A counterexample to convergence for multiscale decompositions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909520104521728 |
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| author | Rebegoldi, Simone Rondi, Luca |
| author_facet | Rebegoldi, Simone Rondi, Luca |
| contents | We discuss the convergence of the multiscale procedure by Modin, Nachman and Rondi, Adv. Math. (2019), which extended to inverse problems the multiscale decomposition of images by Tadmor, Nezzar and Vese, Multiscale Model. Simul. (2004). We show that, for the classical multiscale procedure, the multiscale decomposition might fail even for the linear case with a Banach norm as regularization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A counterexample to convergence for multiscale decompositions Rebegoldi, Simone Rondi, Luca Numerical Analysis 68U10 (primary), 65J22 (secondary) We discuss the convergence of the multiscale procedure by Modin, Nachman and Rondi, Adv. Math. (2019), which extended to inverse problems the multiscale decomposition of images by Tadmor, Nezzar and Vese, Multiscale Model. Simul. (2004). We show that, for the classical multiscale procedure, the multiscale decomposition might fail even for the linear case with a Banach norm as regularization. |
| title | A counterexample to convergence for multiscale decompositions |
| topic | Numerical Analysis 68U10 (primary), 65J22 (secondary) |
| url | https://arxiv.org/abs/2503.00556 |