论文标题
一个重叠的域分解框架，没有双重配方，用于变化成像问题
An Overlapping Domain Decomposition Framework without Dual Formulation for Variational Imaging Problems
论文作者
论文摘要
在本文中，我们提出了一种新型的重叠域分解方法，该方法可以应用于变异成像中的各种问题，例如总变异最小化。最新变异最小化的大多数近期域分解方法都采用Fenchel-Rockafellar双重性，而所提出的方法基于原始公式。因此，所提出的方法不仅可以应用于总变化最小化，还可以应用于具有复杂双重问题（例如高阶模型）的人。在提出的方法中，使用定制重叠域分解方案构建了模型问题与平行结构的等效公式，并具有必需域的概念。作为构造配方的求解器，我们提出了一种解耦的增强拉格朗日方法，以解开相邻子域的耦合。提供了脱钩的增强拉格朗日方法的收敛分析。我们介绍了各种模型问题的实施细节和数值示例，包括总变化最小化和高阶模型。
In this paper, we propose a novel overlapping domain decomposition method that can be applied to various problems in variational imaging such as total variation minimization. Most of recent domain decomposition methods for total variation minimization adopt the Fenchel--Rockafellar duality, whereas the proposed method is based on the primal formulation. Thus, the proposed method can be applied not only to total variation minimization but also to those with complex dual problems such as higher order models. In the proposed method, an equivalent formulation of the model problem with parallel structure is constructed using a custom overlapping domain decomposition scheme with the notion of essential domains. As a solver for the constructed formulation, we propose a decoupled augmented Lagrangian method for untying the coupling of adjacent subdomains. Convergence analysis of the decoupled augmented Lagrangian method is provided. We present implementation details and numerical examples for various model problems including total variation minimizations and higher order models.
