A stable method solving the total variation dictionary model with $L^\infty$ constraints

Abstract : Image restoration plays an important role in image processing, and numerous approaches have been proposed to tackle this problem. This paper presents a modified model for image restoration, that is based on a combination of Total Variation (TV) and Dictionary approaches. Since the well-known TV regularization is non-differentiable, the proposed method utilizes its dual formulation instead of its approximation in order to exactly preserve its properties. The data-fidelity term combines the one commonly used in image restoration and a wavelet thresholding based term. Then, the resulting optimization problem is solved via a first-order primal-dual algorithm. Numerical experiments demonstrate the good performance of the proposed model. In a last variant, we replace the classical TV by the nonlocal TV regularization, which results in a much higher quality of restoration.
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Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2014, 8 (2), pp.507 - 535. <10.3934/ipi.2014.8.507>
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Liyan Ma, Lionel Moisan, Jian Yu, Tieyong Zeng. A stable method solving the total variation dictionary model with $L^\infty$ constraints. Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2014, 8 (2), pp.507 - 535. <10.3934/ipi.2014.8.507>. <hal-00826615v2>

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