Skip to main content
SpringerLink
Log in

Compressed Sensing via Dimension Spread in Dimension-Restricted Systems

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

Compressed sensing (CS) is applied to capture signals at sub-Nyquist rate when the sensing matrix satisfies the restricted isometry property (RIP). When in a dimension-restricted system which has small row dimension and not so good coherence, the RIP and measurement bound will not be satisfied, and compressed sensing can not be applied directly. In this letter, we propose the dimension spread CS to the dimension-restricted system by directed dimension spread and diversity dimension spread, which make the compressed sensing applicable. The spread dimension bounds for the proposed algorithms are deduced to guarantee exact recovery which are also proved by simulations. Meanwhile, the experimental comparisons for the directed dimension spread CS and diversity dimension spread CS are given and different CS recovery algorithms are carried out to show the effectiveness of the proposed algorithms in the dimension-restricted system. The diversity dimension spread CS outperforms the directed dimension spread CS for its effective dimension spread and diversity. The proposed algorithms can be directly applied in channel estimation and multiuser detection in overload system.

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

Access this article

Log in via an institution

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

References

  1. Lustig, M., Donoho, D. L., Santos, J. M., et al. (2008). Compressed sensing MRI. IEEE Signal Processing Magazine, 25(2), 72–82.

    Article  Google Scholar 

  2. Dai, W., Sheikh, M. A., Milenkovic, O., et al. (2009). Compressive sensing DNA microarrays. EURASIP Journal on Bioinformatics and Systems Biology, 2009(2), 1–12.

    Article  Google Scholar 

  3. Ender, J. H. G. (2010). On compressive sensing applied to radar. Signal Processing, 90(5), 1402–1414.

    Google Scholar 

  4. Candes, E. J. (2008). The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathematique, 346(9–10), 589–592.

    Article  MathSciNet  MATH  Google Scholar 

  5. Donoho, D. L., & Elad, M. (2003). Optimally sparse representation in general (nonorthogonal) dictionaries via l(1) minimization. In Proceedings of the national academy of sciences of the United States of America, 2003 (pp. 2197–2202).

  6. Davenport, M., Duarte, M., & Eldar, Y., et al. (2012). Introduction to compressed sensing. In Y. C. Eldar & G. Kutyniok (Eds.), Compressed sensing: Theory and applications. Cambridge: Cambridge University Press.

  7. Wiaux, Y., Puy, G., & Gruetter, R., et al. (2010). Spread spectrum for compressed sensing techniques in magnetic resonance imaging. In 2010 7th IEEE international symposium on biomedical imaging: From nano to macro, 2010 (pp. 756–759).

  8. Eldar, Y. C., & Rauhut, H. (2010). Average case analysis of multichannel sparse recovery using convex relaxzation. IEEE Transactions on Information Theory, 56(1), 505–519.

    Article  MathSciNet  Google Scholar 

  9. Davenport, M. A., Laska, J. N., Boufounos, P., & Baraniuk, R. G. (2009). A simple proof that random matrices are democratic. In Proceedings of CoRR, 2009.

  10. Rakotomamonjy, A. (2011). Surveying and comparing simultaneous sparse approximation (or group-lasso) algorithms. Signal Processing, 91(7), 1505–1526.

    Article  MATH  Google Scholar 

  11. Tropp, J. A., & Gilbert, A. C. (2007). Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory, 53(12), 4655–4666.

    Article  MathSciNet  Google Scholar 

  12. Davies, M. E., & Eldar, Y. C. (2010). Rank awareness for joint sparse recovery. arXiv:1004.4529.

  13. Kim, J. M., Lee, O. K., & Ye, C. Y. (2012). Compressive MUSIC: Revisiting the link between compressive sensing and array signal processing. IEEE Transactions on Information Thoery, 58(1), 278–301.

    Google Scholar 

  14. Cai, T. T., & Wang, L. (2011). Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Transactions on Information Theory, 57(7), 4680–4688.

    Article  MathSciNet  Google Scholar 

  15. Needell, D., & Tropp, J. A. (2009). CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 26(3), 301–321.

    Google Scholar 

  16. Dai, W., & Milenkovic, O. (2009). Subspace pursuit for Compressive sensing signal reconstruction. IEEE Transactions on Information Thoery, 55(5), 2230–2249.

    Google Scholar 

Download references

Acknowledgments

This work is supported by National NSFC 60802009, China National Science and Technology Major Project 2013ZX03003-002-04 and 2010ZX03003-001-02, Sino-Korea International Cooperation Project 2012DFG12250, and Key Laboratory of Universal Wireless Communications Foundation Project.

Author information

Authors and Affiliations

  1. Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan National Laboratory for Optoelectronics, Wuhan, China

    Wei Lu, Desheng Wang & Yingzhuang Liu

  2. University of Southampton, Southampton, UK

    Fan Jin

Authors
  1. Wei Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Desheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yingzhuang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fan Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Lu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lu, W., Wang, D., Liu, Y. et al. Compressed Sensing via Dimension Spread in Dimension-Restricted Systems. Wireless Pers Commun 71, 2625–2636 (2013). https://doi.org/10.1007/s11277-012-0958-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-012-0958-y

Keywords

Search

Navigation