A stable method solving the total variation dictionary model with $L^\infty$ constraints
Liyan Ma, Lionel Moisan, Jian Yu, Tieyong Zeng · Inverse Problems and Imaging · 2014
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 andDictionaryapproaches.Since the well-known TV regularization is non-differentiable,the proposed method utilizes its dual formulation instead of its approximationin order to exactly preserve its properties. The data-fidelity termcombines the one commonly used in image restoration and a waveletthresholding based term. Then, the resulting optimization problem issolved via a first-order primal-dual algorithm.Numerical experiments demonstrate the good performance of theproposed model. In a last variant,we replace the classical TV by the nonlocal TV regularization,which results in a much higher quality of restoration.