Cartoon and texture decomposition for color image in opponent color space

The Meyer model has been successfully applied to decompose cartoon component and texture component for the gray scale image, where the total variation (TV) norm and the G-norm are respectively modeled to capture the cartoon component and the texture component in an energy minimization method. In this paper, we extend this model to the color image in the opponent color space, which is closer to human perception than the RGB space. It is important to extend the TV norm and the G-norm correspondingly because the color image is viewed as a vector-valued vector. We introduce the definition of the L₁ norm and L_∞ norm for the vector-valued vector and accordingly define the TV norm and the G-norm for the color image. In order to handle the numerical difficulty caused by the non-differentiability of the TV norm and G-norm, the dual formulations are used to represent these norm. Then the decomposition problem is reformulated into a minimax problem. A first-order primal-dual algorithm is readily applied to compute the saddle point of the minimax problem. Numerical results are shown the performance of the proposed model.