Skip to main content

Advertisement

Springer Nature Link
Log in

Overcomplete Blind Source Separation Based on Generalized Gaussian Function and SL0 Norm

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

This paper is concerned with overcomplete blind source separation using a two-stage sparse representation method. An algorithm incorporating generalized Gaussian function and smoothed \(l_0 \) norm (GGFSL0), which can be viewed as the extension of smoothed \(l_0 \) norm (SL0), is proposed. Compared with previous methods, GGFSL0 tries to directly minimize the \(l_0 \) norm instead of minimizing the \(l_1 \) norm. Numerical experiments with different parameters, sparsity, noise, and dimension demonstrate the effectiveness of proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. L. Albera, A. Ferréol, P. Comon, P. Chevalier, Blind identification of overcomplete mixtures of sources (BIOME). Linear Algebra Its Appl. 391, 3–30 (2004)

    Article  MATH  Google Scholar 

  2. P. Bofill, M. Zibulevsky, Underdetermined blind source separation using sparse representations. Signal Process. 81(11), 2353–2362 (2001)

    Article  MATH  Google Scholar 

  3. E. Candès, J. Romberg, \(l^1\)-Magic: recovery of sparse signal via convex programming. (2005). http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.212.9120&rep=rep1&type=pdf

  4. D.J. Candès, T. Tao, Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005)

    Article  MATH  Google Scholar 

  5. P. Common, C. Jutten, Handbook of Blind Source Separation: Independent Component Analysis and Applications (Elsevier, Oxford, 2010)

    Google Scholar 

  6. M. Davies, N. Mitianoudis, Simple mixture model for sparse overcomplete ICA. IEEE Proc. Vis. Image Signal Process. 151(1), 35–43 (2004)

    Article  Google Scholar 

  7. D.L. Donoho, For most large underdetermined systems of linear equations the minimal \(l_1 \) norm solution is also the sparsest solution. Commun. Pure Appl. Math. 59(6), 797–829 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. D.L. Donoho, M. Elad, V. Temlyakov, Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inf. Theory 52(1), 6–18 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. P.G. Georgiev, F. Theis, A. Cichocki, Sparse component analysis and blind source separation of underdetermined mixtures. IEEE Trans. Neural Netw. 16(4), 992–996 (2005)

    Article  Google Scholar 

  10. I.F. Gorodnitsky, B.D. Rao, Sparse signal reconstruction from limited data using FOCUSS, a re-weighted minimum norm algorithm. IEEE Trans. Signal Process. 45(3), 600–616 (1997)

    Article  Google Scholar 

  11. R. Gribonval, S. Lesage, A survey of sparse component analysis for blind source separation: Principles, perspectives, and new challenges. in Proceeding European Symposium on Artificial Neural Networks (ESANN), (Belgium, 2006), pp. 323–330.

  12. Z. He, A. Cichocki, Y. Li, S. Xie, S. Sanei, K-hyperline clustering learning for sparse component analysis. Signal Process. 89(6), 1011–1022 (2009)

    Article  MATH  Google Scholar 

  13. S.G. Kim, Underdetermind blind source separation based on subspace representation. IEEE Trans. Signal Process. 57(7), 2604–2614 (2009)

    Article  MathSciNet  Google Scholar 

  14. Y.Q. Li, A. Cichocki, S. Amari, Analysis of sparse representation and blind source separation. Neural Comput. 6(6), 1193–1234 (2004)

    Article  Google Scholar 

  15. H. Mohimani, M. Babaie-Zadeh, C. Jutten, A fast approach for overcomplete sparse decomposition based on smoothed \(l_0 \) norm. IEEE Trans. Signal Process. 57(1), 289–301 (2009)

    Article  MathSciNet  Google Scholar 

  16. G.R. Naik, D.K. Kumar, Determining number of independent sources in undercomplete mixture. EURASIP J. Adv. Signal Process. 2009, 1–5 (2009)

    Article  Google Scholar 

  17. G.R. Naik, D.K. Kumar, An overview of independent component analysis and its applications. Inf. Int. J. Comput. Inf. 35(1), 63–81 (2011)

    MATH  Google Scholar 

  18. G.R. Naik, D.K. Kumar, Dimensional reduction using blind source separation for identifying sources. Int. J. Innov. Comput. Inf. Control 7(2), 989–1000 (2011)

    Google Scholar 

  19. B. Prasad, H. Saruwatari, K. Shikano, Estimation of shape parameter of GGD function by negentropy matching. Neural Process. Lett. 22(3), 377–389 (2005)

    Article  Google Scholar 

  20. V.G. Reju, S.N. Koh, I.Y. Soon, An algorithm for mixing matrix estimation in instantaneous blind source separation. Signal Process. 89(9), 1762–1773 (2009)

    Article  MATH  Google Scholar 

  21. J.J. Thiagarajan, K.N. Ramamurthy, A. Spanias, Mixing matrix estimation using discriminative clustering for blind source separation. Digital Signal Process. 23(1), 9–18 (2013)

    Article  MathSciNet  Google Scholar 

  22. S.L. Xie, L. Yang, J.M. Yang et al., Time-frequency approach to underdetermined blind source separation. IEEE Trans. Neural Netw. Learn. Syst. 23(2), 306–316 (2012)

    Article  Google Scholar 

  23. G.M. Zhang, Z.M. Cui, J.M. Chen, J. Wu, CT image de-noising model based on independent component analysis and curvelet transform. J. Softw. 5(9), 1006–1013 (2010)

    Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers and the editors for their valuable comments and suggestions. This work is supported by Natural Science Foundation of China (No. 61102103), Youth Foundation of Naval University of Engineering (No. HGDQNJJ13005), Natural Science Foundation of Hubei Province (No. 2013CFB414) and the Special Fund for Basic Scientific Research of Central Colleges, China University of Geosciences Wuhan (No. CUGL130247).

Author information

Authors and Affiliations

  1. Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, 430074, China

    Rui Qi

  2. School of Science, Naval University of Engineering, Wuhan, 430033, China

    Rui Qi

  3. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

    Yujie Zhang & Hongwei Li

Authors
  1. Rui Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yujie Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongwei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rui Qi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qi, R., Zhang, Y. & Li, H. Overcomplete Blind Source Separation Based on Generalized Gaussian Function and SL0 Norm. Circuits Syst Signal Process 34, 2255–2270 (2015). https://doi.org/10.1007/s00034-014-9952-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9952-9

Keywords

Search

Navigation