skip to main content
10.1145/3529446.3529460acmotherconferencesArticle/Chapter ViewAbstractPublication PagesipmvConference Proceedingsconference-collections
research-article

Seismic Data Interpolation by the Projected Iterative Soft-threshold Algorithm for Tight Frame

Authors Info & Claims
Published:15 July 2022Publication History

ABSTRACT

Seismic data recovery from missing traces is a crucial step in seismic data pre-processing. Recently researches have proposed many useful methods to reconstruct the seismic data based on compressed sensing. Curvelet frames can be used to sparsely represent the seismic data volume, analysis model has been proposed to reconstruct the seismic data, however, the latest kind of discrete curvelet transform has tight frame property, the recent insights show synthetically model is more suitable for a tight frame. A synthetically model is introduced to seismic data reconstruction; projected iterative soft-threshold algorithm (pFISTA) is used to solve the model. The recovery performs well on synthetic as well as real data by the proposed method. Comparing with the analysis model solved by an iterative soft-threshold algorithm (FISTA) in the curvelet domain, the new method has improved reconstruction efficiency and reduced the computation time.

References

  1. Donoho D L. 2006. Compressed sensing [J]. IEEE Transactions on Information Theory, 52(4): 1289-1306.Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Kumar R, Wason H, Herrmann F J J G. 2015. Source separation for simultaneous towed-streamer marine acquisition–-a compressed sensing approach [J].80(6): WD73-WD88.Google ScholarGoogle Scholar
  3. Sun Y Y, Jia R S, Sun H M, 2018. Reconstruction of seismic data with missing traces based on optimized Poisson Disk sampling and compressed sensing [J]. S0098300417311779.Google ScholarGoogle Scholar
  4. Kreimer N, Sacchi M D. 2012. A tensor higher-order singular value decomposition for prestack seismic data noise reduction and interpolation [J]. Geophysics, 77(3): V113-V22.Google ScholarGoogle ScholarCross RefCross Ref
  5. Ma J. 2013. Three-dimensional irregular seismic data reconstruction via low-rank matrix completion [J]. Geophysics, 78(5): V181-V92.Google ScholarGoogle ScholarCross RefCross Ref
  6. Wang J, Ng M, Perz M. 2010. Seismic data interpolation by greedy local Radon transform [J]. Geophysics, 75(6): WB225-WB34.Google ScholarGoogle Scholar
  7. Xu Z, Sopher D, Juhlin C, 2018. Radon-domain interferometric interpolation for reconstruction of the near-offset gap in marine seismic data [J]. Journal of Applied Geophysics, 151, 125-141.Google ScholarGoogle ScholarCross RefCross Ref
  8. Huang W, Wu R-S, Wang R. 2018. Damped Dreamlet Representation for Exploration Seismic Data Interpolation and Denoising [J]. Ieee Transactions on Geoscience and Remote Sensing, 56(6): 3159-3172.Google ScholarGoogle ScholarCross RefCross Ref
  9. Wang B, Wu R-S, Chen X, 2015. Simultaneous seismic data interpolation and denoising with a new adaptive method based on dreamlet transform [J]. Geophysical Journal International, 201(2): 1182-1194.Google ScholarGoogle ScholarCross RefCross Ref
  10. Naghizadeh M, Sacchi M D. 2010. Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data[J].Geophysics, 75(6): WB189-WB202.Google ScholarGoogle Scholar
  11. Herrmann F J, Hennenfent G. 2008. Non-parametric seismic data recovery with curvelet frames [J]. Geophysical Journal International, 173(1): 233-48.Google ScholarGoogle ScholarCross RefCross Ref
  12. Candes E J, Donoho D L. 2004. New tight frames of curvelets and optimal representations of objects with piecewise C-2 singularities [J]. Communications on Pure and Applied Mathematics, 57(2): 219-266.Google ScholarGoogle ScholarCross RefCross Ref
