Analysis of a wavelet frame based two-scale model for enhanced edges
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929199765258240 |
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| author | Dong, Bin Lin, Ting Shen, Zuowei Xie, Peichu |
| author_facet | Dong, Bin Lin, Ting Shen, Zuowei Xie, Peichu |
| contents | Image restoration is a class of important tasks that emerges from a wide range of scientific disciplines. It has been noticed that most practical images can be modeled as a composition from a sparse singularity set (edges) where the image contents or their gradients change drastically, and cartoon chunks in which a high degree of regularity is dominant. Enhancing edges while promoting regularity elsewhere has been an important criterion for successful restoration in many image classes. In this article, we present a wavelet frame based image restoration model that captures potential edges and facilitates the restoration procedure by a dedicated treatment both of singularity and of cartoon. Moreover, its geometric robustness is enhanced by exploiting subtle inter-scale information available in the coarse image. To substantiate our intuition, we prove that this model converges to one variant of the celebrated Mumford-Shah model when adequate asymptotic specifications are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02688 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis of a wavelet frame based two-scale model for enhanced edges Dong, Bin Lin, Ting Shen, Zuowei Xie, Peichu Functional Analysis 42C40, 68U10 Image restoration is a class of important tasks that emerges from a wide range of scientific disciplines. It has been noticed that most practical images can be modeled as a composition from a sparse singularity set (edges) where the image contents or their gradients change drastically, and cartoon chunks in which a high degree of regularity is dominant. Enhancing edges while promoting regularity elsewhere has been an important criterion for successful restoration in many image classes. In this article, we present a wavelet frame based image restoration model that captures potential edges and facilitates the restoration procedure by a dedicated treatment both of singularity and of cartoon. Moreover, its geometric robustness is enhanced by exploiting subtle inter-scale information available in the coarse image. To substantiate our intuition, we prove that this model converges to one variant of the celebrated Mumford-Shah model when adequate asymptotic specifications are given. |
| title | Analysis of a wavelet frame based two-scale model for enhanced edges |
| topic | Functional Analysis 42C40, 68U10 |
| url | https://arxiv.org/abs/2401.02688 |