Skip to main content
Log in

A Generalized Hard Thresholding Pursuit Algorithm

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

Abstract

Compressed sensing ensures the accurate reconstruction of sparse signals from far fewer samples than required in the classical Shannon–Nyquist theorem. In this paper, a generalized hard thresholding pursuit (GHTP) algorithm is presented that can recover unknown vectors without the sparsity level information. We also analyze the convergence of the proposed algorithm. Numerical experiments are given for synthetic and real-world data to illustrate the validity and the good performance of the proposed algorithm.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1
Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. M. Aharon, M. Elad, A. Bruckstein, K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54(11), 2386–2395 (2006)

    Article  Google Scholar 

  2. A.S. Bandeira, E. Dobriban, D.G. Mixon, W.F. Sawin, Certifying the restricted isometry property is hard. IEEE Trans. Inf. Theory 59(6), 3448–3450 (2013)

    Article  MathSciNet  Google Scholar 

  3. T. Blumensath, Accelerated iterative hard thresholding. Signal Process. 92(3), 752–756 (2012)

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. T. Blumensath, M.E. Davies, Normalised iterative hard thresholding: guaranteed stability and performance. IEEE J. Sel. Top. Signal Process. 4(2), 298–309 (2010)

    Article  Google Scholar 

  6. 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  MATH  Google Scholar 

  7. W. Dai, O. Milenkovic, Subspace pursuit for compressive sensing signal reconstruction. IEEE Trans. Inf. Theory 55(5), 2230–2249 (2009)

    Article  MathSciNet  Google Scholar 

  8. D.L. Donoho, Y. Tsaig, I. Drori, J.-L. Starck, Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Trans. Inf. Theory 58(2), 1094–1121 (2012)

    Article  MathSciNet  Google Scholar 

  9. J. Duarte-Carvajalino, G. Sapiro, Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization. IEEE Trans. Image Process. 18(7), 1395–1408 (2009)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Y. Fu, Q. Zhang, S. Xie, Compressed sensing for sparse error correcting model. Circuits Syst. Signal Process. 32(5), 2371–2383 (2013)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. J. Wang, S. Kwon, B. Shim, Generalized orthogonal matching pursuit. IEEE Trans. Signal Process. 60(12), 6202–6216 (2012)

    Article  MathSciNet  Google Scholar 

  15. H.L. Wu, S. Wang, Adaptive sparsity matching pursuit algorithm for sparse reconstruction. IEEE Signal Process. Lett. 19(8), 471–474 (2012)

    Article  Google Scholar 

  16. L. Zelnik-Manor, K. Rosenblum, Y.C. Eldar, Dictionary optimization for block-sparse representations. IEEE Trans. Signal Process. 60(5), 2386–2395 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We are grateful to the authors of [15] for their code of the ASMP. The work was partially supported by Guangdong-National Ministry of Education IAR project (Grant 2012B091100331), NSFC-Guangdong union project (Grant U0835003), and the NSFC (Grants 61004054, 61104053 and 61103122).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yuli Fu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, H., Fu, Y., Zhang, Q. et al. A Generalized Hard Thresholding Pursuit Algorithm. Circuits Syst Signal Process 33, 1313–1323 (2014). https://doi.org/10.1007/s00034-013-9694-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-013-9694-0

Keywords

Navigation