A TV based restoration model with local constraints. (English) Zbl 1218.94007

Summary: 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.


94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
68U10 Computing methodologies for image processing
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