title: Variational approach for edge-preserving regularization using coupled PDE's.
abstract: This paper deals with edge-preserving regularization for inverse problems in image processing. We first present a synthesis of the main results we have obtained in edge-preserving regularization by using a variational approach. We recall the model involving regularizing functions phi and we analyze the geometry-driven diffusion process of this model in the three-dimensional (3-D) case. Then a half-quadratic theorem is used to give a very simple reconstruction algorithm. After a critical analysis of this model, we propose another functional to minimize for edge-preserving reconstruction purposes. It results in solving two coupled partial differential equations (PDEs): one processes the intensity, the other the edges. We study the relationship with similar PDE systems in particular with the functional proposed by Ambrosio-Tortorelli in order to approach the Mumford-Shah functional developed in the segmentation application. Experimental results on synthetic and real images are presented.
authors.affiliation: Lab. Inf. Signaux et Syst. de Sophia Antipolis, Valbonne, France. teboul@alto.unice.fr
authors.forename: S
authors.initials: S
authors.lastname: Teboul
authors.forename: L
authors.initials: L
authors.lastname: Blanc-Féraud
authors.forename: G
authors.initials: G
authors.lastname: Aubert
authors.forename: M
authors.initials: M
authors.lastname: Barlaud