- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Advances in Numerical Analysis
Volume 2012 (2012), Article ID 750146, 19 pages
Preservation of Fine Structures in PDE-Based Image Denoising
1Department of Computational Engineering, Mississippi State University, Mississippi State, MS 39762, USA
2Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762-5921, USA
Received 25 May 2012; Revised 16 September 2012; Accepted 17 September 2012
Academic Editor: Xue Cheng Tai
Copyright © 2012 Hakran Kim 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.
- L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion. II,” SIAM Journal on Numerical Analysis, vol. 29, no. 3, pp. 845–866, 1992.
- F. Catté, 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.
- T. F. Chan, S. Osher, and J. Shen, “The digital TV filter and nonlinear denoising,” IEEE Transactions on Image Processing, vol. 10, no. 2, pp. 231–241, 2001.
- S. Kim, “PDE-based image restoration: a hybrid model and color image denoising,” IEEE Transactions on Image Processing, vol. 15, no. 5, pp. 1163–1170, 2006.
- A. Marquina and S. Osher, “Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal,” SIAM Journal on Scientific Computing, vol. 22, no. 2, pp. 387–405, 2000.
- M. Nitzberg and T. Shiota, “Nonlinear image filtering with edge and corner enhancement,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 8, pp. 826–833, 1992.
- P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629–639, 1990.
- L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D, vol. 60, no. 1–4, pp. 259–268, 1992.
- Y. L. You, W. Xu, A. Tannenbaum, and M. Kaveh, “Behavioral analysis of anisotropic diffusion in image processing,” IEEE Transactions on Image Processing, vol. 5, no. 11, pp. 1539–1553, 1996.
- S. Angenent, E. Pichon, and A. Tannenbaum, “Mathematical methods in medical image processing,” Bulletin of the American Mathematical Society, vol. 43, no. 3, pp. 365–396, 2006.
- T. F. Chan and J. Shen, Image Processing and Analysis, SIAM, Philadelphia, Pa, USA, 2005.
- S. Kim and H. Lim, “A non-convex diffusion model for simultaneous image denoising and edge enhancement,” Electronic Journal of Differential Equations, vol. 15, pp. 175–192, 2007.
- Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, vol. 22 of University Lecture Series, American Mathematical Society, Providence, RI, USA, 2001.
- S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “Using geometry and iterated refinement for inverse problems (1): total variation based image restoration,” CAM Report #04-13, Department of Mathematics, UCLA, Los Angeles, Calif, USA, 2004.
- S. Kim, “Image denoising by fourth-order pdes,” in Proceedings of the 8th IASTED International Conference on Signal and Image Processing (SIP '06), pp. 249–254, August 2006.
- M. Lysaker, A. Lundervold, and X. C. Tai, “Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time,” IEEE Transactions on Image Processing, vol. 12, no. 12, pp. 1579–1589, 2003.
- S. Osher, A. Solé, and L. Vese, “Image decomposition and restoration using total variation minimization and the norm,” Multiscale Modeling & Simulation, vol. 1, no. 3, pp. 349–370, 2003.
- Y.-L. You and M. Kaveh, “Fourth-order partial differential equations for noise removal,” IEEE Transactions on Image Processing, vol. 9, no. 10, pp. 1723–1730, 2000.
- S. Kim, “Image denoising via diffusion modulation,” International Journal of Pure and Applied Mathematics, vol. 30, no. 1, pp. 71–92, 2006.
- R. Weinstock, Calculus of Variations, Dover Publications, New York, NY, USA, 1974.
- S. Osher and R. Fedkiw, Level Set methods and Dynamic Implicit Surfaces, vol. 153, Springer, New York, NY, USA, 2003.
- J. Douglas, Jr. and J. E. Gunn, “A general formulation of alternating direction methods. I. Parabolic and hyperbolic problems,” Numerische Mathematik, vol. 6, pp. 428–453, 1964.
- J. Douglas, Jr. and S. Kim, “Improved accuracy for locally one-dimensional methods for parabolic equations,” Mathematical Models & Methods in Applied Sciences, vol. 11, no. 9, pp. 1563–1579, 2001.
- Y. Cha and S. Kim, “Edge-forming methods for color image zooming,” IEEE Transactions on Image Processing, vol. 15, no. 8, pp. 2315–2323, 2006.
- Y. Cha and S. Kim, “Edge-forming methods for image zooming,” Journal of Mathematical Imaging and Vision, vol. 25, no. 3, pp. 353–364, 2006.
- H. Kim, Y. Cha, and S. Kim, “Curvature interpolation method for image zooming,” IEEE Transactions on Image Processing, vol. 20, no. 7, pp. 1895–1903, 2011.