A Guide to the TV Zoo
A Guide to the TV Zoo
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DOI：
10.1007/978-3-319-01712-9_1
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发表时间：
2013-01-01
期刊：
影响因子：
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通讯作者：
Osher, Stanley
中科院分区：
文献类型：
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作者：
Burger, Martin;Osher, Stanley
基于正则化的全变分方法和基于正则化的类似方法，由于具有光滑正则化不能实现的特点，在图像处理和反问题中已经成为一种非常流行的工具。特别是，全变分技术取得了特别的成功，因为它们能够实现具有尖锐边缘的卡通类型的重建。由于这一领域在过去十年中出现了爆炸性的新发展，要对分析、计算方案和应用领域的主要结果保持概述是一项困难的任务。通过这些讲座，我们试图提供这样的概述，当然，偏向于我们的主要研究方向。我们专注于全变分方法的基本分析，以及原始ROF去噪模型在各个应用领域的扩展。此外，我们还简要讨论了最新的计算方法，并展望了其在不同学科中的应用前景。
Total variation methods and similar approaches based on regularizations with '1-type norms (and seminorms) have become a very popular tool in image processing and inverse problems due to peculiar features that cannot be realized with smooth regularizations. In particular total variation techniques had particular success due to their ability to realize cartoon-type reconstructions with sharp edges. Due to an explosion of new developments in this field within the last decade it is a difficult task to keep an overview of the major results in analysis, the computational schemes, and the application fields. With these lectures we attempt to provide such an overview, of course biased by our major lines of research.We are focusing on the basic analysis of total variation methods and the extension of the original ROF-denoising model due various application fields. Furthermore we provide a brief discussion of state-of-the art computational methods and give an outlook to applications in different disciplines.