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A Data-Driven Iteratively Regularized Landweber Iteration
Numerical Functional Analysis and Optimization ( IF 1.2 ) Pub Date : 2020-03-24 , DOI: 10.1080/01630563.2020.1740734
A. Aspri 1 , S. Banert 2 , O. Öktem 2 , O. Scherzer 1, 3
Affiliation  

Abstract We derive and analyze a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a black box, which is used to define the iteration process. We prove convergence and stability for the scheme in infinite dimensional Hilbert spaces. These theoretical results are complemented by some numerical experiments for solving linear inverse problems for the Radon transform and a nonlinear inverse problem for Schlieren tomography.

中文翻译:

数据驱动的迭代正则化 Landweber 迭代

摘要 我们推导出并分析了迭代正则化 Landweber 迭代的一个新变体,用于解决线性和非线性不适定逆问题。该方法考虑了用于估计黑盒内部的训练数据,用于定义迭代过程。我们证明了该方案在无限维希尔伯特空间中的收敛性和稳定性。这些理论结果由一些数值实验补充,用于解决 Radon 变换的线性逆问题和纹影断层扫描的非线性逆问题。
更新日期:2020-03-24
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