On nonmonotone chambolle gradient projection algorithms for total variation image restoration

The main aim of this paper is to accelerate the Chambolle gradient projection method for total variation image restoration. In the proposed minimization method model, we use the well known Barzilai-Borwein stepsize instead of the constant time stepsize in Chambolle's method. Further, we adopt the adaptive nonmonotone line search scheme proposed by Dai and Fletcher to guarantee the global convergence of the proposed method. Numerical results illustrate the efficiency of this method and indicate that such a nonmonotone method is more suitable to solve some large-scale inverse problems.