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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 (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 zh * 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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Almansa, A., Ballester, C., Caselles, V. et al. A TV Based Restoration Model with Local Constraints. J Sci Comput 34, 209–236 (2008).

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  • Image restoration
  • Total variation
  • Variational methods
  • Satellite images