论文标题
一种有效的增强拉格朗日方法，具有半植物牛顿求解器的总广义变化
An Efficient Augmented Lagrangian Method with Semismooth Newton Solver for Total Generalized Variation
论文作者
论文摘要
总概括变化（TGV）是针对各种反问题和计算机视觉任务的非常强大且重要的正则化。在本文中，我们提出了一种基于牛顿的半齿的增强拉格朗日方法来解决此问题。增强的拉格朗日方法（也称为乘数的方法）被广泛用于许多平滑或非平滑的变分问题。但是，它的效率通常在很大程度上取决于将耦合和非线性系统同时求解，这是非常复杂的，并且高度耦合到总概括变化。通过有效的原始双偶半牙牛顿方法，用于涉及总体变化的复杂线性子问题，我们研究了一种高效且竞争性的算法，与某种有效的一阶方法相比。通过分析相应函数的度量亚规格，我们给出了所提出的增强拉格朗日方法的全局收敛和局部线性收敛速率。
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.
