Advertisement

A GNC Method for Nonconvex Nonsmooth Image Restoration

  • Xiao-Guang LiuEmail author
  • Qiu-fang Xue
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9317)

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.

Keywords

Nonconvex nonsmooth Augmented lagrangian GNC method 

References

  1. 1.
    Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 2nd edn. Prentice Hall, Upper Saddle River (2002)Google Scholar
  2. 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. 3.
    Geman, D., Reynolds, G.: Constrained restoration and recovery of discontinuities. IEEE Trans. Pattern Anal. Mach. Intell. 14, 367–383 (1992)CrossRefGoogle Scholar
  4. 4.
    Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)zbMATHGoogle Scholar
  5. 5.
    Bian, W., Xue, X.P.: Subgradient-based neural network for nonsmooth nonconvex optimization problem. IEEE Trans. Neural Netw. 20, 1024–1038 (2009)CrossRefGoogle Scholar
  6. 6.
    Blake, A., Zisserman, A.: Visual Reconstruction. MIT Press, Cambridge (1987)Google Scholar
  7. 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)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Sun, W.Y., Yuan, Y.X.: Optimization Theory and Method: Nonlinear Programming. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  9. 9.
    Rockafellar, R.T.: Lagrange muitipliers and optimality. SIAM Rev. 35, 183–238 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imag. Vis. 20, 89–97 (2004)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Chan, T.F., Chen, K.: An optimization based total variation image denoising. SIAM J. Multiscale Model. Sim. 5, 615–645 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Computer Science and TechnologySouthwest University for NationalitiesChengduPeople’s Republic of China
  2. 2.The Department of Applied MathematicsXi’an University of TechnologyXi’anPeople’s Republic of China

Personalised recommendations