A Stable Method Solving the Total Variation Dictionary Model with L-infinity Constraints

Liyan Ma (1) , Lionel Moisan (2) , Jian Yu (1) , Tieyong Zeng (3)

1 SCIT - School of Computer and Information Technology [Beijing]
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 HKBU - Hong Kong Baptist University

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.

Mots clés: Image restoration; total variation; nonlocal total variation; proximal gradient method; wavelet packet decomposition

Domaines: Traitement des images [eess.IV]; Optimisation et contrôle [math.OC]

Liyan Ma, Lionel Moisan, Jian Yu, Tieyong Zeng. A Stable Method Solving the Total Variation Dictionary Model with L-infinity Constraints. 2013. ⟨hal-00826615v1⟩