Multi-resolution deconvolution
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866917173761409024 |
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| author | Karamehmedović, Mirza Maréchal, Pierre Carøe, Martin Sæbye Baalbaki, Lara |
| author_facet | Karamehmedović, Mirza Maréchal, Pierre Carøe, Martin Sæbye Baalbaki, Lara |
| contents | We extend the classical deconvolution framework in Rn to the case with a pseudodifferential-like solution operator with a symbol depending on both the base and cotangent variable. Our framework enables deconvolution with spatially varying resolution while maintaining a set global stability, and it additionally allows rather general distributional convolution kernels. We provide consistency, convergence and stability results, as well as convergence rates. Finally, we include numerical examples supporting our results and demonstrating advantages of the generalized framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-resolution deconvolution Karamehmedović, Mirza Maréchal, Pierre Carøe, Martin Sæbye Baalbaki, Lara Spectral Theory We extend the classical deconvolution framework in Rn to the case with a pseudodifferential-like solution operator with a symbol depending on both the base and cotangent variable. Our framework enables deconvolution with spatially varying resolution while maintaining a set global stability, and it additionally allows rather general distributional convolution kernels. We provide consistency, convergence and stability results, as well as convergence rates. Finally, we include numerical examples supporting our results and demonstrating advantages of the generalized framework. |
| title | Multi-resolution deconvolution |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2512.23342 |