A TV Based Restoration Model with Local Constraints

We propose in this paper a total variation based restoration model which incorporates the image acquisition model z = h ∗ u + n (h denotes the blurring kernel and n a white Gaussian noise) as a set of local constraints. These constraints, one for each pixel of the image, express the fact that the variance of the noise can be estimated from the residuals h ∗ u− z if we use a neighborhood of each pixel. This is motivated by the fact that the usual inclusion of the image acquisition model as a single constraint expressing a bound for the variance of the noise does not give satisfactory results if we wish to simultaneously recover textured regions and obtain a good denoising of the image. We use Uzawa’s algorithm to minimize the total variation subject to the proposed family of local constraints and we display some experiments using this model.