Skip to main content
SpringerLink
Log in

An Orthogonal Matching Pursuit Algorithm Based on Singular Value Decomposition

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

Abstract

A recovery algorithm is one of the most important components in compressive sensing. It is responsible for the recovery of sparse coefficients in some bases of the original signal from a set of non-adaptive and underdetermined linear measurements, and it is a key link between the front-end signal sensing system and back-end processing. In this study, an improved orthogonal matching pursuit algorithm based on singular value decomposition is proposed to overcome the limitations of existing algorithms, which effectively eliminates the correlation between the measured values. The results of simulation experiments show that the proposed algorithm significantly improves the average signal-to-noise ratio, and it performs more robustly than the classical orthogonal matching pursuit 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
Fig. 3

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. E.J. Candès, T. Tao, Near-optimal signal recovery from random projections: universal encoding strategies. IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. E.J. Candès, J. Romberg, Sparsity and incoherence in compressive sampling. Inverse Prob. 23(3), 969–985 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. E.J. Candès, The restricted isometry property and its implications for compressed sensing. C.R. Math. 346(9), 589–592 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. E.J. Candès, M.B. Wakin, An introduction to compressive sampling. IEEE Signal Process. Mag. 25(2), 21–30 (2008)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. M.F. Duarte, M.A. Davenport, D. Takhar et al., Single-pixel imaging via compressive sampling. IEEE Signal Process. Mag. 25(2), 83–91 (2008)

    Article  Google Scholar 

  8. G.H. Golub, C.F. Van Loan, Matrix Computations (JHU Press, Baltimore, 2012)

    MATH  Google Scholar 

  9. M.A. Lexa, M.E. Davies, J.S. Thompson, Reconciling compressive sampling systems for spectrally sparse continuous-time signals. IEEE Trans. Signal Process. 60(1), 155–171 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Ma, G. Plonka, M.Y. Hussaini, Compressive video sampling with approximate message passing decoding. IEEE Trans. Circuits Syst. Video Technol. 22(9), 1354–1364 (2012)

    Article  Google Scholar 

  11. D. Needell, R. Vershynin, Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. Found. Comput. Math. 9(3), 317–334 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. D. Needell, J.A. Tropp, CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. J.A. Tropp, A.C. Gilbert, Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. J.A. Tropp, Greed is good: algorithmic results for sparse approximation. IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. G. Xu, Z. Xu, Compressed sensing matrices from Fourier matrices. IEEE Trans. Inf. Theory 61(1), 469–478 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. H.R. Yang, C. Zhang, D.W. Ding, Compressed sensing theory and reconstruction algorithm. Electron. J. 39(1), 142–148 (2011)

    Google Scholar 

Download references

Acknowledgments

I thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.

Author information

Authors and Affiliations

  1. School of Computer and Information, The University Key Laboratory of Intelligent Perception and Computing of Anhui Province, Anqing Normal University, Anqing, 246011, China

    Cui-juan Zhang

Authors
  1. Cui-juan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cui-juan Zhang.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Cj. An Orthogonal Matching Pursuit Algorithm Based on Singular Value Decomposition. Circuits Syst Signal Process 39, 492–501 (2020). https://doi.org/10.1007/s00034-019-01182-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-019-01182-2

Keywords

Search

Navigation