Journal of Applied Mathematics
Volume 2011 (2011), Article ID 240370, 20 pages
http://dx.doi.org/10.1155/2011/240370
Research Article

A Class of Fourth-Order Telegraph-Diffusion Equations for Image Restoration

Weili Zeng,1 Xiaobo Lu,2 and Xianghua Tan3

1ITS Research Center, School of Transportation, Southeast University, Nanjing 210096, China
2School of Automation, Southeast University, Nanjing 210096, China
3School of Mathematics and Computer Science, Hunan Normal University, Nanjing 210096, China

Received 14 March 2011; Revised 17 May 2011; Accepted 2 June 2011

Academic Editor: E. S. Van Vleck

Copyright © 2011 Weili Zeng 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.

Abstract

A class of nonlinear fourth-order telegraph-diffusion equations (TDE) for image restoration are proposed based on fourth-order TDE and bilateral filtering. The proposed model enjoys the benefits of both fourth-order TDE and bilateral filtering, which is not only edge preserving and robust to noise but also avoids the staircase effects. The existence, uniqueness, and stability of the solution for our model are proved. Experiment results show the effectiveness of the proposed model and demonstrate its superiority to the existing models.