Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 912373, 21 pages
http://dx.doi.org/10.1155/2013/912373
Research Article

A Convex Adaptive Total Variation Model Based on the Gray Level Indicator for Multiplicative Noise Removal

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 28 March 2013; Accepted 14 May 2013

Academic Editor: Guoyin Li

Copyright © 2013 Gang Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. I. Rudin, P. L. Lions, and S. Osher, “Multiplicative denoising and deblurring: theory and algorithms,” in Geometric Level Set Methods in Imaging, Vision, and Graphics, Chapter Multiplicative Denoising and De-Blurring: Theory and Algorithms, S. Osher and N. Paragios, Eds., pp. 103–120, 2003. View at Google Scholar
  2. M. Tur, C. Chin, and J. W. Goodman, “When is speckle noise multiplicative?” Applied Optics, vol. 21, no. 7, pp. 1157–1159, 1982. View at Publisher · View at Google Scholar
  3. J. W. Goodman, Statistical Properties of Laser Speckle Patterns, vol. 11 of Topics in Applied Physics, Springer, 2nd edition, 1984.
  4. D. C. Munson Jr. and R. L. Visentin, “A signal processing view of strip-mapping synthetic aperture radar,” IEEE Transactions on Accoustics, Speech, and Signal Processing, vol. 37, no. 12, pp. 2131–2147, 1989. View at Google Scholar
  5. G. Aubert and J.-F. Aujol, “A variational approach to removing multiplicative noise,” SIAM Journal on Applied Mathematics, vol. 68, no. 4, pp. 925–946, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D, vol. 60, pp. 259–268., 1992. View at Google Scholar
  7. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 1972.
  8. J. Shi and S. Osher, “A nonlinear inverse scale space method for a convex multiplicative noise model,” SIAM Journal on Imaging Sciences, vol. 1, no. 3, pp. 294–321, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. Darbon, M. Sigelle, and F. Tupin, “Contrast preservation filtering using nice-levelable functions and applications to SAR imaging,” IEEE Transactions on Image Processing, 2007. View at Google Scholar
  10. L. I. Rudin, P. L. Lions, and S. Osher, “Multiplicative denoising and deblurring: theory and algorithms,” in Geometric Level Set Methods in Imaging, Vision, and Graphics, Chapter Multiplicative Denoising and De- Blurring: Theory and Algorithms, S. Osher and N. Paragios, Eds., pp. 103–120, 2003. View at Google Scholar
  11. Y.-M. Huang, M. K. Ng, and Y.-W. Wen, “A new total variation method for multiplicative noise removal,” SIAM Journal on Imaging Sciences, vol. 2, no. 1, pp. 20–40, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Y. Huang, M. K. Ng, and Y.-W. Wen, “A fast total variation minimization method for image restoration,” Multiscale Modeling & Simulation, vol. 7, no. 2, pp. 774–795, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Z. Jin and X. Yang, “Analysis of a new variational model for multiplicative noise removal,” Journal of Mathematical Analysis and Applications, vol. 362, no. 2, pp. 415–426, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. D. M. Strong and T. F. Chan, “Spatially and scale adaptive total variation based regularization and anisotropic diffusion in image processing,” Tech. Rep. CAM96-46, Univeristy of California, Los Angeles, Calif, USA, 1996. View at Google Scholar
  15. T. Le, R. Chartrand, and T. J. Asaki, “A variational approach to reconstructing images corrupted by Poisson noise,” Journal of Mathematical Imaging and Vision, vol. 27, no. 3, pp. 257–263, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  16. Y. Chen and M. Rao, “Minimization problems and associated flows related to weighted p energy and total variation,” SIAM Journal on Mathematical Analysis, vol. 34, no. 5, pp. 1084–1104, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. P. Kornprobst, R. Deriche, and G. Aubert, “Image sequence analysis via partial differential equations,” Journal of Mathematical Imaging and Vision, vol. 11, no. 1, pp. 5–26, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  18. A. Chambolle, “An algorithm for mean curvature motion,” Interfaces and Free Boundaries, vol. 6, no. 2, pp. 195–218, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhauser, 1994.
  20. Y. Chen, S. Levine, and M. Rao, “Variable exponent, linear growth functionals in image restoration,” SIAM Journal on Applied Mathematics, vol. 66, no. 4, pp. 1383–1406, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. X. Zhou, “An evolution problem for plastic antiplanar shear,” Applied Mathematics and Optimization, vol. 25, no. 3, pp. 263–285, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, vol. 23, American Mathematical Society, Providence, RI, USA, 1967, Translated from the Russian by S. Smith. Translations of Mathematical Monographs.
  23. R. Hardt and X. Zhou, “An evolution problem for linear growth functionals,” Communications in Partial Differential Equations, vol. 19, no. 11-12, pp. 1879–1907, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. B. Song, Topics in variational PDE image segmentation, inpainting and denoising [Ph.D. thesis], University of California Los Angeles, Angeles, Calif, USA, 2003.
  25. S. Durand, J. Fadili, and M. Nikolova, “Multiplicative noise removal using L1 fidelity on frame coefficients,” Journal of Mathematical Imaging and Vision, vol. 36, pp. 201–226, 2010. View at Google Scholar