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Mathematical Problems in Engineering
Volume 2016, Article ID 3567095, 11 pages
http://dx.doi.org/10.1155/2016/3567095
Research Article

- and -Norm Joint Regularization Based Sparse Signal Reconstruction Scheme

Southwest Jiaotong University, Chengdu, Sichuan 610031, China

Received 10 May 2016; Revised 7 July 2016; Accepted 10 July 2016

Academic Editor: Nazrul Islam

Copyright © 2016 Chanzi Liu et al. 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. 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
  2. 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
  3. R. G. Baraniuk, “Compressive sensing,” IEEE Signal Processing Magazine, vol. 24, no. 4, pp. 118–124, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Transactions on Information Theory, vol. 53, no. 12, pp. 4655–4666, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. D. L. Donoho, Y. Tsaig, and J. L. Starck, “Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit,” Tech. Rep., Stanford University, 2006. View at Google Scholar
  6. W. Dai and O. Milenkovic, “Subspace pursuit for compressive sensing: closing the gap between performance and complexity,” IEEE Transactions on Information Theory, vol. 55, no. 5, pp. 2230–2249, 2009. View at Google Scholar
  7. E. van den Berg and M. P. Friedlander, “In pursuit of a root,” Tech. Rep. TR-2007-19, Department of Computer Science, University of British Columbia, 2007. View at Google Scholar
  8. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE Journal on Selected Topics in Signal Processing, vol. 1, no. 4, pp. 586–597, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. E. J. Candès, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted l1 minimization,” Journal of Fourier Analysis and Applications, vol. 14, no. 5, pp. 877–905, 2008. View at Google Scholar
  10. D. Wipf and S. Nagarajan, “Iterative reweighted l1 and l2 methods for finding sparse solution,” IEEE Journal of Selected Topics in Signal Processing, vol. 4, no. 6, pp. 317–329, 2010. View at Publisher · View at Google Scholar
  11. E. J. Candès and J. Romberg, “l1-Magic: a collection of MATLAB routines for solving the convex optimization programs central to compressive,” 2006, http://www.acm.caltech.edu/ l1magic/
  12. R. Chartrand, “Exact reconstruction of sparse signals via nonconvex minimization,” IEEE Signal Processing Letters, vol. 14, no. 10, pp. 707–710, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Transactions on Signal Processing, vol. 56, no. 6, pp. 2346–2356, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. 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
  15. X. Lu, Y. Wang, and Y. Yuan, “Sparse coding from a Bayesian perspective,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 6, pp. 929–939, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Liu, T.-Z. Huang, I. W. Selesnick, X.-G. Lv, and P.-Y. Chen, “Image restoration using total variation with overlapping group sparsity,” Information Sciences, vol. 295, pp. 232–246, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  17. G. Liu, T.-Z. Huang, and J. Liu, “High-order TVL1-based images restoration and spatially adapted regularization parameter selection,” Computers and Mathematics with Applications, vol. 67, no. 10, pp. 2015–2026, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. M.-G. Shama, T.-Z. Huang, J. Liu, and S. Wang, “A convex total generalized variation regularized model for multiplicative noise and blur removal,” Applied Mathematics and Computation, vol. 276, pp. 109–121, 2016. View at Publisher · View at Google Scholar · View at Scopus
  19. X.-L. Zhao, F. Wang, T.-Z. Huang, M. K. Ng, and R. J. Plemmons, “Deblurring and sparse unmixing for hyperspectral images,” IEEE Transactions on Geoscience and Remote Sensing, vol. 51, no. 7, pp. 4045–4058, 2013. View at Publisher · View at Google Scholar · View at Scopus
  20. Y. Cai, M. Donatelli, D. Bianchi, and T.-Z. Huang, “Regularization preconditioners for frame-based image deblurring with reduced boundary artifacts,” SIAM Journal on Scientific Computing, vol. 38, no. 1, pp. B164–B189, 2016. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. Y. Lou, P. Yin, Q. He, and J. Xin, “Computing sparse representation in a highly coherent dictionary based on difference of L1 and L2,” Journal of Scientific Computing, vol. 64, no. 1, pp. 178–196, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. M. Elad, Sparse and Redundant Representations, Springer, New York, NY, USA, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed sensing,” in Compressed Sensing Theory and Applications, chapter 1, pp. 1–64, Cambridge University Press, Cambridge, UK, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. G. Davis, S. Mallat, and M. Avellaneda, “Adaptive greedy approximations,” Constructive Approximation, vol. 13, no. 1, pp. 57–98, 1997. View at Publisher · View at Google Scholar
  25. J. Jin, Y. Gu, and S. Mei, “A stochastic gradient approach on compressive sensing signal reconstruction based on adaptive filtering framework,” IEEE Journal on Selected Topics in Signal Processing, vol. 4, no. 2, pp. 409–420, 2010. View at Publisher · View at Google Scholar · View at Scopus
  26. K. Koh, S. Kim, and S. Boyd, “A method for large-scale l1-regularized logistic regression,” in Proceedings of the National Conference on Artificial Intelligence, pp. 565–571, 2007.
  27. R. Chartrand and W. Yin, “Iteratively reweighted algorithms for compressive sensing,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '08), pp. 3869–3872, Las Vegas, Nev, USA, April 2008. View at Publisher · View at Google Scholar · View at Scopus
  28. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” The Annals of Statistics, vol. 32, no. 2, pp. 407–499, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus