Volume 57, pp. 127-152, 2022.

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

Thorsten Hohage and Frank Werner


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.

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Key words

inverse problem, variational regularization, error bounds, operator noise, random noise

AMS subject classifications

65J20, 60H30, 60H40

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