A projected gradient algorithm based on the augmented Lagrangian strategy for image restoration and texture extraction

Based on the augmented Lagrangian strategy, we construct a projected gradient algorithm for image restoration and texture extraction. The proposed algorithm is established on the basis of a mixed model which combines the Rudin–Osher–Fatemi (ROF) model with the Lysaker–Lundevold–Tai (LLT) model to reduce the staircase effect and blur phenomenons. The proof of the convergence of the proposed algorithm is provided. Moreover, we show that the dual methods based on convex analysis which have been proposed in some papers can be actually deduced from the augmented Lagrangian strategy. Some numerical examples are supplied to illustrate the efficiency of the proposed algorithm.

Research Highlights
► We proposed a model based on the Rudin-Osher-Fatemi(ROF) model with the Lysaker-Lundevold-Tai(LLT) model to reduce the staircase effect and blur phenomenons.
► We construct a projected gradient algorithm based on the augmented Lagrangian strategy.
► The convergence of the proposed algorithm was proved.
► We give some numerical examples to illustrated the efficiency of the proposed algorithm.