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Abstract

Summary

We propose a modification to a sparsity constraint based on the ratio of l1 and l2 norms for solving blind seismic deconvolution problems in which the data consist of linear convolutions of different sparse reflectivities with the same source wavelet. We also extend the approach to the Estimation of Primaries by Sparse Inversion (EPSI) model, which includes surface related multiples. Minimizing the ratio of l1 and l2 norms has been previously shown to promote sparsity in a variety of applications including blind deconvolution. Most existing implementations are heuristic or require smoothing the l1/l2 penalty. Lifted versions of l1/l2 constraints have also been proposed but are challenging to implement. Inspired by the lifting approach, we propose to split the sparse signals into positive and negative components and apply an l1/l2 constraint to the difference, thereby obtaining a constraint that is easy to implement without smoothing the l1 or l2 norms. We show that a method of multipliers implementation of the resulting model can recover source wavelets that are not necessarily minimum phase and approximately reconstruct the sparse reflectivities. Numerical experiments demonstrate robustness to the initialization as well as to noise in the data.

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/content/papers/10.3997/2214-4609.201413420
2015-06-01
2025-01-20

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References

  1. Ahmed, A., Recht, B. and Romberg, J.
    [2012] Blind deconvolution using convex programming. arXiv preprint arXiv: 1211.5608, 40.
     [Google Scholar]
  2. Benichoux, A.
    [2013] A fundamental pitfall in blind deconvolution with sparse and shift-invariant priors. …on Acoustics, Speech, ….
     [Google Scholar]
  3. Bertsekas, D.P.
    [1982] Constrained Optimization and Lagrange Multiplier Methods. Academic Press, Inc.
     [Google Scholar]
  4. Claerbout, J. and Muir, F.
    [1973] Robust modeling with erratic data. Geophysics, 38.
     [Google Scholar]
  5. D’Aspremont, A., Ghaoui, L.E., Jordan, M. and Lanckriet, G.
    [2007] A direct formulation for sparse PCA using semidefinite programming. SIAM review, 1–15.
     [Google Scholar]
  6. Donoho, D.
    [1992] superresoution via sparsity constraints. SIAM J. Math. Anal, 23(5), 1309–1331.
     [Google Scholar]
  7. Dossal, C. and Mallat, S.
    [2005] Sparse spike deconvolution with minimum scale. In Proceedings of Signal Processing with Adaptive Sparse Structured Representations, (4), 123–126.
     [Google Scholar]
  8. Esser, E. and Herrmann, F.
    [2014] Application of a Convex Phase Retrieval Method to Blind Seismic Deconvolution.
     [Google Scholar]
  9. Gray, W.
    [1979] Variable norm deconvolution.
     [Google Scholar]
  10. Lamoureux, M. and Margrave, G.
    [2007] An analytic approach to minimum phase signals. CREWES Research Report, 19(1), 1–12.
     [Google Scholar]
  11. Lin, T. and Herrmann, F.
    [2014] Multilevel Acceleration Strategy for the Robust Estimation of Primaries by Sparse Inversion.
     [Google Scholar]
  12. Long, X., Solna, K. and Xin, J.
    [2014] Two l1 based nonconvex methods for constructing sparse mean reverting portfolios. UCLA CAM Reports [14–55], 1–29.
     [Google Scholar]
  13. Repetti, A., Pham, M. and Duval, L.
    [2014] Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed l1/l2 Regularization, 1–11.
     [Google Scholar]
  14. Santosa, F. and Symes, W.W.
    [1986] Linear Inversion of Band-Limited Reflection Seismograms. SIAM Journal on Scientific and Statistical Computing, 7(4), 1307–1330.
     [Google Scholar]
  15. Schmidt, M.
    [2012] minFunc. Http://www.cs.ubc.ca/schmidtm/Software/minFunc.html.
     [Google Scholar]
  16. Ulrych, T. and Sacchi, M.
    [2006] Information-Based Inversion and Processing with Applications, Volume 36 (Handbook of Geophysical Exploration: Seismic Exploration). Elsevier Science.
     [Google Scholar]
  17. van Groenestijn, G. and Verschuur, D.
    [2009] Estimating primaries by sparse inversion and application to near-offset data reconstruction. Geophysics, 74(3).
     [Google Scholar]
  18. Verschuur, D.J., Berkhout, A.J. and Wapenaar, C.P.A.
    [1992] Adaptive surface related multiple elimination. Geophysics, 57(9), 1166–1177.
     [Google Scholar]
  19. White, R. and O’ Brien, P.
    [1974] Estimation of the primary seismic pulse. Geophysical Prospecting.
     [Google Scholar]
  20. Wiggins, R.
    [1978] Minimum entropy deconvolution. Geoexploration, 16, 21–35.
     [Google Scholar]
/content/papers/10.3997/2214-4609.201413420
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A Lifted l1/l2 Constraint for Sparse Blind Deconvolution
Conference Proceedings 2015, 1 (2015); https://doi.org/10.3997/2214-4609.201413420
/content/papers/10.3997/2214-4609.201413420
/content/papers/10.3997/2214-4609.201413420
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