Skip to main content
SpringerLink
Log in

A Lorentzian IHT for Complex-Valued Sparse Signal Recovery

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

Abstract

In this paper, robust complex-valued sparse signal recovery is considered in the presence of impulse noise. A generalized Lorentzian norm is defined for complex-valued signals. A complex Lorentzian iterative hard thresholding algorithm is proposed to realize the signal recovery. Simulations are given to demonstrate the validity of our results.

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

Similar content being viewed by others

References

  1. T. Adali, P.J. Schreier, Optimization and estimation of complex-valued signals: theory and applications in filtering, blind source separation. IEEE Signal Process. Mag. 31(5), 112–128 (2014)

    Article  Google Scholar 

  2. D.E. Berraki, S.M.D. Armour, A.R. Nix, Application of compressive sensing in sparse spatial channel recovery for beamforming in mmWave outdoor systems, in IEEE WCNC, pp. 887–892 (2014)

  3. R.G. Baraniuk, Compressive sensing [lecture notes]. IEEE Signal Process. Mag. 24(4), 118–121 (2007)

    Article  Google Scholar 

  4. R.G. Baraniuk, P. Steeghs, Compressive radar imaging, in IEEE radar conference, pp. 128–133 (2007)

  5. T. Blumensath, M.E. Davies, Normalized iterative hard thresholding: guaranteed stability and performance. IEEE J. Sel. Top. Signal Process. 4(6), 298–309 (2010)

    Article  Google Scholar 

  6. Z. Ben-Haim, Y.C. Eldar, The Cramér–Rao bound for estimating a sparse parameter vector. IEEE Trans. Signal Process. 58(6), 3384–3389 (2010)

    Article  MathSciNet  Google Scholar 

  7. R.E. Carrillo, K.E. Barner, Lorentzian iterative hard thresholding: robust compressed sensing with prior information. IEEE Trans. Signal Process. 61(19), 4822–4833 (2013)

    Article  MathSciNet  Google Scholar 

  8. R.E. Carrillo, K.E. Barner, T.C. Aysal, Robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise. IEEE J. Sel. Top. Signal Process. 4(2), 392–408 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Y. Ji, Z. Yang, W. Li, Bayesian sparse reconstruction method of compressed sensing in the presence of impulsive noise. Circuits Syst. Signal Process. 32(6), 2971–2998 (2013)

    Article  MathSciNet  Google Scholar 

  11. E.T. Northardt, I. Bilik, Y.I. Abramovich, Spatial compressive sensing for direction-of-arrival estimation with bias mitigation via expected likelihood. IEEE Trans. Signal Process. 61(5), 1183–1195 (2013)

    Article  MathSciNet  Google Scholar 

  12. E. Ollila, H.-J. Kim, V. Koivunen, Robust iterative hard thresholding for compressed sensing, in IEEE ISCCSP, pp. 226–229 (2014)

  13. E. Ollila, Multichannel sparse recovery of complex-valued signals using Huber’s criterion, in IEEE CoSeRa, pp. 26–30 (2015)

  14. C. Studer, P. Kuppinger, G. Pope, H. Bolcskei, Recovery of sparsely corrupted signals. IEEE Trans. Inf. Theory 58(5), 3115–3130 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. L. Stanković, M. Daković, S. Vujović, Reconstruction of sparse signals in impulsive disturbance environments. Circuits Syst. Signal Process. 36(2), 767–794 (2017)

    Article  MATH  Google Scholar 

  16. V. Stojanovic, N. Nedic, Joint state and parameter robust estimation of stochastic nonlinear systems. Int. J. Robust Nonlinear Control 26(14), 3058–3074 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. V. Stojanovic, N. Nedic, D. Prsic, L. Dubonjic, Optimal experiment design for identification of ARX models with constrained output in non-Gaussian noise. Appl. Math. Model. 40(13–14), 6676–6689 (2016)

    Article  MathSciNet  Google Scholar 

  18. V. Stojanovic, N. Nedic, Robust identification of OE model with constrained output using optimal input design. J. Franklin Inst. 353(2), 576–593 (2016)

    Article  MathSciNet  Google Scholar 

  19. V. Stojanovic, N. Nedic, Identification of time-varying OE models in presence of non-Gaussian noise: application to pneumatic servo drives. Int. J. Robust Nonlinear Control 26(18), 3974–3995 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. G.A. Tsihrintzis, C.L. Nikias, Fast estimation of the parameters of alpha-stable impulsive interference. IEEE Trans. Signal Process. 44(6), 1492–1503 (1996)

    Article  Google Scholar 

  21. W.J. Zeng, H.C. So, X. Jiang, Outlier-robust greedy pursuit algorithms in \(\ell _{p}\)-space for sparse approximation. IEEE Trans. Signal Process. 64(1), 60–75 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported partially by NSFC (Grant: 61471174), Guangzhou Science Research Project (Grant: 2014J4100247) and SCUT Xinghua Talents Program (Grant: J2RS-D6161650).

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China

    Rui Hu, Yuli Fu, Zhen Chen, Youjun Xiang & Jie Tang

Authors
  1. Rui Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuli Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhen Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Youjun Xiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jie Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuli Fu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, R., Fu, Y., Chen, Z. et al. A Lorentzian IHT for Complex-Valued Sparse Signal Recovery. Circuits Syst Signal Process 37, 862–872 (2018). https://doi.org/10.1007/s00034-017-0575-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-017-0575-9

Keywords

Search

Navigation