Bounded variation spaces with generalized Orlicz growth related to image denoising
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916696750555136 |
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| author | Eleuteri, Michela Harjulehto, Petteri Hästö, Peter |
| author_facet | Eleuteri, Michela Harjulehto, Petteri Hästö, Peter |
| contents | Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth. Our setup covers earlier variable exponent and double phase models. We study the norm and modular of the new space and derive a formula for the modular in terms of the Lebesgue decomposition of the derivative measure and a location dependent recession function. We also show that the modular can be obtained as the $Γ$-limit of uniformly convex approximating energies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_15256 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bounded variation spaces with generalized Orlicz growth related to image denoising Eleuteri, Michela Harjulehto, Petteri Hästö, Peter Functional Analysis 35J60, 26B30, 35B40, 35J25, 46E35, 49J27, 49J45 Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth. Our setup covers earlier variable exponent and double phase models. We study the norm and modular of the new space and derive a formula for the modular in terms of the Lebesgue decomposition of the derivative measure and a location dependent recession function. We also show that the modular can be obtained as the $Γ$-limit of uniformly convex approximating energies. |
| title | Bounded variation spaces with generalized Orlicz growth related to image denoising |
| topic | Functional Analysis 35J60, 26B30, 35B40, 35J25, 46E35, 49J27, 49J45 |
| url | https://arxiv.org/abs/2211.15256 |