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A Relaxed Split Bregman Iteration for Total Variation Regularized Image Denoising

  • Jun Zhang
  • Zhi-Hui Wei
  • Liang Xiao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7390)

Abstract

The split Bregman iteration is an efficient tool for solving the total variation regularized minimization problems and has received considerable attention in recent years. In denoising case, it can remove noise well, but fails to preserve textures efficiently. In this paper, we reinterpret the split Bregman iteration from the perspective of function matching, and reveal the reason why it can not preserve textures well. To improve the performance of texture preservation, we develop a relaxed split Bregman iteration for total variation regularized image denoising. Numerical results show that for partly textured images, the new method can remove noise in the non-textured region and preserve textures in the textured region adaptively, and therefore it can improve the result both visually and in terms of the peak signal to noise ratio efficiently.

Keywords

Split Bregman Iteration Texture Preservation Function Matching 

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References

  1. 1.
    Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear Total Variation Based Noise Removal Algorithms. Physica D: Nonlinear Phenomena 60(1–4), 259–268 (1992)zbMATHCrossRefGoogle Scholar
  2. 2.
    Chambolle, A.: An Algorithm for Total Variation Minimization and Applications. Journal of Mathematical Imaging and Vision 20(1), 89–97 (2004)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Goldstein, T., Osher, S.: The Split Bregman Method for L1 Regularized Problems. SIAM Journal on Imaging Sciences 2(2), 323–343 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Setzer, S., Steidl, G., Teuber, T.: Deblurring Poissonian Images by Split Bregman Techniques. Journal of Visual Communication and Image Representation 21(3), 193–199 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Liu, X., Huang, L.: Split Bregman Iteration Algorithm for Total Bounded Variation Regularization Based Image Deblurring. Journal of Mathematical Analysis and Applica-tions 372(2), 486–495 (2010)zbMATHCrossRefGoogle Scholar
  6. 6.
    Goldstein, T., Bresson, X., Osher, S.: Geometric Applications of The Split Bregman Method: Segmentation and Surface Reconstruction. Journal of Scientific Computing 45, 272–293 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Yin, W., Osher, S., Goldfarb, D., Darbon, J.: Bregman Iterative Algorithms for l1-minimization with Applications to Compressed Sensing. SIAM Journal on Imaging Sciences 1(1), 143–168 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An Iterative Regularization Method for Total Variation-based Image Restoration. Multiscale Modeling and Simulation 4(2), 460–489 (2006)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Gilboa, G., Sochen, N., Zeevi, Y.Y.: Variational Denoising of Partly Textured Images by Spatially Varying Constraints. IEEE Transactions on Image Processing 15(8), 2281–2289 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jun Zhang
    • 1
  • Zhi-Hui Wei
    • 2
  • Liang Xiao
    • 2
  1. 1.School of ScienceNanjing University of Science and TechnologyNanjingP.R. China
  2. 2.School of Computer Science and TechnologyNanjing University of Science and TechnologyNanjingP.R. China

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