A primal-dual method for the Meyer model of cartoon and texture decomposition

In this paper, we study the original Meyer model of cartoon and texture decomposition in image processing. The model, which is a minimization problem, contains an l₁-based TV-norm and an l_∞-based G-norm. The main idea of this paper is to use the dual formulation to represent both TV-norm and G-norm. The resulting minimization problem of the Meyer model can be given as a minimax problem. A first-order primal-dual algorithm can be developed to compute the saddle point of the minimax problem. The convergence of the proposed algorithm is theoretically shown. Numerical results are presented to show that the original Meyer model can decompose better cartoon and texture components than the other testing methods.