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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 856876, 8 pages
Variational Image Denoising Approach with Diffusion Porous Media Flow
Institute of Computer Science, The Romanian Academy, 700481 Iasi, Romania
Received 23 October 2012; Revised 15 December 2012; Accepted 16 December 2012
Academic Editor: Dragoş-Pătru Covei
Copyright © 2013 Tudor Barbu. 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.
- A. K. Jain, Fundamentals of Digital Image Processing, Prentice Hall, Englewood Cliffs, NJ, USA, 1989.
- R. Gonzalez and R. Woods, Digital Image Processing, Prentice Hall, New York, NY, USA, 2nd edition, 2001.
- K. Nallaperumal, R. K. Selvakumar, S. Arumugaperumal, S. Annam, and N. Vishwanath, “Hansa filter: a fuzzy adaptive nonlinear Gaussian filter: an adaptive non local algorithm,” International Journal of Imaging and Engineering, vol. 2, no. 1, 2008.
- F. Guichard, L. Moisan, and J.-M. Morel, “A review of P.D.E. models in image processing and image analysis,” Journal de Physique, vol. 4, pp. 137–154, 2001.
- J. Weickert, Anisotropic Diffusion in Image Processing, European Consortium for Mathematics in Industry, B. G. Teubner, Stuttgart, Germany, 1998.
- L. Alvarez, “Images and PDE's,” in ICAOS '96 (Paris, 1996), M.-O. Berger, R. Deriche, I. Herlin, J. Jaffré, and J.-M. Morel, Eds., vol. 219 of Lecture Notes in Control and Information Sciences, pp. 3–14, Springer, London, UK, 1996.
- T. Barbu and V. Barbu, “A PDE approach to image restoration problem with observation on a meager domain,” Nonlinear Analysis: Real World Applications, vol. 13, no. 3, pp. 1206–1215, 2012.
- T. Barbu, V. Barbu, V. Biga, and D. Coca, “A PDE variational approach to image denoising and restoration,” Nonlinear Analysis: Real World Applications, vol. 10, no. 3, pp. 1351–1361, 2009.
- T. Barbu, “A PDE based model for sonar image and video denoising,” AnAlele Stiintifice Ale Universitatii Ovidius, Constanta, Seria Matematica, vol. 19, no. 3, pp. 51–58, 2011.
- P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” in Proceedings of IEEE Computer Society Workshop on Computer Vision, pp. 16–27, 1987.
- F. Catte, P. L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM Journal on Numerical Analysis, vol. 29, no. 1, pp. 182–193, 1992.
- J. Kačur and K. Mikula, “Slow and fast diffusion effects in image processing,” Computing and Visualization in Science, vol. 13, no. 4, pp. 185–195, 2001.
- V. Barbu, Nonlinear Differential Equations of Montone Type in Banach Spaces, Springer, New York, NY, USA, 2010.
- H. Brezis, “Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations,” in Contributions to Nonlinear Functional Analysis, E. Zarantonello, Ed., Acdemic Press, New York, NY, USA, 1971.
- J. Calder, A. Mansouri, and A. Yezzi, “New possibilities in image diffusion and sharpening via high-order Sobolev gradient flows,” Journal of Mathematical Imaging and Vision, vol. 40, no. 3, pp. 248–258, 2011.
- J. Calder, A. Mansouri, and A. Yezzi, “Image sharpening via Sobolev gradient flows,” SIAM Journal on Imaging Sciences, vol. 3, no. 4, pp. 981–1014, 2010.
- Z. Jin and X. Yang, “Strong solutions for the generalized Perona-Malik equation for image restoration,” Nonlinear Analysis: Theory, Methods and Applications, vol. 73, no. 4, pp. 1077–1084, 2010.
- M. J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, “Robust anisotropic diffusion,” IEEE Transactions on Image Processing, vol. 7, no. 3, pp. 421–432, 1998.
- J. Weickert, B. M. ter Haar Romeny, and M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE Transactions on Image Processing, vol. 7, no. 3, pp. 398–410, 1998.
- S. Kim and H. Lim, “A non-convex diffusion model for simultaneous image denoising and edge enhancement,” in Proceedings of the 6th Mississippi State-UBA Conference on Differential Equations and Computational Simulations, vol. 15 of Electron. J. Differ. Equ. Conf., pp. 175–192, Southwest Texas State Univ., San Marcos, Tex, USA, 2007.
- S. T. Acton, “Edge enhancement of infrared imagery by way of the anisotropic diffusion pyramid,” in Proceedings of IEEE International Conference on Image Processing (ICIP '96), vol. 1, pp. 865–868, Lausanne, Switzerland, September 1996.