Uniform multi-penalty regularization for linear ill-posed inverse problems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916619705384960 |
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| author | Bortolotti, Villiam Landi, Germana Zama, Fabiana |
| author_facet | Bortolotti, Villiam Landi, Germana Zama, Fabiana |
| contents | This study examines, in the framework of variational regularization methods, a multi-penalty regularization approach which builds upon the Uniform PENalty (UPEN) method, previously proposed by the authors for Nuclear Magnetic Resonance (NMR) data processing. The paper introduces two iterative methods, UpenMM and GUpenMM, formulated within the Majorization-Minimization (MM) framework. These methods are designed to identify appropriate regularization parameters and solutions for linear inverse problems utilizing multi-penalty regularization. The paper demonstrates the convergence of these methods and illustrates their potential through numerical examples in one and two-dimensional scenarios, showing the practical utility of point-wise regularization terms in solving various inverse problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14163 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform multi-penalty regularization for linear ill-posed inverse problems Bortolotti, Villiam Landi, Germana Zama, Fabiana Numerical Analysis This study examines, in the framework of variational regularization methods, a multi-penalty regularization approach which builds upon the Uniform PENalty (UPEN) method, previously proposed by the authors for Nuclear Magnetic Resonance (NMR) data processing. The paper introduces two iterative methods, UpenMM and GUpenMM, formulated within the Majorization-Minimization (MM) framework. These methods are designed to identify appropriate regularization parameters and solutions for linear inverse problems utilizing multi-penalty regularization. The paper demonstrates the convergence of these methods and illustrates their potential through numerical examples in one and two-dimensional scenarios, showing the practical utility of point-wise regularization terms in solving various inverse problems. |
| title | Uniform multi-penalty regularization for linear ill-posed inverse problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2309.14163 |