Modern regularization methods for inverse problems
Modern regularization methods for inverse problems
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DOI：
10.1017/s0962492918000016
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发表时间：
2018-01-01
期刊：
影响因子：
14.2
通讯作者：
Burger, Martin
中科院分区：
文献类型：
--
作者：
Benning, Martin;Burger, Martin
正则化方法是求解反问题的重要工具。它们被用来引入先验知识，并允许一个强大的近似不适定（伪）逆。在过去的二十年里，人们的兴趣已经从线性正则化方法转移到非线性正则化方法，甚至是线性反问题。本文的目的是提供一个合理的全面的概述，这种转向现代非线性正则化方法，包括其分析，应用和未来的研究问题，特别是我们将讨论变分方法和技术，从他们派生，因为他们最近吸引了很多兴趣和链接到其他领域，如图像处理和压缩传感。我们进一步指出统计逆问题，多尺度分解和学习理论的发展。
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses. In the last two decades interest has shifted from linear to nonlinear regularization methods, even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this shift towards modern nonlinear regularization methods, including their analysis, applications and issues for future research.In particular we will discuss variational methods and techniques derived from them, since they have attracted much recent interest and link to other fields, such as image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions and learning theory.