论文标题
逆问题的正规化
Regularization of Inverse Problems
论文作者
论文摘要
这些研究生班的讲义介绍了希尔伯特空间中线性和非线性不良操作员方程的正则化理论。涵盖的是正规化方法的一般框架及其通过光谱过滤器进行分析，以及Tikhonov正则化，陆地迭代的具体示例，通过离散化线性反向问题的正规化。在非线性环境中，讨论了Tikhonov正则化和迭代正则化（Landweber，Levenberg-Marquardt和迭代式正则化Gauß-Newton方法）。功能分析的必要背景也简要概述。音符以统计逆问题的简短前景结束，从频繁主义者和贝叶斯的角度来看。
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral filters as well as the concrete examples of Tikhonov regularization, Landweber iteration, regularization by discretization for linear inverse problems. In the nonlinear setting, Tikhonov regularization and iterative regularization (Landweber, Levenberg-Marquardt, and iteratively regularized Gauß-Newton methods) are discussed. The necessary background from functional analysis is also briefly summarized. The notes end with a brief outlook to statistical inverse problems from both a frequentist and a Bayesian point of view.
