Skip to main content
SpringerLink
Log in

A GNC Method for Nonconvex Nonsmooth Image Restoration

  • Conference paper
  • First Online:
Smart Graphics (SG 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9317))

Included in the following conference series:

  • 464 Accesses

Abstract

The augmented Lagrangian duality method have superior restoration performance for nonconvex nonsmooth images. However, an effective initial value could not be obtained for the augmented Lagrangian duality when it is used alone. To overcome this drawback, a hybrid method based on the augmented Lagrangian duality method and the graduated nonconvex method(GNC) is proposed. The better restored performance of the proposed method are illustrated by some numerical results.

This work was supported in part by grants from the Fundamental Research Funds for the Central Universities of Southwest University for Nationalities (2015NZYQN30).

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 2nd edn. Prentice Hall, Upper Saddle River (2002)

    Google Scholar 

  2. Guo, X.X., Li, F., Ng, M.K.: A fast \(\ell _1-\text{TV}\) algorithm for image restoration. SIAM J. Sci. Comput., 2322–2341 (2009)

    Google Scholar 

  3. Geman, D., Reynolds, G.: Constrained restoration and recovery of discontinuities. IEEE Trans. Pattern Anal. Mach. Intell. 14, 367–383 (1992)

    Article  Google Scholar 

  4. Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)

    MATH  Google Scholar 

  5. Bian, W., Xue, X.P.: Subgradient-based neural network for nonsmooth nonconvex optimization problem. IEEE Trans. Neural Netw. 20, 1024–1038 (2009)

    Article  Google Scholar 

  6. Blake, A., Zisserman, A.: Visual Reconstruction. MIT Press, Cambridge (1987)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. Sun, W.Y., Yuan, Y.X.: Optimization Theory and Method: Nonlinear Programming. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  9. Rockafellar, R.T.: Lagrange muitipliers and optimality. SIAM Rev. 35, 183–238 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imag. Vis. 20, 89–97 (2004)

    Article  MathSciNet  Google Scholar 

  11. Chan, T.F., Chen, K.: An optimization based total variation image denoising. SIAM J. Multiscale Model. Sim. 5, 615–645 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang, Y.L., Yang, J.F., Yin, W.T., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imag. Sci. 1, 248–272 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Southwest University for Nationalities, Chengdu, 610041, Sichuan, People’s Republic of China

    Xiao-Guang Liu

  2. The Department of Applied Mathematics, Xi’an University of Technology, Xi’an, 710054, Shaanxi, People’s Republic of China

    Qiu-fang Xue

Authors
  1. Xiao-Guang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiu-fang Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiao-Guang Liu .

Editor information

Editors and Affiliations

  1. Southwest University for Nationalities, Chengdu, China

    Yaxi Chen

  2. Inria/IRISA Rennes, Rennes, France

    Marc Christie

  3. Southwest University for Nationalities, Chengdu, China

    Wenrong Tan

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Liu, XG., Xue, Qf. (2017). A GNC Method for Nonconvex Nonsmooth Image Restoration. In: Chen, Y., Christie, M., Tan, W. (eds) Smart Graphics. SG 2015. Lecture Notes in Computer Science(), vol 9317. Springer, Cham. https://doi.org/10.1007/978-3-319-53838-9_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-53838-9_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53837-2

  • Online ISBN: 978-3-319-53838-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation