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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.12847 |
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| _version_ | 1866910620722397184 |
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| author | Antil, Harbir Mizuno, Daiki Shirakawa, Ken Ukai, Naotaka |
| author_facet | Antil, Harbir Mizuno, Daiki Shirakawa, Ken Ukai, Naotaka |
| contents | This paper is devoted to the mathematical analysis of a system of pseudo-parabolic partial differential equations governed by an energy functional, associated with anisotropic monochrome image processing. The energy functional is based on the one proposed by [Berkels et al. Cartoon extraction based on anisotropic image classification, SFB 611, 2006], which incorporates an orientation auto-adjustment mechanism, and our energy is a simplified version which reduces the order of derivatives to improve computational efficiency. The aim of this paper is to establish a stable minimization process that addresses some instability of the algorithm caused by the reduction of derivative order. As a part of the study, we here prove Main Theorems concerned with the well-posedness of the pseudo-parabolic system, and provide a mathematically rigorous guarantee for the stability of the image denoising process derived from our system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12847 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A gradient system based on anisotropic monochrome image processing with orientation auto-adjustment Antil, Harbir Mizuno, Daiki Shirakawa, Ken Ukai, Naotaka Analysis of PDEs This paper is devoted to the mathematical analysis of a system of pseudo-parabolic partial differential equations governed by an energy functional, associated with anisotropic monochrome image processing. The energy functional is based on the one proposed by [Berkels et al. Cartoon extraction based on anisotropic image classification, SFB 611, 2006], which incorporates an orientation auto-adjustment mechanism, and our energy is a simplified version which reduces the order of derivatives to improve computational efficiency. The aim of this paper is to establish a stable minimization process that addresses some instability of the algorithm caused by the reduction of derivative order. As a part of the study, we here prove Main Theorems concerned with the well-posedness of the pseudo-parabolic system, and provide a mathematically rigorous guarantee for the stability of the image denoising process derived from our system. |
| title | A gradient system based on anisotropic monochrome image processing with orientation auto-adjustment |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.12847 |