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.

This paper deals with segmentation and edge-preserving restoration. We use an active contour method to segment an image which may not be very noisy with regard to its edges. In order to both restore and segment a noisy image, we propose in this paper to derive a system of two partial differential equations, one for edge-preserving restoration (using edges given by segmentation), and the other for segmentation (using the restored image).

This paper deals with edge-preserving regularization for image reconstruction. We use a non-quadratic regularization term involving a /spl phi/-function applied on the intensity gradient modulus. During the process, small gradients are smoothed while high gradients are preserved. In order to take into account the noise more specifically, we propose to use the explicit version of the regularization term involving the edge variable. We add a nonlinear constraint on this edge variable, in order to remove the noise. It allows edge enhancement while smoothing the noise, even in the case where the edge and noise generate the same high gradient modulus. We have previously proposed a model composed of two coupled partial differential equations (PDE) on the image intensity and image edges. In this paper, we show that, for a particular regularization intensity function, the two coupled PDE can be slightly modified in order to correspond to the Euler equations associated with the minimization of a global criterion. This new criterion contains a nonlinear regularization term on both the intensity and the edges. We use convergence towards Mumford and Shah (1989) functional to improve our results.