论文标题
对非线性陆地迭代的某些启发式停止规则的数值比较
A numerical comparison of some heuristic stopping rules for nonlinear Landweber iteration
论文作者
论文摘要
选择合适的正则化参数是反问题的大多数正则化方法的重要组成部分。在没有可靠估算噪声水平的情况下，可以使用启发式参数选择规则来完成此任务。尽管在线性问题的情况下，他们已经得到了相当充分的理解和测试，但对于非线性问题的行为，在各自的迭代正则化情况下，他们的行为并不多。因此，在本文中，当用于确定各种非线性反问题的LandWeber迭代索引时，我们会数字研究其中一些规则的性能。这些是从不同实际相关的领域中选择的，例如积分方程，参数估计和断层扫描。
The choice of a suitable regularization parameter is an important part of most regularization methods for inverse problems. In the absence of reliable estimates of the noise level, heuristic parameter choice rules can be used to accomplish this task. While they are already fairly well-understood and tested in the case of linear problems, not much is known about their behaviour for nonlinear problems and even less in the respective case of iterative regularization. Hence, in this paper, we numerically study the performance of some of these rules when used to determine a stopping index for Landweber iteration for various nonlinear inverse problems. These are chosen from different practically relevant fields such as integral equations, parameter estimation, and tomography.
