Compressive sensing method with Huber norm minimization constraint on reconstruction error

LI Zhong-xiao1 LI Yongqiang2,3 GU Bing-luo2,3 LI Zhen-chun2,3

(1.School of Electronic Information, Qingdao University, Qingdao, Shandong Province, China 266071)
(2.School of Geosciences, China University of Petroleum (East China), Qingdao, Shandong Province, China 266580)
(3.Evaluation and Detection Technology Laboratory of Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao, Shandong Province, China 266071)

【Abstract】Seismic data contain strong noise outliers. The compressive sensing (CS) method based on L2 norm minimization constraint on reconstruction error assumes that the reconstruction error satisfies Gaussian distribution. Therefore, the CS method above cannot remove super-Gaussian noise outliers. To better remove outliers and improve interpolation accuracy, Huber norm is used instead of L2 norm to implement the minimization constraint on reconstruction error. The minimization constraint of Huber norm is equivalent to the L1 norm minimization constraint on large reconstruction error (noise outlier) and the L2 norm minimization constraint on small reconstruction error (Gaussian random noise). Therefore, the proposed method is robust when dealing with noise outlier. Furthermore, theoretical pseudo-seismic data are introduced to convert the Huber norm minimization problem to the L2 norm minimization problem, in order to solve the Huber-L0 minimization problem of the proposed CS method based on Huber norm minimization constraint on construction error. Additionally, the affection of Gaussian noise intensity, noise outlier intensity and parameter selection on interpolation accuracy is tested. The processing results of synthetic and field data demonstrate that the proposed CS method based on the Huber norm minimization constraint of the construction error can better remove the noise outliers and preserve effective signals compared with the CS method based on the L2 norm minimization constraint of the construction error.

【Keywords】 compressive sensing method; interpolation; Huber norm; pseudo-seismic data; noise outlier; elimination;


【Funds】 National Natural Science Foundation of China (41804110) National Key R&D Program of China (2016YFC060110501) Natural Science Foundation of Shandong Province, China (ZR2016DB09)

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This Article


CN: 13-1095/TE

Vol 55, No. 01, Pages 80-91+135+7

February 2020


Article Outline


  • 0 Introduction
  • 1 Mathematical model and optimization
  • 2 Solution for optimization
  • 3 Example of numerical tests
  • 4 Conclusion
  • References