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A TV Based Restoration Model with Local Constraints

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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−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.

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Authors and Affiliations

  1. InCo, Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    A. Almansa

  2. Departament Tecnologia, Universitat Pompeu Fabra, Passeig de Circumvalació, 8, 08003, Barcelona, Spain

    C. Ballester & V. Caselles

  3. Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, 207 Church Street S.E., Minneapolis, MN, 55455, USA

    G. Haro

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  1. A. Almansa
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  2. C. Ballester
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  3. V. Caselles
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  4. G. Haro
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Correspondence to A. Almansa.

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Almansa, A., Ballester, C., Caselles, V. et al. A TV Based Restoration Model with Local Constraints. J Sci Comput 34, 209–236 (2008). https://doi.org/10.1007/s10915-007-9160-x

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  • DOI: https://doi.org/10.1007/s10915-007-9160-x

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