Skip to main content
SpringerLink
Log in

Reconstructing Sparse Signals from Dyadic Wavelet Transform Modulus Maxima

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

Abstract

The problem of how to recover a signal from its dyadic wavelet transform modulus maxima is considered. Based on the additional assumption that the signal has sparse representations in some transformed domains, a regularization-based reconstruction approach is proposed. The resulting minimization problem can be efficiently solved by iterative thresholding algorithm. Numerical experiments show the effectiveness of the proposed 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
Fig. 4

Similar content being viewed by others

References

  1. Z. Berman, J.S. Baras, Properties of the multiscale maxima and zero-crossings representations. IEEE Trans. Signal Process. 41(12), 3216–3231 (1993)

    Article  MATH  Google Scholar 

  2. V. Bruni, D. Vitulano, Wavelet-based signal de-noising via simple singularities approximation. Signal Processing 86(4), 859–876 (2006)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  4. A.E. Cetin, R. Ansari, Signal recovery from wavelet transform maxima. IEEE Trans. Signal Process. 42(1), 194–196 (1994)

    Article  Google Scholar 

  5. Z. Cvetkovic, M. Vetterli, Discrete-time wavelet extrema representation: design and consistent reconstruction. IEEE Trans. Signal Process. 43(3), 681–693 (1995)

    Article  Google Scholar 

  6. M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing (Springer, New York, 2010)

    Book  Google Scholar 

  7. Y.C. Eldar, G. Kutyniok, Compressed Sensing: Theory and Applications (Cambridge University Press, Cambridge, 2012)

    Book  Google Scholar 

  8. N.F. Law, A.W.C. Liew, Wavelet maxima reconstruction by conjugate gradient. Electron. Lett. 33(23), 1928–1929 (1997)

    Article  Google Scholar 

  9. A.W.C. Liew, D.T. Nguyen, Reconstruction from wavelet transform modulus maxima using non-expansive projections. Electron. Lett. 31(13), 1038–1039 (1995)

    Article  Google Scholar 

  10. S. Mallat, Z. Zhong, Characterization of signals from multiscale edges. IEEE Trans. Patt. Anal. Mach. Intell. 14(7), 710–732 (1992)

    Article  Google Scholar 

  11. S. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, 3rd edn. (Academic Press, Burlington, 2009)

    Google Scholar 

  12. S. Meignen, P.Y. Guméry, Reconstruction of finite signal derivatives from multiscale extrema representations: application to transient estimation and signal approximation. IEEE Trans. Inf. Theory 51(3), 1049–1062 (2005)

    Article  Google Scholar 

  13. A. Ouahabi, S. Femmam, Wavelet-based multifractal analysis of 1-D and 2-D signals: new results. Analog Integr. Circ. Signal Process. 69(1), 3–15 (2011)

    Article  Google Scholar 

  14. Z.K. Penga, F.L. Chua, P.W. Tse, Singularity analysis of the vibration signals by means of wavelet modulus maximal method. Mech. Syst. Signal Process. 21(2), 780–794 (2007)

    Article  Google Scholar 

  15. C.L. Tu, W.L. Hwang, J. Ho, Analysis of singularities from modulus maxima of complex wavelets. IEEE Trans. Inf. Theory 51(3), 1049–1062 (2005)

    Article  MathSciNet  Google Scholar 

  16. E. Wesfreid, V.L. Billat, Y. Meyer, Multifractal analysis of heartbeat time series in human races. Appl. Comput. Harmon. Anal. 18(3), 329–335 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  17. Z. Zhang, C. Chui, K. Liu, Iterative-hard threshold algorithm with momentum. Electron. Lett. 47(4), 257–259 (2011)

    Article  Google Scholar 

  18. M. Zibulevsky, M. Elad, L1–L2 optimization in signal and image processing. IEEE Signal Process. Mag. 27(3), 76–88 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is supported by the “973” National Basic Research Program of China (2010CB731900) and the Fundamental Research Funds for the Central Universities of China. The authors would like to thank the reviewers for their comments and suggestions that helped to improve the quality of this paper.

Author information

Authors and Affiliations

  1. Department of Information Science, Xi’an Jiaotong University, Xi’an , 710049, China

    Zhuosheng Zhang, Haixing Lv & Qingbao Zhou

  2. Department of Microelectronics, Xi’an Jiaotong University, Xi’an , 710049, China

    Hanqiu Zhang

Authors
  1. Zhuosheng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haixing Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qingbao Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hanqiu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhuosheng Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Z., Lv, H., Zhou, Q. et al. Reconstructing Sparse Signals from Dyadic Wavelet Transform Modulus Maxima. Circuits Syst Signal Process 33, 2667–2674 (2014). https://doi.org/10.1007/s00034-014-9752-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9752-2

Keywords

Search

Navigation