压缩感知框架下基于K-奇异值分解字典学习的地震数据重建  

Seismic data reconstruction based on K-SVD dictionary learning under compressive sensing framework

作　　者：周亚同[1,2] 王丽莉 蒲青山 

机构地区：[1]河北工业业大学信息工程学院,天津300401 [2]北京大学数学科学学院,北京100871 [3]东方地球物理公司国际勘探事业部,河北涿州072751

出　　处：《石油地球物理勘探》2014年第4期652-660,2,共9页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目(60972106);河北省自然科学基金项目(F2013202254);天津市自然科学基金项目(11JCYBJC00900)联合资助

摘　　要：针对地震勘探中由于采集成本及采集环境等诸多因素导致地震数据不完整或者不规则问题,本文提出了一种压缩感知框架下基于K-奇异值分解(K-SVD)字典学习的地震数据重建算法。基本思路是首先对大量地震样本数据进行K-SVD字典训练得到超完备字典,然后引入缺失地震数据的采样矩阵作为测量矩阵。在重建阶段则采用正则化正交匹配追踪(ROMP)实现缺失地震数据的恢复。与传统的基于Curvelet变换或基于傅里叶变换等地震数据重建算法采用单一基函数不同,本文引入的超完备字典能够自适应地根据训练样本数据进行特征提取,并能根据待处理数据的本身特点自适应选取变换基函数。超完备字典为地震数据自适应稀疏扩展提供了更大灵活性,有利于更好地重建数据。合成地震数据以及实际海洋数据重建实验验证了本文算法的可行性及有效性。A novel seismic data reconstruction method combined with compressive sensing and K-SVD dictionary learning is presented in this paper to deal with incomplete or irregular seismic data due to acquisition cost or environmental factors.First we obtain an over complete dictionary by training K-SVD dictionary learning on a large number of seismic data samples,then we introduce the sampling matrix of irregular seismic data as a measurement matrix.After that,the seismic data is reconstructed by the regularized orthogonal matching pursuit algorithm.Unlike conventional reconstruction algorithms based on curvelet transform or Fourier transform using single orthogonal basis,the over complete dictionary introduced in this paper extracts adaptively feature through the training samples,and can adaptively select transform basis according to the characteristics of processed data itself.The over complete dictionary provides a flexible way to seismic data sparse extension,and could lead to a better reconstruction result.Exper-iments on the synthetic seismic data and real marine seismic data have verified the feasibility and efficiency of the method.

关 键 词：压缩感知 K-奇异值分解(K-SVD) 字典学习 地震数据重建 正则化正交匹配追踪 

分 类 号：P631[天文地球—地质矿产勘探]