L infinity total generalized variation for color image recovery

For solving color image recovery problems, we previously proposed an L_∞ vectorial total variation (L_∞-VTV) as a regularization term considering the inter color channel dependency. However, the result images suffer from pseudo contours known as staircasing effect. For suppressing this, Bredies et al. proposed to add higher-order derivative terms to VTV. However, since it does not consider the inter channel dependency properly, it cannot reduce pseudo color noises on the edge regions. Based on these observations, we proposed a new convex regularization term L_∞ vectorial total generalized variation (L_∞-VTGV) by combining two ideas: using L_∞ norm for penalizing the violation of the inter color channel dependency and introducing higher order derivative term. Furthermore, we address the effective numerical algorithm for various image recovery problems using L_∞-VTGV as a regularization term. Experimental results shows that our proposed method can outperform the conventional methods.