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Mathematical Problems in Engineering
Volume 2015, Article ID 427153, 11 pages
http://dx.doi.org/10.1155/2015/427153
Research Article

A Seismic Blind Deconvolution Algorithm Based on Bayesian Compressive Sensing

1School of Electrical Engineering & Automation, Tianjin University, Tianjin 300072, China
2Department of Disaster Prevention Equipment, Institute of Disaster Prevention, Beijing 101601, China

Received 19 March 2015; Accepted 20 April 2015

Academic Editor: Wanquan Liu

Copyright © 2015 Yanqin Li and Guoshan Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Ma, “Compressed sensing for surface characterization and metrology,” IEEE Transactions on Instrumentation and Measurement, vol. 59, no. 6, pp. 1600–1615, 2010. View at Publisher · View at Google Scholar · View at Scopus
  2. M. F. Duarte and R. G. Baraniuk, “Spectral compressive sensing,” Applied and Computational Harmonic Analysis, vol. 35, no. 1, pp. 111–129, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. Y. Erlich, A. Gordon, M. Brand, G. J. Hannon, and P. P. Mitra, “Compressed genotyping,” IEEE Transactions on Information Theory, vol. 56, no. 2, pp. 706–723, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. A. Amir and O. Zuk, “Bacterial community reconstruction using compressed sensing,” Journal of Computational Biology, vol. 18, no. 11, pp. 1723–1741, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. M. F. Duarte, M. A. Davenport, D. Takbar et al., “Single-pixel imaging via compressive sampling: building simpler, smaller, and less-expensive digital cameras,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 83–91, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. M. A. Herman and T. Strohmer, “High-resolution radar via compressed sensing,” IEEE Transactions on Signal Processing, vol. 57, no. 6, pp. 2275–2284, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” in Infrared Technology and Applications XXXVIII, Proceedings of SPIE, pp. 835303–835303-10, Baltimore, Md, USA, 2012. View at Publisher · View at Google Scholar
  8. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489–509, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. W. Qisong, Y. D. Zhang, M. G. Amin, and B. Himed, “Multi-task bayesian compressive sensing exploiting intra-task dependency,” IEEE Signal Processing Letters, vol. 22, no. 4, pp. 430–434, 2015. View at Publisher · View at Google Scholar
  11. S. D. Babacan, R. Molina, and A. K. Katsaggelos, “Bayesian compressive sensing using Laplace priors,” IEEE Transactions on Image Processing, vol. 19, no. 1, pp. 53–63, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. Minato, T. Matsuoka, and T. Tsuji, “Singular-value decomposition analysis of source illumination in seismic interferometry by multidimensional deconvolution,” Geophysics, vol. 78, no. 3, pp. Q25–Q34, 2013. View at Google Scholar
  13. S. H. Ju, “A deconvolution scheme for determination of seismic loads in finite-element analyses,” Bulletin of the Seismological Society of America, vol. 103, no. 1, pp. 258–267, 2013. View at Publisher · View at Google Scholar · View at Scopus
  14. G. M. Menanno and A. Mazzotti, “Deconvolution of multicomponent seismic data by means of quaternions: theory and preliminary results,” Geophysical Prospecting, vol. 60, no. 2, pp. 217–238, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. K. Wapenaar, J. van der Neut, E. Ruigrok et al., “Seismic interferometry by crosscorrelation and by multidimensional deconvolution: a systematic comparison,” Geophysical Journal International, vol. 185, no. 3, pp. 1335–1364, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. B. Nsiri, T. Chonavel, J.-M. Boucher, and H. Nouzé, “Blind submarine seismic deconvolution for long source wavelets,” IEEE Journal of Oceanic Engineering, vol. 32, no. 3, pp. 729–743, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. Li and G. Zhang, “Blind seismic deconvolution using variational Bayesian method,” Journal of Applied Geophysics, vol. 110, pp. 82–89, 2014. View at Publisher · View at Google Scholar
  18. S. Yildirim, A. T. Cemgil, M. Aktar, Y. Özakin, and A. Ertüzün, “A Bayesian deconvolution approach for receiver function analysis,” IEEE Transactions on Geoscience and Remote Sensing, vol. 48, no. 12, pp. 4151–4163, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. S. Yuan and S. Wang, “Spectral sparse Bayesian learning reflectivity inversion,” Geophysical Prospecting, vol. 61, no. 4, pp. 735–746, 2013. View at Publisher · View at Google Scholar · View at Scopus
  20. E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21–30, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. C. P. Robert, The Bayesian Choice, Springer, New York, NY, USA, 2007. View at MathSciNet
  22. A. Gholami, “Residual statics estimation by sparsity maximization,” Geophysics, vol. 78, no. 1, pp. V11–V19, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. D. L. Wang, Z. F. Tong, C. Tang, and H. Zhu, “An iterative curvelet thresholding algorithm for seismic random noise attenuation,” Applied Geophysics, vol. 7, no. 4, pp. 315–324, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. A. Heimer and I. Cohen, “Multichannel seismic deconvolution using Markov-Bernoulli random-field modeling,” IEEE Transactions on Geoscience and Remote Sensing, vol. 47, no. 7, pp. 2047–2058, 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. A. T. Cemgil, C. Févotte, and S. J. Godsill, “Variational and stochastic inference for Bayesian source separation,” Digital Signal Processing, vol. 17, no. 5, pp. 891–913, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. S. Kim and C. D. Yoo, “Underdetermined blind source separation based on subspace representation,” IEEE Transactions on Signal Processing, vol. 57, no. 7, pp. 2604–2614, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. C. Févotte and S. J. Godsill, “A Bayesian approach for blind separation of sparse sources,” IEEE Transactions on Audio, Speech and Language Processing, vol. 14, no. 6, pp. 2174–2188, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. C. Févotte, Bayesian Audio Source Separation, Springer, New York, NY, USA, 2007.
  29. D. Tzikas, A. Likas, and N. Galatsanos, “Variational bayesian blind image deconvolution with student-t priors,” in Proceedings of the 14th IEEE International Conference on Image Processing (ICIP '07), pp. I109–I112, IEEE, San Antonio, Tex, USA, September 2007. View at Publisher · View at Google Scholar · View at Scopus
  30. M. Beal, Variational algorithms for approximate Bayesian inference [Ph.D. thesis], Gatsby Computational Neuroscience Unit, Univercity College, London, UK, 2003.
  31. B. Amizic, L. Spinoulas, R. Molina, and A. K. Katsaggelos, “Compressive blind image deconvolution,” IEEE Transactions on Image Processing, vol. 22, no. 10, pp. 3994–4006, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. O. Rosec, J.-M. Boucher, B. Nsiri, and T. Chonavel, “Blind marine seismic deconvolution using statistical MCMC methods,” IEEE Journal of Oceanic Engineering, vol. 28, no. 3, pp. 502–512, 2003. View at Publisher · View at Google Scholar · View at Scopus
  33. N. Kazemi and M. D. Sacchi, “Sparse multichannel blind deconlution,” Geophysics, vol. 79, no. 5, pp. 143–152, 2014. View at Publisher · View at Google Scholar