Skip to main content
SpringerLink
Log in

The Improvement of Compressive Sampling and Matching Pursuit Algorithm Based on Pre-estimation

  • Published:
International Journal of Wireless Information Networks Aims and scope Submit manuscript

Abstract

This paper presents a novel iterative greedy reconstruction algorithm for compressed sensing, called the compressive sampling and matching pursuit algorithm based on pre-estimation (PCoSaMP). Compression sampling matching pursuit algorithm (CoSaMP) is widely applied to image reconstruction owing to its high precision of reconstruction, robustness, and simple operation. In this paper, we propose a new method, the PCoSaMP, to properly overcome the shortcomings in CoSaMP for choosing too much optional atoms and imprecise choice. The concept of the maximum estimation, which is called M, is proposed as a key point. The M is calculated from the current support set of target signals in each iteration using the largest correlation test method. At the next step, the M is regard as a selection condition for the optional atoms to decrease the number of candidate atoms and increase its accuracy. The simulation results show that this algorithm can precisely reconstruct the original signal. Under the same sampling rate, compared to the original algorithm, the proposed method can greatly shorten the recovery time, improve the PSNR and reconstruction performance.

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
Fig. 6

Similar content being viewed by others

References

  1. D. L. Donoho, “Compressed Sensing,” IEEE Trans. Information Theory, vol. 52, no. 4, pp. 1289–1306, Apr 2006.

  2. E. J. Candes, M. B. Wakin, “An introduction to compressive sampling,” IEEE Siganl Process., vol 25, no. 2, pp. 21–30, Mar 2008.

  3. E. Candes, J. Romberg, T. Tao, “Stable Signal Recovery From Incomplete and accurate Measurement,” Communication on Pure and Applied Mathematics, vol 59, no. 8, pp. 1207–1223, 2006.

  4. X. Y. Wang, Y. Wang, “Fast-varying channel estimation method base on basis expansion models in IEEE 802.16e system,” China Sciencepaper, vol. 8, no. 4, pp. 295–198, 2013.

  5. S. Qaisar, R. M. Bilal, W. Iqbal, M. Naureen, “Compressed sensing: from theory to application, a survey,” Journal of Communications and Networks, vol. 15, no. 5, pp. 443–456, 2013.

  6. T. Goldstein, L. Xu, K. F. Kelly and R. Baraniuk, “The STONE Transform: Multi-Resolution Image Enhancement and Compressive Video,” IEEE Transactions on Image Processing, vol. 24, no. 12, pp. 5581–5593, August 2015.

  7. R. Koller, L. Schmid, N. Matsuda, T. Niederberger, L. Spinoulas, O. Cossairt, G. Schuster, A. K. Katsaggelos, “High spatio-temporal resolution video with compressed sensing,” Optics Express, vol. 23, no. 12, pp. 5992–6007, June 2015.

  8. 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, December 2007.

  9. D. L. Donoho, Y. Tsaig, I. Drori and J. L. Starck, “Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit,” IEEE Transactions on Information Theory, vol. 58, no. 2, pp. 1094–1121, February 2012.

  10. W. Dai and O. Milenkovic, “Subspace Pursuit for Compressive Sensing Signal Reconstruction,” IEEE Transactions on Information Theory, vol. 55, no. 5, pp. 2230–2249, May 2009.

  11. D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Applied & Computational Harmonic Analysis, vol. 26, no. 12, pp. 93–100, May 2008.

  12. Y. D. Yue, J. Q. Yu, Y.Y Wei, X. Liu, T. T. Cui, “A Improved CoSaMP Algorithm Based on Correlation Coefficient for Compressed Sensing Image Reconstruction,” Journal of Computational Information Systems, vol. 9, no. 18, pp. 7325–7331, 2013.

  13. S. S. Chen, D. L. Donoho and M. A. Saunders, “Atomic Decomposition by Basis Pursuit,” Siam Journal on Scientific Computing, vol. 58, no. 1, pp. 33–61, August 1998.

  14. E. J. Candes, M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process., vol. 25, no. 3, pp. 21–30. Mar 2008.

  15. Y. G. Cen, R. Z. Zhao, Z. J. Miao, L. H. Cen, L. H. Cui, “A new approach of conditions on δ2s(Φ) for s-sparse recovery,” Science China Information Sciences, vol. 57, no. 4, pp. 1–7, 2014.

  16. Y. Tsaig, D. L. Donoho, “Extensions of Compressed Sensing,” Signal Processing, vol. 86, no. 3, pp. 549–571, 2006.

  17. P. Anandan, R. S. Sabeenian, “Image Compression Techniques using Curvelet, Contourlet Ridgelet and Wavelet Transformsa–A Review,” Biometrics and Bioinformatics, vol. 5, no. 7, pp. 267–270, 2013.

  18. G. Plonka, J. Ma, “Curvelet-wavelet regularized split Bregman iteration for compressed sensing,” International Journal of Wavelets, Multiresolution and Information Processing, vol. 9, no. 1, pp. 79–110, 2011.

Download references

Acknowledgments

Project supported by the National Nature Science Foundation of China (No. 61171140), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130031110032), Tianjin Key Technology Program of the Ministry of Science and Technology (No. 14ZCZDNC00014).

Author information

Authors and Affiliations

  1. College of Electronic Information and Optical Engineering, Nankai University, Tianjin, 300071, China

    Guiling Sun, Yangyang Li, Haojie Yuan, Jingfei He & Tianyu Geng

Authors
  1. Guiling Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yangyang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haojie Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jingfei He
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tianyu Geng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guiling Sun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, G., Li, Y., Yuan, H. et al. The Improvement of Compressive Sampling and Matching Pursuit Algorithm Based on Pre-estimation. Int J Wireless Inf Networks 23, 129–134 (2016). https://doi.org/10.1007/s10776-016-0310-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10776-016-0310-7

Keywords

Search

Navigation