数据压缩重建
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摘要
在地震资料处理领域,数据的压缩和重建是非常重要的问题,但往往由于数据的严重缺失或采样原因而达不到理想的效果.新发展起来的压缩感知理论为重建欠采样数据提供了可能,而选用合适的采样方法是其中的关键技术之一.本文基于傅里叶变换和压缩感知理论,采用泊松碟采样,对不完整地震数据进行恢复重建.数值实验表明,与传统的单纯随机采样方法相比,泊松碟采样方法在保持采样随机性的同时,使采样点的分布更加均匀,有效地调节了采样间距,从而达到更好的恢复效果,可以有效地指导地震数据采集设计及重建.
Compression and reconstruction are very common and necessary in seismic data processing, but usually it is impossible to get high-quality results, due to severely missing traces or sampling problems.A newly developed theory, named compressive sensing, provides the possibility for recovering undersampled data, where proper sampling scheme is one of the key techniques.In this paper, we employ Poisson Disk sampling, which possesses blue-noise pattern spectrum, to improve the recovery quality based on Fourier transform and compressive sensing. Experiments show that Poisson Disk sampling can achieve better recovery than simply random sampling, due to its ability to distribute samples more uniformly and keep randomness at the same time.
Compression and reconstruction are very common and necessary in seismic data processing, but usually it is impossible to get high-quality results, due to severely missing traces or sampling problems.A newly developed theory, named compressive sensing, provides the possibility for recovering undersampled data, where proper sampling scheme is one of the key techniques.In this paper, we employ Poisson Disk sampling, which possesses blue-noise pattern spectrum, to improve the recovery quality based on Fourier transform and compressive sensing. Experiments show that Poisson Disk sampling can achieve better recovery than simply random sampling, due to its ability to distribute samples more uniformly and keep randomness at the same time.
引文
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[21] Donoho D L,Huo X M.Uncertainty principles and ideal atomic decomposition.IEEE Transactions on Information Theory,2001,47(7) :2845～2862
[22] Hennenfent G,Herrmann F J.Simply denoise:wavefield reconstruction via jittered undersampling.Geophysics,2008,73(3) :V19～V28
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[2] 刘喜武,刘洪,刘彬.反假频非均匀地震数据重建方法研究.地球物理学报,2004,47(2) :299～305 Liu X W,Liu H,Liu B.A study on algorithm for reconstruction of de-alias uneven seismic data.Chinese J.Geophys.(in Chinese),2004 ,47(2) :299～305
[3] 孟小红,郭良辉,张致付等.基于非均匀快速傅里叶变换的最小二乘反演地震数据重建.地球物理学报,2008,51(1) :235～241 Meng X H,Guo L H,Zhang Z F,et al.Reconstruction of seismic data with least squares inversion based on nonuniform fast Fourier transform.Chinese J.Geophys.(in Chinese),2008,51(1) :235～241
[4] Candes E J.Compressive sampling.The International Congress of Mathematicians.Spain:Madrid,2006
[5] Donoho D L.Compressed sensing.IEEE Transactions on Information Theory,2006,52(4) :1289～1306
[6] Sacchi M D,Ulrych T J,Walker C J.Interpolation and extrapolation using a high-resolution discrete fourier transform.IEEE Transactions on Signal Processing,1998,46(1) :31～38
[7] Xu S,Zhang Y,Pham D,et al.Antileakage fourier transform for seismic data regularization.Geophysics,2005,70(4) :V87～V95
[8] Zwartjes P M,Sacchi M D.Fourier reconstruction of nonuniformly sampled aliased data.Geophysics,2007,72(1) :V21～V32
[9] Herrmann F J,Hennenfent G.Non-parametric seismic data recovery with curvelet frames.Geophysical Journal International,2008,173(1) :233～248
[10] Lustig M,Donoho D L,Santos J M,et al.Compressed sensing MRI.IEEE Signal Processing Magazine,2008,25(2) :72～82
[11] Trad D,Ulrych T,Sacchi M.Latest view of sparse radon transform.Geophysics,2003,68(1) :386～399
[12] 张军华,吕宁,田连玉等.地震资料去噪方法技术综合评述.地球物理学进展,2006,21(2) :546～553 ZhangJ H,LüN,Tian L Y,et al.An overview of the methods and techniques for seismic data noise attenuation.Progress in Geophysics(in Chinese),2006,21(2) :546～553
[13] 周立杰,王维宏.叠前含随机噪声地震数据抛物Radon变换法重建.勘探地球物理进展,2007,30(4) :280～285 Zhou L J,Wang W H.Prestack noisy seismic wavefield reconstruction based on parabolic Radon transform.Progress in Exploration Geophysics(in Chinese),2007,30(4) :280～285
[14] 仝中飞.Curvelet阈值迭代法在地震数据去噪和插值中的应用研究[硕士论文].长春:吉林大学,2009 Tong Z F.The study on seismic data denoising and interpolation with curvelet thresholding iterative method[Master's thesis](in Chinese).Changchun:Jinlin University,2009
[15] 张军华,仝兆岐,何潮观等.在f-k域实现三维波场道内插. 石油地球物理勘探,2003,38(1) :27～30 Zhang J H ,Tong Z J ,He C G,et al.3-D seismic trace interpolation in f-k domain.Oil Geophysical Prospecting(in Chinese),2003,38(1) :27～30
[16] 国九英,周兴元,俞寿朋.FX域等道距道内插.石油地球物理勘探,1996,31(1) :28～34 Guo J Y ,Zhou X Y ,Yu S P.Iso-interval trace interpolation in F-X domain.Oil Geophysical Prospecting(in Chinese),1996,31(1) :28～34
[17] 国九英,周兴元.FK域等道距道内插.石油地球物理勘探,1996,31(2) :211～218 Guo J Y,Zhou X Y.Iso-interval trace interpolation in F-K domain.Oil Geophysical Prospecting(in Chinese),1996,31(2) :211～218
[18] Dippe M A Z,Wold E H.Antialiasing through stochastic sampling.Proceedings of SIGGRAPH' 85 Conference,1985,19(3) :69～78
[19] Tang G,Shahidi R,Herrmann F J,et al.Higher dimensional blue-noise sampling schemes for curvelet based seismic data recovery.The 79~(th)SEG Annual Meeting,Houston,Expanded Abstracts,2009
[20] Lustig M,Alley M,Vasanawala S,et al.Autocalibrating parallel imaging compressed sensing using L1 SPIR-iT with Poisson Disc sampling and joint sparsity constraints.The ISMRM Workshop on Data Sampling and Image Reconstruction,Sedona 09,2009
[21] Donoho D L,Huo X M.Uncertainty principles and ideal atomic decomposition.IEEE Transactions on Information Theory,2001,47(7) :2845～2862
[22] Hennenfent G,Herrmann F J.Simply denoise:wavefield reconstruction via jittered undersampling.Geophysics,2008,73(3) :V19～V28
[23] Berg E D,Friedlander M P.Probing the Pareto frontier for basis pursuit solutions.SIAM J.on Scientific Computing,2008,31(2) :890～912
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