Higher-Order TV Methods-Enhancement via Bregman Iteration
Higher-Order TV Methods-Enhancement via Bregman Iteration
复制标题
DOI：
10.1007/s10915-012-9650-3
复制
发表时间：
2013-02-01
影响因子：
2.5
通讯作者：
Mueller, Jahn
中科院分区：
文献类型：
--
作者：
Benning, Martin;Brune, Christoph;Mueller, Jahn
在这项工作中，我们分析和比较两个最近的变分模型的图像去噪，并提高其重建应用布雷格曼迭代策略。图像去噪中的标准技术之一，ROF模型（cf. Rudin等人在Physica D 60：259-268，1992中），众所周知的是用于恢复信号或图像的尖锐边缘，但也用于产生阶梯状伪影。为了克服这些依赖于模型的缺陷，已经提出了包含高阶导数的全变分修改（参见图10）。Chambolle和狮子在Numer。76：167-188，1997; Bredies等人，SIAM J. Imaging Sci. 3（3）：492-526，2010）。这些模型减少了楼梯，以合理的参数选择。然而，不同阶导数的组合导致其他不期望的副作用，我们还将在几个示例中强调这一点。本文的目标是分析不同模型的能力和局限性，并通过引入Bregman迭代来提高它们的重建质量。除了一般的建模和分析，我们讨论有效的数值实现Bregman迭代及其修改版本。
In this work we analyze and compare two recent variational models for image denoising and improve their reconstructions by applying a Bregman iteration strategy. One of the standard techniques in image denoising, the ROF-model (cf. Rudin et al. in Physica D 60:259-268, 1992), is well known for recovering sharp edges of a signal or image, but also for producing staircase-like artifacts. In order to overcome these model-dependent deficiencies, total variation modifications that incorporate higher-order derivatives have been proposed (cf. Chambolle and Lions in Numer. Math. 76:167-188, 1997; Bredies et al. in SIAM J. Imaging Sci. 3(3):492-526, 2010). These models reduce staircasing for reasonable parameter choices. However, the combination of derivatives of different order leads to other undesired side effects, which we shall also highlight in several examples.The goal of this paper is to analyze capabilities and limitations of the different models and to improve their reconstructions in quality by introducing Bregman iterations. Besides general modeling and analysis we discuss efficient numerical realizations of Bregman iterations and modified versions thereof.