Skip to main content
SpringerLink
Log in

A New Total Variation Denoising Algorithm for Piecewise Constant Signals Based on Non-convex Penalty

  • Conference paper
  • First Online:
Neural Computing for Advanced Applications (NCAA 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1449))

Included in the following conference series:

Abstract

Total variation signal denoising is an effective nonlinear filtering method, which is suitable for the restoration of piecewise constant signals disturbed by white Gaussian noises. Towards efficient denoising of piecewise constant signals, a new total variation denoising algorithm based on an improved non-convex penalty function is proposed in this paper. While ensuring the objective function is convex, a new non-convex penalty is designed. The denoising efficiency is improved by updating the dynamic total variational adjustment in the penalty function to the static adjustment. Experimental results demonstrated that the proposed denoising algorithm improved the denoising efficiency without affecting the denoising effect. The overall performance was shown better than the current excellent denoising algorithm.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight 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

References

  1. Little, M.A., Jones, N.S.: Generalized methods and solvers for noise removal from piecewise constant signals: Part I - background theory. Proc. R. Soc. A. 467(2135), 3088–3114 (2011)

    Article  Google Scholar 

  2. Storath, M., Weinmann, A., Demaret, L.: Jump-sparse and sparse recovery using potts functionals. IEEE Trans. Signal Process. 62(14), 3654–3666 (2014)

    Article  MathSciNet  Google Scholar 

  3. Condat, L.: A direct algorithm for 1-D total variation denoising. IEEE Signal Process. Lett. 20(11), 1054–1057 (2013)

    Article  Google Scholar 

  4. Du, H., Liu, Y.: Minmax-concave total variation denoising. Signal Image Video P. 12, 1027–1034 (2018)

    Google Scholar 

  5. Pan, H., Jing, Z., Qiao, L., Li, M.: Visible and infrared image fusion using \(l_0\)-generalized total variation model. Sci. China Inf. Sci. 61, 049103 (2018)

    Google Scholar 

  6. Li, M.: A fast algorithm for color image enhancement with total variation regularization. Sci. China Inf. Sci. 53(9), 1913–1916 (2010)

    Article  MathSciNet  Google Scholar 

  7. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60(1–4), 259–268 (1992)

    Article  MathSciNet  Google Scholar 

  8. Lanza, A., Morigi, S., Sgallari, F.: Convex image denoising via nonconvex regularization with parameter selection. J. Math. Imaging Vis. 56(2), 195–220 (2016)

    Article  Google Scholar 

  9. Luo, X., Wang, X., Suo, Z., Li, Z.: Efficient InSAR phase noise reduction via total variation regularization. Science China Information Sciences 58(8), 1–13 (2015). https://doi.org/10.1007/s11432-014-5244-z

  10. Selesnick, I., Lanza, A., Morigi, S., Sgallari, F.: Non-convex total variation regularization for convex denoising of signals. J. Math. Imaging Vis. 62, 825–841 (2020)

    Article  MathSciNet  Google Scholar 

  11. Selesnick, I.: Total variation denoising via the moreau envelope. IEEE Signal Process. Lett. 24(2), 216–220 (2017)

    Article  MathSciNet  Google Scholar 

  12. Zhang, X., Xu, C., Li, M., Sun, X.: Sparse and low-rank coupling image segmentation model via nonconvex regularization. Int. J. Pattern Recog. Artif. Intell. 29(2), 1555004 (2018)

    Article  MathSciNet  Google Scholar 

  13. Liu, Y., Du, H., Wang, Z., Mei, W.: Convex MR brain imagereconstruction via non-convex total variation minimization. Int. J. Imag. Syst. Technol. 28(4), 246–253 (2018)

    Article  Google Scholar 

  14. Yang, J.: An algorithmic review for total variation regularizeddata fitting problems in image processing. Oper. Res. Trans. 21(4), 69–83 (2017)

    MathSciNet  MATH  Google Scholar 

  15. Nikolova, M., Ng, M.K., Tam, C.: Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction. IEEE Trans. Image Process. 19(12), 3073–3088 (2010)

    Article  MathSciNet  Google Scholar 

  16. Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011). https://doi.org/10.1007/978-1-4419-9467-7

    Book  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the Hubei Province Natural Science Foundation under Grant 2020CFA031, the Inner Mongolia Natural Science Foundation under Grant 2019BS06004, and the National Natural Science Foundation of China under Grants 61773354 and 61903345.

Author information

Authors and Affiliations

  1. School of Automation, China University of Geosciences, Wuhan, 430074, China

    Donghao Lv, Weihua Cao, Wenkai Hu & Min Wu

  2. School of Information Engineering, Inner Mongolia University of Science and Technology, Baotou, 014010, China

    Donghao Lv

  3. Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan, China

    Donghao Lv, Weihua Cao, Wenkai Hu & Min Wu

  4. Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan, China

    Donghao Lv, Weihua Cao, Wenkai Hu & Min Wu

Authors
  1. Donghao Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weihua Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenkai Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Min Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weihua Cao .

Editor information

Editors and Affiliations

  1. Harbin Institute of Technology, Shenzhen, China

    Haijun Zhang

  2. Nanfang College of Sun Yat-sen University, Guangzhou, China

    Zhi Yang

  3. Hefei University of Technology, Hefei, China

    Zhao Zhang

  4. Chongqing University, Chongqing, China

    Zhou Wu

  5. South China Normal University, Guangzhou, China

    Tianyong Hao

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Lv, D., Cao, W., Hu, W., Wu, M. (2021). A New Total Variation Denoising Algorithm for Piecewise Constant Signals Based on Non-convex Penalty. In: Zhang, H., Yang, Z., Zhang, Z., Wu, Z., Hao, T. (eds) Neural Computing for Advanced Applications. NCAA 2021. Communications in Computer and Information Science, vol 1449. Springer, Singapore. https://doi.org/10.1007/978-981-16-5188-5_45

Download citation

  • DOI: https://doi.org/10.1007/978-981-16-5188-5_45

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-5187-8

  • Online ISBN: 978-981-16-5188-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation