A TV Based Restoration Model with Local Constraints

Authors:
A. Almansa;C. Ballester;V. Caselles;G. Haro
Affiliations:
InCo, Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay 11300;Departament Tecnologia, Universitat Pompeu Fabra, Barcelona, Spain 08003;Departament Tecnologia, Universitat Pompeu Fabra, Barcelona, Spain 08003;Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA 55455
Venue:
Journal of Scientific Computing
Year:
2008

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Abstract

We propose in this paper a total variation based restoration model which incorporates the image acquisition model z=h * U+n (where z represents the observed sampled image, U is the ideal undistorted image, h denotes the blurring kernel and n is 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 z驴h * U 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.