Skip to main content

A Blind Adaptive Matching Pursuit Algorithm for Compressed Sensing Based on Divide and Conquer

  • Conference paper
Book cover Advances in Electronic Engineering, Communication and Management Vol.2

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 140))

Abstract

The existing reconstruction algorithms are mainly implemented based on the known sparsity of original signal. In this paper, a new algorithm called blind adaptive matching pursuit (BAMP) is proposed in this paper, which can recover the original signal fast in the case of unknown sparsity based on the divide and conquer method. Firstly, the range of sparsity is determined by trial and error test. Secondly, the efficient support set is screened out rapidly by adaptive grouping and support extension. Last but not least, reconstructed signal is obtained by pruning. The results of simulation show that the new algorithm can reconstruct signal faster and get better precision than other similar algorithms in the same conditions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baraniuk, R.G.: Compressive Sensing. IEEE Signal Processing Magazine 24, 118–121 (2007)

    Article  Google Scholar 

  2. Donoho, D.L.: Compressed sensing. IEEE Trans. on Information Theory 52, 1289–1306 (2006)

    Article  MathSciNet  Google Scholar 

  3. Donoho, D.L., Tsaig, Y.: Extensions of compressed sensing. Signal Process. 86, 533–548 (2006)

    Article  MATH  Google Scholar 

  4. Guangming, S., Danhua, L., Dahua, G., Zhe, L., Jie, L., Liangjun, W.: Advances in Theory and Application of Compressed Sensing (in Chinese). Acta Electronica Sinica 37, 1070–1081 (2009)

    Google Scholar 

  5. Do, T.T., Gan, L., Nguyen, N.S.: Sparsity adaptive matching pursuit algorithm for practical compressed sensing. In: Asilomar Conference on Signals, Systems and Computers (2008)

    Google Scholar 

  6. Needell, D., Tropp, J.A.: CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples. Commun. ACM 53, 93–100 (2010)

    Article  Google Scholar 

  7. Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic Decomposition by Basis Pursuit. SIAM J. Sci. Comput. 20, 33–61 (1998)

    Article  MathSciNet  Google Scholar 

  8. Mallat, S., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. on Signal Processing 41, 3397–3415 (1993)

    Article  MATH  Google Scholar 

  9. Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE T. Inform. Theory 53, 4655–4666 (2007)

    Article  MathSciNet  Google Scholar 

  10. Donoho, D.L., Tsaig, Y., Drori, I., Starck, J.: Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit (2006)

    Google Scholar 

  11. Blumensath, T., Davies, M.E.: Iterative thresholding for sparse approximation. Fourier Anal. 14, 629–654 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Gilbert, A., Strauss, M., Tropp, J., Vershynin, R.: Algorithmic linear dimension reduction in the l 1 norm for sparse vectors, http://www.math.ucdavis.edu/~vershynin/papers/algorithmic-dim-reduction.pdf

  13. Gilbert, A.C., Strauss, M.J., Trop, J.A., Al, E.: One sketch for all: Fast algorithms for compressed sensing. In: Proceedings of the 39th Annual ACM Symposium on Theory of Computing, pp. 237–246. Association for Computing Machiner (2007)

    Google Scholar 

  14. Zongnian, Z., Rentai, H., Jingwen, Y.: A Blind Sparsity Reconstruction Algorithm for Compressed Sensing Signal (in Chinese). Acta Electronica Sinica 39, 18–22 (2011)

    Google Scholar 

  15. Yaxin, L., Ruizhen, Z., Shaohai, H., Chunhui, J.: Regularized Adaptive Matching Pursuit Algorithm for Signal Reconstruction Based on Compressive Sensing (in Chinese). Journal of Electronics & Information Technology 32, 2713–2717 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Berlin Heidelberg

About this paper

Cite this paper

Tian, W., Rui, G., Fu, Z. (2012). A Blind Adaptive Matching Pursuit Algorithm for Compressed Sensing Based on Divide and Conquer. In: Jin, D., Lin, S. (eds) Advances in Electronic Engineering, Communication and Management Vol.2. Lecture Notes in Electrical Engineering, vol 140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27296-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27296-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27295-0

  • Online ISBN: 978-3-642-27296-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics