  Total generalization variation (TGV) is a very powerful and important
regularization for various inverse problems and computer vision tasks. In this
paper, we proposed a semismooth Newton based augmented Lagrangian method to
solve 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 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 methods for the complicated linear
subproblems involving total generalized variation, we investigated a highly
efficient and competitive algorithm compared to some efficient 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.
