Fixed-Point Algorithms for Inverse Problems in Science and Engineering
Fixed-Point Algorithms for Inverse Problems in Science and Engineering
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DOI：
10.1007/978-1-4419-9569-8
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
Heinz H. Bauschke;R. Burachik;P. Combettes;V. Elser;D. R. Luke;Henry Wolkowicz
中科院分区：
文献类型：
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作者：
Heinz H. Bauschke;R. Burachik;P. Combettes;V. Elser;D. R. Luke;Henry Wolkowicz
凸函数的邻近算子是投影算子概念在凸集上的自然延伸。该工具在凸优化问题的分析和数值求解中发挥着核心作用，最近被引入反问题领域，特别是在信号处理领域，它变得越来越重要。在本文中，我们回顾了与信号处理相关的邻近算子的基本属性，并提出了基于这些算子的优化方法。这些近端分裂方法被证明可以在统一框架中捕获和扩展几种众所周知的算法。讨论了邻近方法在信号恢复和合成中的应用。
The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numerical solution of convex optimization problems, has recently been introduced in the arena of inverse problems and, especially, in signal processing, where it has become increasingly important. In this paper, we review the basic properties of proximity operators which are relevant to signal processing and present optimization methods based on these operators. These proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework. Applications of proximal methods in signal recovery and synthesis are discussed.