  13. Candes E J, Donoho D L. 2005. Continuous Curvelet Transform - I. Resolution of the wavefront set [J]. Applied and Computational HarmonicAnalysis, 19(2): 162-197.Google ScholarGoogle ScholarCross RefCross Ref
  14. Candes E J, Donoho D L. 2005. Continuous Curvelet Transform - II. Discretization and frames [J]. Applied and Computational Harmonic Analysis, 19(2): 198-222.Google ScholarGoogle ScholarCross RefCross Ref
  15. Herrmann F J, Moghaddam P, Stolk C C. 2008. Sparsity- and continuity-promoting seismic image recovery with curvelet frames [J]. Applied and Computational Harmonic Analysis, 24(2): 150-173.Google ScholarGoogle ScholarCross RefCross Ref
  16. Shahidi R, Tang G, Ma J, 2013. Application of randomized sampling schemes to curvelet-based sparsity-promoting seismic data recovery [J]. Geophysical Prospecting, 61(5): 973-997.Google ScholarGoogle ScholarCross RefCross Ref
  17. Tang G, Ma J. 2011. Application of Total-Variation-Based Curvelet Shrinkage for Three-Dimensional Seismic Data Denoising [J]. Ieee Geoscience and Remote Sensing Letters, 8(1): 103-107.Google ScholarGoogle ScholarCross RefCross Ref
  18. Gorszczyk A, Adamczyk A, Malinowski M. 2014. Application of curvelet denoising to 2D and 3D seismic data - Practical considerations [J]. Journal of Applied Geophysics, 105,78-94.Google ScholarGoogle ScholarCross RefCross Ref
  19. Yang H, Long Y, Lin J, 2017. A seismic interpolation and denoising method with curvelet transform matching filter [J]. Acta Geophysica, 65(5): 1029-1042.Google ScholarGoogle ScholarCross RefCross Ref
  20. Tang W, Ma J, Herrmann F. 2019. Optimized Compressed Sensing for Curvelet-based Seismic Data Reconstruction [M]. preprint, 280, 1928.Google ScholarGoogle Scholar
  21. Yang P, Gao J, Chen W. 2012. Curvelet-based POCS interpolation of nonuniformly sampled seismic records [J]. Journal of Applied Geophysics, 79, 90-99.Google ScholarGoogle ScholarCross RefCross Ref
  22. Ma J, Plonka G J S P M I. 2010. The Curvelet Transform [J]. 27(2): 118-33.Google ScholarGoogle Scholar
  23. Cai J-F, Dong B, Osher S, 2012. Image restoration: total variation, wavelet frames, and beyond [J]. Journal of the American Mathematical Society, 25(4): 1033-1089.Google ScholarGoogle ScholarCross RefCross Ref
  24. Liu Y, Zhan Z, Cai J, 2016. Projected Iterative Soft-thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging [J]. 35(9): 2130-2140.Google ScholarGoogle Scholar
  25. Hao Y, Huang H, Luo Y, 2018. Nonstationary acoustic-impedance inversion algorithm via a novel equivalent Q-value estimation scheme and sparse regularizations [J]. Geophysics, 83(6): R681-R698.Google ScholarGoogle ScholarCross RefCross Ref
  26. Martin G S, Wiley R, Marfurt K J. 2006. Marmousi2: An elastic upgrade for Marmousi [J]. 25(2): 156-166.Google ScholarGoogle Scholar

Recommendations

Comments

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Sign in
  • Published in

    cover image ACM Other conferences
    IPMV '22: Proceedings of the 4th International Conference on Image Processing and Machine Vision
    March 2022
    121 pages
    ISBN:9781450395823
    DOI:10.1145/3529446

    Copyright © 2022 ACM

    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    • Published: 15 July 2022

    Permissions

    Request permissions about this article.

    Request Permissions

    Check for updates

    Qualifiers

    • research-article
    • Research
    • Refereed limited

PDF Format

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

HTML Format

View this article in HTML Format .

View HTML Format