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.
翻译:总体化变异(TGV)对于各种反面问题和计算机视觉任务来说,是一种非常强大和重要的规范化。在本文中,我们提出了一种基于半斯穆特牛顿(Newton)的强化拉格朗加增法来解决这个问题。增强的拉格朗加法(也称为乘数法)被广泛用于解决许多平滑或非平稳变异问题。然而,其效率通常主要取决于同时解决并存和非线性系统,这非常复杂,而且与总体化变异高度相联。由于对复杂的线性子问题(包括全面普遍变异)采用了高效的原始-双半斯莫特牛顿法,我们调查了一种效率高、竞争性的算法,与某种高效的第一阶法相比。通过对相应功能的多例次规则的分析,我们给出了拟议扩大拉格朗加法的全球趋同率和地方线性趋同率。