title: Nonlinear regularized reaction-diffusion filters for denoising of images with textures.
abstract: Denoising is always a challenging problem in natural imaging and geophysical data processing. In this paper, we consider the denoising of texture images using a nonlinear reaction-diffusion equation and directional wavelet frames. In our model, a curvelet shrinkage is used for regularization of the diffusion process to preserve important features in the diffusion smoothing and a wave atom shrinkage is used as the reaction in order to preserve and enhance interesting oriented textures. We derive a digital reaction-diffusion filter that lives on graphs and show convergence of the corresponding iteration process. Experimental results and comparisons show very good performance of the proposed model for texture-preserving denoising.
authors.affiliation: Department of Mathematics, University of Duisburg-Essen, Campus Duisburg, Duisburg, Germany. plonka@math.uni-duisburg.de
authors.forename: Gerlind
authors.initials: G
authors.lastname: Plonka
authors.forename: Jianwei
authors.initials: J
authors.lastname: Ma
mesh_terms: D000465:Algorithms; D016477:Artifacts; D005374:Filtration / Q000379:methods*; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D017711:Nonlinear Dynamics; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity