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Total Variation denoising, proposed by Rudin, Osher and Fatemi in [22], is an image processing variational technique that has attracted considerable attention in the past fifteen years. It is an advantageous technique for preserving image edges but tends to sharpen excessively smooth transitions. With the purpose of alleviating this staircase effect some generalizations of Total Variation denoising have been introduced in [17,18,19]. In this paper we propose a fast and robust algorithm for the solution of the variational problems that generalize Total Variation image denoising [22]. This method extends the primal-dual Newton method, proposed by Chan, Golub and Mulet in [7] for total variation restoration, to these variational problems. We perform some experiments for assessing the efficiency of this scheme with respect to the fixed point method that generalizes the lagged diffusivity fixed point method proposed by Vogel and Oman in [24].

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