Applied Mathematics & Information Sciences

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Based on the augmented Lagrangian strategy, we propose a projected gradient method for solving the high-order model in image restoration problems. Based on the Berm`udez and Moreno (BM) algorithm, the convergence of the proposed method is proved. We also give the relationship that the semi-implicit gradient descent method can be deduced from the projected gradient method. Some numerical experiments are arranged to demonstrate the efficiency of the proposed method for restoring the gray-level and color images.

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