Advances in Numerical Analysis
Volume 2012 (2012), Article ID 750146, 19 pages
http://dx.doi.org/10.1155/2012/750146
Research Article

Preservation of Fine Structures in PDE-Based Image Denoising

Hakran Kim,1 Velinda R. Calvert,2 and Seongjai Kim2

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.

Abstract

Image denoising processes often lead to significant loss of fine structures such as edges and textures. This paper studies various innovative mathematical and numerical methods applicable for conventional PDE-based denoising models. The method of diffusion modulation is considered to effectively minimize regions of undesired excessive dissipation. Then we introduce a novel numerical technique for residual-driven constraint parameterization, in order for the resulting algorithm to produce clear images whose corresponding residual is as free of image textures as possible. A linearized Crank-Nicolson alternating direction implicit time-stepping procedure is adopted to simulate the resulting model efficiently. Various examples are presented to show efficiency and reliability of the suggested methods in image denoising.