Parameter selection and solution algorithm for TGV-based image restoration model

In this paper, image restoration problem is formulated to solve a total generalized variation (TGV)-based minimization problem. The minimization problem includes an unknown regularization parameter. A Morozov’s discrepancy principle-based method is used to choose a suitable regularization parameter. Computationally, by introducing two dual variables, the TGV-based image restoration problem is reformulated as a convex-concave saddle-point problem. Meanwhile, the Chambolle–Pock’s first-order primal–dual algorithm is transformed into a different equivalent form which can be seen as a proximal-based primal–dual algorithm. Then, the different equivalent form is used to solve the saddle-point problem. At last, compared with several existing state-of-the-art methods, experimental results demonstrate the performance of our proposed method.