计算机应用 ›› 2016, Vol. 36 ›› Issue (4): 1167-1172.DOI: 10.11772/j.issn.1001-9081.2016.04.1167

• 行业与领域应用 • 上一篇    下一篇

基于一致性稀疏表示的地震信号补全算法

王立夫, 孙怡   

  1. 大连理工大学 信息与通信工程学院, 辽宁 大连 116024
  • 收稿日期:2015-09-06 修回日期:2015-11-05 出版日期:2016-04-10 发布日期:2016-04-08
  • 通讯作者: 孙怡
  • 作者简介:王立夫(1985-),男,辽宁大连人,博士,主要研究方向:计算机视觉、机器学习; 孙怡(1964-),女,辽宁沈阳人,教授,博士生导师,博士,主要研究方向:图像处理。
  • 基金资助:
    国家自然科学基金资助项目(41174044)。

Inpainting of seismic signal using consistent sparse representation method

WANG Lifu, SUN Yi   

  1. School of Information and Communication Engineering, Dalian University of Technology, Dalian Liaoning 116024, China
  • Received:2015-09-06 Revised:2015-11-05 Online:2016-04-10 Published:2016-04-08
  • Supported by:
    This work is partially supported by the National Natural Science Foundation of China (41174044).

摘要: 针对由于记录仪器的故障和保存媒介的缺陷导致的地震信号中一部分波形出现的缺失,提出一种基于一致性稀疏表示(CSR)的地震波补全算法。首先,通过稀疏表示(SR)模型表示每一帧地震信号;随后,采用主分量分析(PCA)的方法提取在频谱的分布上的帧间一致性信息;最后,利用地震信号的每帧的稀疏性和用帧与帧之间频谱分布的一致性,对缺损的信号进行恢复。在对历史地震信号进行的仿真实验中,当缺损的部分的跨度达到帧数据量的50%时,传统的稀疏表示恢复算法的误差已经很大,而一致性稀疏表示模型仍然能够得到很好的结果。仿真实验结果表明,一致性稀疏表示模型的补全效果要远好于传统稀疏表示模型的补全效果。

关键词: 信号恢复, 稀疏表示, 地震信号补全, 主分量分析, 频谱

Abstract: Focusing on the issue that some portions of seismic waveforms were lost due to the mechanical failure of recording devices and damage of seismograms, an inpainting method based on Consistent Sparse Representation (CSR) model was proposed. Firstly, each seismic frame was represented individually in Sparse Representation (SR) model. Secondly, the consistency between spectra of seismic frames was employed. Principal Component Analysis (PCA) method was introduced to extract this consistency between seismic frames. Finally, combining the sparseness of each seismic frame and the consistency between seismic frames, the proposed algorithm was used to inpaint the lost portion. The simulation experiments showed that when the missing duration interval was 50% of the frame length, the inpainting method based on traditional sparse representation model obtained incorrect results whereas the inpainting method based on consistent sparse representation model recovered the lost portion well. The simulation experiments indicate that the performance of the consistent sparse representation inpainting method is much better than the traditional sparse representation inpainting method.

Key words: signal restoration, sparse representation, sesimic signal inpainting, Principal Component Analysis (PCA), spectrum

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