Functions of bounded Musielak-Orlicz-type deformation and anisotropic Total Generalized Variation for image-denoising problems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910000483401728 |
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| author | Bertazzoni, Giacomo Davoli, Elisa Riccò, Samuele Zappale, Elvira |
| author_facet | Bertazzoni, Giacomo Davoli, Elisa Riccò, Samuele Zappale, Elvira |
| contents | In the first part of this paper we introduce the space of bounded deformation fields with generalized Orlicz growth. We establish their main properties, provide a modular representation, and characterize a decomposition of the modular into an absolutely continuous part and a singular part weighted via a recession function. A further analysis in the variable exponent case is also provided. The second part of the paper contains a notion of Musielak-Orlicz anisotropic Total Generalized Variation. We establish a duality representation, and show well-posedness of the corresponding image reconstruction problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functions of bounded Musielak-Orlicz-type deformation and anisotropic Total Generalized Variation for image-denoising problems Bertazzoni, Giacomo Davoli, Elisa Riccò, Samuele Zappale, Elvira Analysis of PDEs In the first part of this paper we introduce the space of bounded deformation fields with generalized Orlicz growth. We establish their main properties, provide a modular representation, and characterize a decomposition of the modular into an absolutely continuous part and a singular part weighted via a recession function. A further analysis in the variable exponent case is also provided. The second part of the paper contains a notion of Musielak-Orlicz anisotropic Total Generalized Variation. We establish a duality representation, and show well-posedness of the corresponding image reconstruction problem. |
| title | Functions of bounded Musielak-Orlicz-type deformation and anisotropic Total Generalized Variation for image-denoising problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.09237 |