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arXiv · 2411.19736

Higher order error estimates for regularization of inverse problems under non-additive noise

Diana-Elena Mirciu·Elena Resmerita
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Abstract

In this work we derive higher order error estimates for inverse problems distorted by non-additive noise, in terms of Bregman distances. The results are obtained by means of a novel source condition, inspired by the dual problem. Specifically, we focus on variational regularization having the Kullback-Leibler divergence as data-fidelity, and a convex penalty term. In this framework, we provide an interpretation of the new source condition, and present error estimates also when a variational formulation of the source condition is employed. We show that this approach can be extended to variational regularization that incorporates more general convex data fidelities.

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Diana-Elena Mirciu, Elena Resmerita. 2024-11-29. Higher order error estimates for regularization of inverse problems under non-additive noise. https://arxiv.org/abs/2411.19736

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