123
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Nonlocal total variation system for the restoration of textured images

, &
Pages 1749-1768 | Received 21 Jan 2020, Accepted 20 Oct 2020, Published online: 10 Dec 2020

References

  • L. Afraites, A. Atlas, F. Karami, et al., Some class of parabolic systems applied to image processing, Discrete Contin. Dyn. Syst. Ser. B 21 18(6) (2016), pp. 1671–1687.
  • F. Andreu, J.M. Mazón, J.D. Rossi, and J. Toledo, A nonlocal p-Laplacian evolution equation with Neumann boundary conditions, J. Math. Pures Appl. 90(2) (2008), pp. 201–227.
  • J.F. Aujol and A. Chambolle, Dual norms and images decomposition models, Int. J. Comput. Vis.63(1) (2005), pp. 85–104.
  • A. Buades, B. Coll, and J.M. Morel, A review of image denoising algorithms, with a new one, Multiscale Model. Simul. 4(2) (2005), pp. 490–530.
  • K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, mage denoising by sparse 3−D transform-domain collaborative filtering, IEEE Trans. Image Process 16(8) (2007), pp. 2080–2095.
  • A. Elmoataz, X. Desquesnes, and O. Lézoray, Non-local morphological PDEs and p-Laplacian equation on graphs with applications in image processing and machine learning, IEEE. J. Sel. Top. Signal. Process. 6 (2012), pp. 764–779.
  • A. Elmoataz, O. Lezoray, and S. Bougleux, Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing, IEEE Trans. Image Process 17 (2008), pp. 1047–1060.
  • A. Elmoataz, D. Xavier, L. Zakaria, and L. Olivier, Nonlocal infinity Laplacian equation on graphs with applications in image processing and machine learning, Math. Comput. Simul. 102 (2014), pp. 53–163.
  • G. Gilboa and S. Osher, Nonlocal linear image regularization and supervised segmentation, Multiscale Model. Simul. 6(2) (2007), pp. 595–630.
  • G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Model. Simul. 0(3) (2008), pp. 1005–1028.
  • T. Goldstein and S. Osher, The split Bregman method for L1-regularized problems, SIAM J. Imaging Sci. 2(2) (2009), pp. 323–343.
  • Z. Guo, Q. Liu, J. Sun, and B. Wu, Reaction-diffusion systems with p(x)-growth for image denoising, Nonlinear Anal. Real World Appl. 12(5) (2011), pp. 2904–2918.
  • Z. Guo, J. Yin, and Q. Liu, On a reaction–diffusion system applied to image decomposition and restoration, Math. Comput. Model. 53(5–6) (2011), pp. 1336–1350.
  • F. Karami, D. Meskine, and K. Sadik, A new nonlocal model for the restoration of textured images, J. Appl. Anal. Comput. 9(6) (2019), pp. 2070–2095.
  • S. Kindermann, S. Osher, and P.W. Jones, Deblurring and denoising of images by nonlocal functionals, Multiscale Model. Simul. 4(4) (2005), pp. 1091–1115.
  • L.H. Lieu and L.A. Vese, Image restoration and decomposition via bounded total variation and negative Hilbert-Sobolev spaces, with a new one, Appl. Math. Optim. 58 (2008), pp. 167–193.
  • Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, The Fifteenth Dean Jacquelines B. Lewis Memorial Lectures, University Lecture Series, Vol. 22, American Mathematical Society, Providence, 2001.
  • S. Osher, A. Solé, and L. Vese, Image decomposition and restoration using total variation minimization and the H−1 norm, SIAM J. Multiscale Model. and Simul. 1(3) (2003), pp. 349–370.
  • L.P. Yaroslavsky, Digital Picture Processing, an Introduction, Springer-Verlag, Berlin, 1985.
  • X. Zhang, M. Burger, X. Bresson, and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction, SIAM. J. Imaging Sci. 3 (2010), pp. 253–276.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.