A Data-Driven Iteratively Regularized Landweber Iteration

被引：18
|
作者：
Aspri, A. [1 ]
Banert, S. [2 ]
Oktem, O. [2 ]
Scherzer, O. [1 ,3 ]
机构：
[1] Johann Radon Inst Computat & Appl Math RICAM, Linz, Austria
[2] KTH Royal Inst Technol, Stockholm, Sweden
[3] Univ Vienna, Computat Sci Ctr, Vienna, Austria
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2020年 / 41卷 / 10期
关键词：
Black box strategy; expert and data driven regularization; Iteratively regularized Landweber iteration; PRESSURE;
D O I：
10.1080/01630563.2020.1740734
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：1190 / 1227
页数：38
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