Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model
Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model
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DOI：
10.1007/978-3-642-02256-2_42
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发表时间：
2009-05
影响因子：
44.1
通讯作者：
X. Tai;Chunlin Wu
中科院分区：
文献类型：
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作者：
X. Tai;Chunlin Wu
近几十年来，ROF模型（总变差（TV）最小化）由于其良好的边缘保持特性在图像恢复中取得了巨大的成功。然而，最小化问题的不可微性带来了计算困难。已经提出了不同的技术来克服这个困难。其中被认为特别有效的方法包括CGM（Chan，Golub和Mulet）[7] Chambolle [6]和分裂Bregman迭代[14]的对偶方法，以及基于分裂和惩罚的方法[28] [29]。在本文中，我们表明大多数这些方法都可以归类在同一框架下。对偶法和分裂Bregman迭代法是求解同一方程组的两种不同的迭代过程，而这两种迭代过程都是由拉格朗日法和罚函数法得到的。我们只显示了ROF模型的这种关系。但是，它提供了一个统一的框架来理解其他模型的这些方法。最后，通过实例验证了该算法的准确性和有效性.
In the recent decades the ROF model (total variation (TV) minimization) has made great successes in image restoration due to its good edge-preserving property. However, the non-differentiability of the minimization problem brings computational difficulties. Different techniques have been proposed to overcome this difficulty. Therein methods regarded to be particularly efficient include dual methods of CGM (Chan, Golub, and Mulet) [7] Chambolle [6] and split Bregman iteration [14], as well as splitting-and-penalty based method [28] [29]. In this paper, we show that most of these methods can be classified under the same framework. The dual methods and split Bregman iteration are just different iterative procedures to solve the same system resulted from a Lagrangian and penalty approach. We only show this relationship for the ROF model. However, it provides a uniform framework to understand these methods for other models. In addition, we provide some examples to illustrate the accuracy and efficiency of the proposed algorithm.