ERROR ESTIMATES FOR VARIATIONAL REGULARIZATION OF INVERSE PROBLEMS WITH GENERAL NOISE MODELS FOR DATA AND OPERATOR

被引：3

作者：

Hohage, Thorsten ^{[1
]}

Werner, Frank ^{[2
]}

机构：

[1] Univ Gottingen, Inst Numer & Appl Math, D-37083 Gottingen, Germany

[2] Univ Wurzburg, Inst Math, D-97074 Wurzburg, Germany

来源：

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2022年 / 57卷

关键词：

inverse problem; variational regularization; error bounds; operator noise; random noise; OPTIMAL CONVERGENCE-RATES; ILL-POSED PROBLEMS; TIKHONOV REGULARIZATION;

D O I：

10.1553/etna_vol57s127

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with variational regularization of inverse problems where both the data and the forward operator are given only approximately. We propose a general approach to derive error estimates which separates the analysis of smoothness of the exact solution from the analysis of the effect of errors in the data and the operator. Our abstract error bounds are applied to both discrete and continuous data, random and deterministic types of error, as well as Huber data fidelity terms for impulsive noise.

引用

页码：127 / 152

页数：26

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