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A Nonlocal Model for Image Restoration with Gamma Distributed Multiplicative Noise

  • Fahd Karami
  • Driss Meskine
  • Omar OubbihEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10884)

Abstract

The question of eliminating the multiplicative noise has attracted much interest in many research studies. In this work, we are interested with the one that are follows the Gamma distribution. The rationale of this paper is to shed light on a brief comparative study of some local and nonlocal models, for denoising images contaminated with the noise of this type. The improved method of Split Bregman is used to implement those models. The totality of experiments indicates that the proposed nonlocal method gives better results than some other methods.

Keywords

Multiplicative gamma noise Nonlocal TV operator Nonlocal weberized TV Split bregman iteration 

References

  1. 1.
    Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J.: A nonlocal \(p\)-Laplacian evolution equation with nonhomogeneous Dirichlet boundary conditions. SIAM J. Math. Anal. 40(5), 1815–1851 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aubert, G., Aujol, J.F.: A variational approach to removing multiplicative noise. SIAM J. Appl. Math. 68(4), 925–946 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bioucas-Dias, J.M., Figueiredo, M.A.T.: Total variation restoration of speckled images using a split-Bregman algorithm. In: Image Proceedings of IEEE (ICIP) (2009)Google Scholar
  4. 4.
    Dong, F., Zhang, H., Kong, D.X.: Nonlocal total variation models for multiplicative noise removal using split Bregman iteration. J. Math. Comput. Model. 55(3–4), 939–954 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Elmoataz, A., Lezoray, O., Bougleux, S.: Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing. IEEE Trans. Image Process. 17(7), 1047–1060 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gilboa, G., Osher, S.: Nonlocal operators with application to image processing. Multiscale Model. Simul. 7(3), 1005–1028 (2008)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Goldstein, T., Osher, S.: The split Bregman method for \(L1\) regularized problems. SIAM J. Imaging Sci. 2(2), 323–343 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Huang, L.L., Xiao, L., Wei, Z.H.: Multiplicative noise removal via a novel variational model. J. Image Video Process. (2010). Article ID 250768Google Scholar
  9. 9.
    Huang, Y.M., Ng, M.K., Wen, Y.W.: A new total variation method for multiplicative noise removal. SIAM J. Imaging Sci. 2(1), 20–40 (2009)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Ramamoorthy, S., Siva Subramanian, R., Gandhi, D.: An efficient method for speckle reduction in ultrasound liver images for e-health applications. In: Natarajan, R. (ed.) ICDCIT 2014. LNCS, vol. 8337, pp. 311–321. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-04483-5_32CrossRefGoogle Scholar
  11. 11.
    Rudin, L., Lions, P.L., Osher, S.: Multiplicative denoising and deblurring: theory and algorithms. In: Osher, S., Paragios, N. (eds.) Geometric Level Set Methods in Imaging, Vision, and Graphics, pp. 103–119. Springer, New York (2003).  https://doi.org/10.1007/0-387-21810-6_6CrossRefGoogle Scholar
  12. 12.
    Shen, J.: On the foundations of vision modeling: I. Weber’s law and Weberized TV restoration. J. Phys. D: Nonlinear Phenom. 175(3–4), 241–251 (2003)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Shi, J., Osher, S.: A nonlinear inverse scale space method for a convex multiplicative noise model. SIAM J. Imaging Sci. 1(3), 294–321 (2008)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Steidl, G., Teuber, T.: Removing multiplicative noise by Douglas-Rachford splitting methods. J. Math Imaging Vis. 36(2), 168–184 (2010)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Sveinsson, J.R., Benediktsson, J.A.: Speckle reduction and enhancement of SAR images in the wavelet domain. In: Proceedings of the International Geoscience and Remote Sensing Symposium, vol. 1, pp. 63–66 (1996)Google Scholar
  16. 16.
    Weber, E.H.: De pulsu, resorptione, auditu et tactu, in Annotationes anatomicae et physio-logicae. Koehler, Leipzig (1834)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.MMSC, École Supérieure de Technologie d’EssaouiraUniversité Cadi AyyadEssaouiraMorocco

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