| 基于压缩感知的Curvelet域联合迭代地震数据重建 |
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| 引用本文： | 白兰淑, 刘伊克, 卢回忆, 王一博, 常旭. 基于压缩感知的Curvelet域联合迭代地震数据重建[J]. 地球物理学报, 2014, 57(9): 2937-2945, doi: 10.6038/cjg20140919 |
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| 作者姓名： | 白兰淑 刘伊克 卢回忆 王一博 常旭 |
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| 作者单位： | 1. 中国科学院地质与地球物理研究所, 北京 100029; 2. 中国科学院大学, 北京 100049 |
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| 基金项目： | 国家自然科学基金（40930421和41074091）和国家油气专项（2011ZX05008-006）项目资助. |
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| 摘 要： | 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（Curvelet Recovery by Sparsity-promoting Inversion method）、Bregman迭代阈值算法（the linearized Bregman method）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.
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| 关 键 词： | 压缩感知 Curvelet变换 地震数据重建 稀疏表示 |
| 收稿时间： | 2012-11-14 |
| 修稿时间： | 2014-06-03 |
Curvelet-domain joint iterative seismic data reconstruction based on compressed sensing |
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| BAI Lan-Shu, LIU Yi-Ke, LU Hui-Yi, WANG Yi-Bo, CHANG Xu. Curvelet-domain joint iterative seismic data reconstruction based on compressed sensing[J]. Chinese Journal of Geophysics (in Chinese), 2014, 57(9): 2937-2945, doi: 10.6038/cjg20140919 |
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| Authors: | BAI Lan-Shu LIU Yi-Ke LU Hui-Yi WANG Yi-Bo CHANG Xu |
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| Affiliation: | 1. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China; 2. Graduate University, Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | Because of limited acquisition conditions in the field, seismic data is usually incomplete which would affect following data processing. To solve this problem, data reconstruction has been widely studied. Some methods based on compressed sensing has been developed in recent years, such as Curvelet Recovery by Sparsity-promoting Inversion method(CRSI), and the linearized Bregmen iterative threshold method. CRSI reconstructs randomly lacked seismic data to get a high-SNR data, taking advantage of seismic waveform's sparse representation in the Curvelet domain based on the steepest descent algorithm that ensures accuracy and stability of the iteration, but its convergence speed is slow. The linearized Bregman threshold method converges fast, but becomes unstable in later iterations because it adds back residuals to the result, which leads to comparatively lower SNR of the final recovered data. Combining advantages of the two methods, we propose a new joint Curvelet-domain iterative threshold algorithm that combines the recovery quantities from both the CRSI and the Bregman method with respective weights of two items, which are adjusted exponentially during each iteration. The test results of the model and real seismic data demonstrate that this method is fast and stable in iteration and yields high-SNR reconstructed data. |
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| Keywords: | Compressive sensing Curvelet Data reconstruction Sparse representation |
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