杨冠雨^1,2,,
栾锡武^3,,,
孟凡顺^1,2,
黄军^1,2
1. 中国海洋大学海洋地球科学学院, 青岛 266100
2. 海底科学与探测技术教育部重点实验室, 青岛 266100
3. 青岛海洋科学与技术试点国家实验室海洋矿产资源评价与探测技术功能实验室, 青岛 266100

基金项目: 中国-东盟海上合作基金项目（12120100500017001）和国家科技重大专项（2016ZX05027-002）联合资助


详细信息

作者简介: 杨冠雨, 男, 1990年生, 中国海洋大学海洋地球科学学院在读博士研究生, 主要从事地震勘探成像和反演计算的研究.E-mail:yangguanyuok@126.com

通讯作者: 栾锡武, 男, 1966年生, 研究员, 主要从事海洋地球物理研究.E-mail:xluan@qnlm.ac

中图分类号: P631

收稿日期:2018-07-05
修回日期:2020-04-26
上线日期:2020-09-05

Seismic data reconstruction based on Shearlet transform and total generalized variation regularization

YANG GuanYu^1,2,,
LUAN XiWu^3,,,
MENG FanShun^1,2,
HUANG Jun^1,2
1. College of Marine Geosciences, Ocean University of China, Qingdao 266100, China
2. Key Lab of Submarine Geosciences and Prospecting Techniques. MOE. China, Qingdao 266100, China
3. Laboratory for Marine Mineral Resources, Pilot National Laboratory for Marine Science and Technology(Qingdao), Qingdao 266100, China


More Information

Corresponding author: LUAN XiWu,E-mail:xluan@qnlm.ac

MSC: P631

--> Received Date: 05 July 2018
Revised Date: 26 April 2020
Available Online: 05 September 2020


摘要
摘要:压缩感知技术通常利用地震信号在某一变换域内的稀疏性质，将随机缺失的地震数据重建问题转化为L1正则化问题.本文首先通过Shearlet变换获得地震信号的稀疏性质，再将广义全变分（TGV）约束引入L1正则化模型，构建了基于Shearlet变换的双正则化模型用于重建地下介质的图像.与传统L1正则化方法相比，基于Shearlet变换的双正则化方法不仅考虑了信号的稀疏性，同时兼顾了地下介质结构的复杂性，可以较好的重建地下结构体的图像.最后采用交替方向乘子法（ADMM）求解所建模型，每个子问题均可得到显式解.数值实验对比了基于小波变换、Shearlet变换的L1正则化方法和TGV正则化方法，结果表明基于Shearlet变换的双正则化方法对于随机采样50%数据的情况具有较好的重建结果，同时对于有限范围的连续缺失数据的重建亦具有一定的有效性.
关键词: 压缩感知/
地震数据重建/
Shearlet变换/
广义全变分/
交替方向乘子法

Abstract:Compressed sensing technology usually transforms random seismic data reconstruction problem into L1 regularization problem, which exploits the sparsity of signals in a certain transform domain. Firstly, we obtain the sparse property of seismic signals by Shearlet transform, and the total generalized variation constraints are introduced into the L1 regularization model. Then a double regularization model based on Shearlet transformation is constructed, which can reconstruct the seismic image better than the traditional single regularization model, since the double regularization model not only considers the sparseness of the signal, but also takes into account the complexity of the underground medium structure. Finally, the alternating direction method of multipliers is used to solve the proposed model, each subproblem has a closed-form solution. The numerical experiments compare the single regularization method, including the L1 regularization method based on wavelet transform and Shearlet transform and the total generalized variation regularization method. The results show that the proposed double regularization method based on Shearlet can reconstruct the original data better with the 50% sampling rate. And it is also effective for the reconstruction of a limited range of non-random missing data.
Key words:Compressive sensing/
Seismic data reconstruction/
Shearlet transform/
Total generalized variation/
Alternating direction method of multipliers



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