Image Restoration Models with Optimal Transport and Total Variation Regularization
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908274954076160 |
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| author | Huang, Weijia Huang, Zhongyi Yang, Wenli Zhu, Wei |
| author_facet | Huang, Weijia Huang, Zhongyi Yang, Wenli Zhu, Wei |
| contents | In this paper, we propose image restoration models using optimal transport (OT) and total variation regularization. We present theoretical results of the proposed models based on the relations between the dual Lipschitz norm from OT and the G-norm introduced by Yves Meyer. We design a numerical method based on the Primal-Dual Hybrid Gradient (PDHG) algorithm for the Wasserstain distance and the augmented Lagrangian method (ALM) for the total variation, and the convergence analysis of the proposed numerical method is established. We also consider replacing the total variation in our model by one of its modifications developed in \cite{zhu}, with the aim of suppressing the stair-casing effect and preserving image contrasts. Numerical experiments demonstrate the features of the proposed models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Image Restoration Models with Optimal Transport and Total Variation Regularization Huang, Weijia Huang, Zhongyi Yang, Wenli Zhu, Wei Numerical Analysis 65K10, 68U10, 90C30 In this paper, we propose image restoration models using optimal transport (OT) and total variation regularization. We present theoretical results of the proposed models based on the relations between the dual Lipschitz norm from OT and the G-norm introduced by Yves Meyer. We design a numerical method based on the Primal-Dual Hybrid Gradient (PDHG) algorithm for the Wasserstain distance and the augmented Lagrangian method (ALM) for the total variation, and the convergence analysis of the proposed numerical method is established. We also consider replacing the total variation in our model by one of its modifications developed in \cite{zhu}, with the aim of suppressing the stair-casing effect and preserving image contrasts. Numerical experiments demonstrate the features of the proposed models. |
| title | Image Restoration Models with Optimal Transport and Total Variation Regularization |
| topic | Numerical Analysis 65K10, 68U10, 90C30 |
| url | https://arxiv.org/abs/2503.14947 |