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Seismic data denoising using double sparsity dictionary and alternating direction method of multipliers

LIANG ZHANG1,2 ,  LIGUO HAN1 ,  AO CHANG1 ,  JINWEI FANG3 ,  PAN ZHANG1 ,  YONG HU1 ,  ZHENGGUANG LIU2
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1 College of Geo-exploration Science and Technology, Jilin University, Changchun 130026, P.R. China.,
2 Institute of Geosciences and Info-Physics, Central South University, Changsha, Hunan 410083, P.R. China.,
3 CNPC Key Lab of Geophysical Exploration, China University of Petroleum-Beijing, Beijing 102249, P.R. China.,
JSE 2020, 29(1), 49–71;
Submitted: 3 August 2018 | Accepted: 11 October 2019 | Published: 1 February 2020
© 2020 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Zhang, L., Han, L.G., Chang, A., Fang, J.W., Zhang, P., Hu, Y. and Liu, Z.G., 2020. Seismic data denoising using double sparsity dictionary and alternating direction method of multipliers. Journal of Seismic Exploration, 29: 49-71. Recently, the dictionary learning plays a more and more important role in seismic ata denoising. Compared with the fixed-basis transform (e.g., Fourier transform, wavelet ansform, curvelet transform, contourlet transform and shearlet transform), the denoising f dictionary learning is better because of adaptive sparse representation of seismic data. owever, dictionary learning often produces artifacts due to no prior-constraint structural nformation. In this paper, we propose a new denoising approach, which has double sparsity and combines the advantage of fixed-basis transform and dictionary learning. The whole work-flow of the new denoising approach is as follows. Firstly, we can obtain sparse coefficients of seismic data via shearlet transform. Secondly, sparse coefficients are divided into some suitable size blocks which are regarded as training sets. Thirdly, the alternating direction method of multipliers (ADMM) is used in sparse coding to update ictionary coefficients. Then, the data-driven tight frame (DDTF) is used in dictionary updating to update dictionary atoms. Again, the ADMM is used to resolve the convex optimization problem, and we reshape output blocks to obtain new sparse coefficients. Finally, the hard-thresholding and inverse shearlet transform are applied to new sparse oefficients to achieve denoising. The synthetic data and field data experiments show that e new denoising approach obtain better result than fixed-basis transform and dictionary earning. In conclusion, the new denoising approach can attenuate artifacts and improve e quality of seismic data denoising.

Keywords
seismic data denoising
shearlet transform
DDTF
ADMM
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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