全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

基于压缩感知的Curvelet域联合迭代地震数据重建

DOI: 10.6038/cjg20140919, PP. 2937-2945

Keywords: 压缩感知,Curvelet变换,地震数据重建,稀疏表示

Full-Text   Cite this paper   Add to My Lib

Abstract:

由于野外采集环境的限制,常常无法采集得到完整规则的野外地震数据,为了后续地震处理、解释工作的顺利进行,地震数据重建工作被广泛的研究.自压缩感知理论的提出,相继出现了基于该理论的多种迭代阈值方法,如CRSI方法(CurveletRecoverybySparsity-promotingInversionmethod)、Bregman迭代阈值算法(thelinearizedBregmanmethod)等.CSRI方法利用地震波形在Curvelet的稀疏特性,通过一种基于最速下降的迭代算法在Curvelet变换域恢复出高信噪比地震数据,该迭代算法稳定,收敛,但其收敛速度慢.Bregman迭代阈值法与CRSI最大区别在于每次迭代时把上一次恢复结果中的阈值前所有能量都保留到本次恢复结果中,从而加快了收敛速度,但随着迭代的进行重构数据中噪声干扰越来越严重,导致最终恢复出的数据信噪比低.综合两种经典方法的优缺点,本文构造了一种新的联合迭代算法框架,在每次迭代中将CRSI和Bregman的恢复量加权并同时加回本次迭代结果中,从而加快了迭代初期的收敛速度,又避免了迭代后期噪声干扰的影响.合成数据和实际数据试算结果表明,我们提出的新方法不仅迭代快速收敛稳定,且能得到高信噪比的重建结果.

References

[1]  Ali F E, El-Dokany I M, Saad A A, et al. 2008. Curvelet fusion of MR and CT images. Progress in Electromagnetics Research C, 3: 215-224, doi: 10.2528/PIERC08041305.
[2]  Applebaum L, Howard S D, Searle S, et al. 2009. Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery. Applied and Computational Harmonic Analysis, 26(2): 283-290, doi: 10.1016/j.acha.2008.08.002.
[3]  Bochner S, Chandrasekharan K. 1949. Fourier Transforms. Princeton: Princeton University Press.
[4]  Bregman L M. 1967. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics, 7(3): 200-217, doi: 10.1016/0041-5553(67)90040-7.
[5]  Candès E J, Donoho D L. 2005a. Continuous curvelet transform I: resolution of the Wavefront Set. Applied and Computational Harmonic Analysis, 19(2): 162-197, doi: 10.1016/j.acha.2005.02.003.
[6]  Candès E J, Demanet L, Donoho D L, et al. 2006b. Fast discrete curvelet transforms. SIAM Multiscale Model. Simul., 5(3): 861-899, doi: 10.1137/05064182X.
[7]  Candès E J, Romberg J, Tao T. 2006c. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. on Information Theory, 52(2): 489-509, doi: 10.1109/TIT.2005.862083.
[8]  Candès E J, Romberg J K, Tao T. 2006d. Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure and Applied Mathematics, 59(8): 1207-1223, doi: 10.1002/cpa.20124.
[9]  Candes E J. 2008. The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathematique, 346(9-10): 589-592, doi: 10.1016/j.crma.2008.03.014.
[10]  Chen S B, Donoho D L, Saunders M A. 1994. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20(1): 33-61, doi: 10.1137/S003614450037906x.
[11]  Chui C K. 1992. An Introduction to Wavelets. San Diego: Academic Press.
[12]  Herrmann F J, Wang D, Hennenfent G. 2007. Multiple prediction from incomplete data with the focused Curvelet transform. Presented at the SEG International Exposition and 77th Annual Meeting.
[13]  Herrmann F J, Hennenfent G. 2008. Non-parametric seismic data recovery with Curvelet frames. Geophysical Journal of International, 173(1): 233-248, doi: 10.1111/j.1365-246X.2007.03698.x.
[14]  Landweber L. 1951. An iteration formula for Fredholm integral equations of the first kind. American Journal of Mathematics, 73(3): 615-624, doi: 10.2307/2372313.
[15]  Leiserson C E, Rivest R L, Stein C, et al. 2001. Introduction to Algorithms, Chapter 16 "Greedy Algorithms": The MIT Press.
[16]  Ma J W. 2011. Improved iterative Curvelet thresholding for compressed sensing. IEEE Transactions on Instrumentation and Measurement, 60(1): 126-136, doi: 10.1109/TIM.2010.2049221.
[17]  Mallat S. 2008. A Wavelet Tour of Signal Processing: The Sparse Way. San Diego: Academic Press.
[18]  Mallat S G, Zhang Z. 1993. Matching Pursuits with time-frequency dictionaries. IEEE Trans. Signal Process, 41(12): 3397-3415, doi: 10.1109/78.258082.
[19]  Yarham C, Boeniger U, Herrmann F. 2006. Curvelet-based ground roll removal. 2006 SEG Annual Meeting.
[20]  Yin W T. 2010. Analysis and generalizations of the Linearized Bregman Method. SIAM J. Imaging Sci., 3(4): 856-877, doi: 10.1137/090760350.
[21]  Candès E J, Donoho D L. 2005b. Continuous curvelet transform: II. discretization and frames. Applied and Computational Harmonic Analysis, 19(2):198-222, doi: 10.1016/j.acha.2005.02.004.
[22]  Candès E J, Tao T. 2006a. Near optimal signal recovery from random projections: universal encoding strategies. IEEE Transactions on Information Theory, 52(12): 5406-5425, doi: 10.1109/TIT.2006.885507.
[23]  Daubechies I, Defrise M, De Mol C. 2004. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on Pure and Applied Mathematics, 57(11): 1413-1457, doi: 10.1002/cpa.20042.
[24]  Deans S R. 1983. The Radon Transform and Some of Its Applications. New York: John Wiley & Sons.
[25]  Donoho D L. 2006. Compressed sensing. IEEE Transactions on Information Theory, 52(4): 1289-1306, doi: 10.1109/TIT.2006.871582.
[26]  Donoho D L, Tsaig Y, Drori I, et al. 2012. Sparse solution of underdetermined systems of linear equations by Stagewise Orthogonal Matching Pursuit. IEEE Trans. on information Theory, 58(2): 1094-1121, doi: 10.1109/TIT.2011.2173241.
[27]  Pati Y C, Rezaiifar R, Krishnaprasad P S. 1993. Orthogonal Matching Pursuit: recursive function approximation with application to wavelet decomposition. In Asilomar Conf. on Signals, Systems and Computers in 1993.
[28]  Plancherel M. 1910. Contribution à l''étude de la représentation d''une fonction arbitraire par les integrals définies. Rendiconti del Circolo Matematico di Palermo, 30(1): 289-335, doi: 10.1007/BF03014877.
[29]  Starck J L, Murtagh F, Candès E J, et al. 2003. Gray and color image contrast enhancement by the Curvelet Transform. IEEE Transaction on Image Processing, 12(6): 706-717, doi: 10.1109/TIP.2003.813140.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133