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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/2410.16149 |
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| _version_ | 1866912079899787264 |
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| author | Beinert, Robert Bresch, Jonas |
| author_facet | Beinert, Robert Bresch, Jonas |
| contents | We introduce a novel relaxation strategy for denoising hyperbolic-valued data. The main challenge is here the non-convexity of the hyperbolic sheet. Instead of considering the denoising problem directly on the hyperbolic space, we exploit the Euclidean embedding and encode the hyperbolic sheet using a novel matrix representation. For denoising, we employ the Euclidean Tikhonov and total variation (TV) model, where we incorporate our matrix representation. The major contribution is then a convex relaxation of the variational ansätze allowing the utilization of well-established convex optimization procedures like the alternating directions method of multipliers (ADMM). The resulting denoisers are applied to a real-world Gaussian image processing task, where we simultaneously restore the pixelwise mean and standard deviation of a retina scan series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16149 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Denoising Hyperbolic-Valued Data by Relaxed Regularizations Beinert, Robert Bresch, Jonas Numerical Analysis Optimization and Control 94A08, 94A12, 65J22, 90C22, 90C25 We introduce a novel relaxation strategy for denoising hyperbolic-valued data. The main challenge is here the non-convexity of the hyperbolic sheet. Instead of considering the denoising problem directly on the hyperbolic space, we exploit the Euclidean embedding and encode the hyperbolic sheet using a novel matrix representation. For denoising, we employ the Euclidean Tikhonov and total variation (TV) model, where we incorporate our matrix representation. The major contribution is then a convex relaxation of the variational ansätze allowing the utilization of well-established convex optimization procedures like the alternating directions method of multipliers (ADMM). The resulting denoisers are applied to a real-world Gaussian image processing task, where we simultaneously restore the pixelwise mean and standard deviation of a retina scan series. |
| title | Denoising Hyperbolic-Valued Data by Relaxed Regularizations |
| topic | Numerical Analysis Optimization and Control 94A08, 94A12, 65J22, 90C22, 90C25 |
| url | https://arxiv.org/abs/2410.16149 |