VARIATIONAL APPROACH FOR EDGE-PRESERVING REGULARIZATION USING COUPLEDPDES

This paper deals with edge-preserving regularization for inverse probl ems in image processing, We first present a synthesis of the main resu lts we have obtained in edge-preserving regularization by using a vari ational approach, We recall the model involving regularizing functions phi and we analyze the geometry-driven diffusion process of this mode l in the three-dimensional (3-D) case, Then 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 the edge-preserving reconstruction purpose, It results in solving two coupled partial differential equations (PDE's): one processes the inte nsity, the other the edges, We study the relationship with similar PDE systems in particular with the functional proposed by Ambrosio-Tortor elli [1], [2] in order to approach the Mumford-Shah functional [3] dev eloped in the segmentation application, Experimental results on synthe tic and real images are presented.