An Efficient Augmented Lagrangian Method with Semismooth Newton Solver for Total Generalized Variation
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Total generalization variation (TGV) is a very powerful and important regularization for image restoration and various computer vision tasks. In this paper, we proposed a semismooth Newton method based augmented Lagrangian method to solve this problem. Augmented Lagrangian method (also called as method of multipliers) is widely used for lots of smooth or nonsmooth variational problems. However, its efficiency usually heavily depends on solving the coupled and nonlinear system together and simultaneously, which is very complicated and highly coupled for total generalization variation. With efficient primal-dual semismooth Newton method for the complicated linear subproblems involving total generalized variation, we investigated a highly efficient and competitive algorithm compared to some popular first-order method. With the analysis of the metric subregularities of the corresponding functions, we give both the global convergence and local linear convergence rate for the proposed augmented Lagrangian methods with semismooth Newton solvers.
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