Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 764639, 20 pages
Research Article

A Decomposition and Noise Removal Method Combining Diffusion Equation and Wave Atoms for Textured Images

DCCE/IBILCE, UNESP-São Paulo State University, Rua Cristóvão Colombo 2265, 15054-000 São José do Rio Preto, SP, Brazil

Received 29 June 2009; Revised 18 December 2009; Accepted 6 February 2010

Academic Editor: Panos Liatsis

Copyright © 2010 Wallace Correa de Oliveira Casaca and Maurílio Boaventura. 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.


We propose a new method that is aimed at denoising images having textures. The method combines a balanced nonlinear partial differential equation driven by optimal parameters, mathematical morphology operators, weighting techniques, and some recent works in harmonic analysis. Furthermore, the new scheme decomposes the observed image into three components that are well defined as structure/cartoon, texture, and noise-background. Experimental results are provided to show the improved performance of our method for the texture-preserving denoising problem.