An efficient augmented Lagrangian method with semismooth Newton solver for total generalized variation

Abstract

<p style='text-indent:20px;'>Total generalization variation (TGV) is a very powerful and important regularization for various inverse problems and computer vision tasks. In this paper, we propose a semismooth Newton based augmented Lagrangian method for solving this problem. The augmented Lagrangian method (also called as method of multipliers) is widely used for lots of smooth or nonsmooth variational problems. However, its efficiency heavily depends on solving the corresponding coupled and nonlinear system together and simultaneously. With efficient primal-dual semismooth Newton methods for the challenging and highly coupled nonlinear subproblems involving total generalized variation, we develop a highly efficient and competitive augmented Lagrangian method compared with some fast 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.</p>