Skip to main content
SpringerLink
Log in

Binary generalized orthogonal matching pursuit

  • Original Paper
  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

In signal processing, it is usually to meet the recovery of K-sparse binary signal. In order to reconstruct the K-sparse binary signal, the binary generalized orthogonal matching pursuit (BgOMP) algorithm is proposed in this paper. By using mutual coherence and restricted isometry property (RIP), the theoretical performance of the BgOMP algorithm is also investigated. Based on the results of simulation tests, BgOMP is better than the binary MP (BMP) algorithm.

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

Similar content being viewed by others

Data Availability

Anyone who want to study the data can email the corresponding author.

References

  1. Candes, E., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005)

    Article  MathSciNet  Google Scholar 

  2. Cohen, A., Dahmen, W., DeVore, R.: Compressed sensing and best k-term approximation. J. Amer. Math. Soc. 22, 211–231 (2009)

    Article  MathSciNet  Google Scholar 

  3. Wen, J., Li, D., Zhu, F.: Stable recovery of sparse signals via \(\ell _p\)-minimization. Appl. Comput. Harmon. Anal. 38(1), 161–176 (2015)

    Article  MathSciNet  Google Scholar 

  4. Fuchs, J.: Recovery of exact sparse representations in the presence of bounded noise. IEEE Trans. Inf. Theory 51(10), 3601–3608 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. Candes, E.: The restricted isometry property and its implications for compressed sensing, C. R. Acad. Sci. Paris, Ser I 346(11), 589–592 (2008)

  7. Cai, T., Wang, L.: Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Trans. Inf. Theory 57(7), 4680–4688 (2011)

    Article  MathSciNet  Google Scholar 

  8. Candes, E., Tao, T.: The dantzig selector: Statistical estimation when p is much larger than n. Ann. Statist 35, 2313–2351 (2007)

    MathSciNet  Google Scholar 

  9. Wen, J., Zhou, Z., Wang, J., Tang, X., Mo, Q.: A sharp condition for exact support recovery with orthogonal matching pursuit. IEEE Trans. Signal Process. 65(6), 1370–1382 (2017)

    Article  MathSciNet  Google Scholar 

  10. Jeganathan, J., Ghrayeb, A., Szczecinski, L., Generalized space shift keying modulation for MIMO channels, in,: IEEE 19th International Symposium on Personal. Indoor and Mobile Radio Commu- nications 2008, 1–5 (2008)

  11. Chen, Z., Sohrabi, F., Yu, W.: Sparse activity detection for massive connectivity. IEEE Trans. Signal Process. 66(7), 1890–1904 (2018)

    Article  MathSciNet  Google Scholar 

  12. Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  Google Scholar 

  13. Candes, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)

    Article  MathSciNet  Google Scholar 

  14. Pati, Y., Rezaiifar, R., Krishnaprasad, P.: Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition, in Proc. 27th Annu. Asilomar Conf. Signals, Systems, and Computers, vol. 1, pp. 40–44 (1993)

  15. Wang, J., Seokbeop, K., Byonghyo, S.: Generalized orthogonal matching pursuit. IEEE Trans. Signal Process. 60(12), 6202–6216 (2012)

    Article  MathSciNet  Google Scholar 

  16. Wen, J., Zhou, Z., Li, D., Tang, X.: A novel sufficient condition for generalized orthogonal matching pursuit. IEEE Commun. Lett. 21(4), 805–808 (2017)

    Article  Google Scholar 

  17. Li, H., Wen, J.: Generalized covariance-assisted matching pursuit. Signal Process. 163(5), 232–237 (2019)

    Article  Google Scholar 

  18. Blumensath, T., Davies, M.: Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27(3), 265–274 (2009)

    Article  MathSciNet  Google Scholar 

  19. Foucart, S.: Hard thresholding pursuit: an algorithm for compressive sensing. SIAM J. Numer. Anal. 49(6), 2543–2563 (2011)

    Article  MathSciNet  Google Scholar 

  20. Wen, J., Li, H.: Binary sparse signal recovery with binary matching pursuit. Inverse Prob. 37(6), 065014–065036 (2021)

    Article  MathSciNet  Google Scholar 

  21. Xu, Z.: The performance of orthogonal multi-matching pursuit under the restricted isometry property. J. Comp. Math. 33, 495–516 (2015)

    Article  MathSciNet  Google Scholar 

  22. Donoho, D., Huo, X.: Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inf. Theory 47(7), 2845–2862 (2001)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (grant nos. 12226341, 61907014).

Author information

Authors and Affiliations

  1. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Science, Henan Normal University, Jianshe Road, Xinxiang, 453007, Henan, China

    Haifeng Li & Hao Ying

  2. College of Information Science and Technology, Jinan University, Huangpu, Guangzhou, 510632, Guangdong, China

    Xiaoli Liu

Authors
  1. Haifeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao Ying
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoli Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haifeng Li.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, H., Ying, H. & Liu, X. Binary generalized orthogonal matching pursuit. Japan J. Indust. Appl. Math. 41, 1–12 (2024). https://doi.org/10.1007/s13160-023-00585-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13160-023-00585-8

Keywords

Mathematics Subject Classification

Search

Navigation