Error estimates for variational regularization of inverse problems with general noise models for data and operator

Electronic Transactions on Numerical Analysis

article

Thorsten Hohage¹  Frank Werner² 

[1] Institute for Numerical and Applied Mathematics, University of Göttingen;Institute of Mathematics, University of Würzburg

关键词: inverse problem;    variational regularization;    error bounds;    operator noise;    random noise;   

DOI  :  10.1553/etna_vol57s127

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 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.

【 授权许可】

Unknown