Higher order error estimates for regularization of inverse problems under non-additive noise
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913806286848000 |
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| author | Mirciu, Diana-Elena Resmerita, Elena |
| author_facet | Mirciu, Diana-Elena Resmerita, Elena |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher order error estimates for regularization of inverse problems under non-additive noise Mirciu, Diana-Elena Resmerita, Elena Numerical Analysis Functional Analysis 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. |
| title | Higher order error estimates for regularization of inverse problems under non-additive noise |
| topic | Numerical Analysis Functional Analysis |
| url | https://arxiv.org/abs/2411.19736 |