The graduated nonconvex method(GNC) and augmented Lagrangian duality have superior restoration performance for nonconvex nonsmooth image restoration.However

the global convergence of the general GNC could not be guaranteed and an effective initial value could not be obtained for the augmented Lagrangian duality when they are used separately.To overcome these drawbacks

we propose a hybrid method based on the GNC and augmented Lagrangian duality by transforming the original problem into equality constrained optimization

then its dual convergence has been strictly proven.The proposed method could get an effective initial value and does not require the convexity and smoothness of the underlying problem.Moreover

an adaptive energy function is generated by the dual iterations.Experimental results show that the proposed method could enhance the quality of restored images and the efficiency of algorithm effectively.