Scalable iterative data-adaptive RKHS regularization
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916078468202496 |
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| author | Li, Haibo Feng, Jinchao Lu, Fei |
| author_facet | Li, Haibo Feng, Jinchao Lu, Fei |
| contents | We present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method, for solving ill-posed linear inverse problems. The method searches for solutions in subspaces where the true solution can be identified, with the data-adaptive RKHS penalizing the spaces of small singular values. At the core of the method is a new generalized Golub-Kahan bidiagonalization procedure that recursively constructs orthonormal bases for a sequence of RKHS-restricted Krylov subspaces. The method is scalable with a complexity of $O(kmn)$ for $m$-by-$n$ matrices with $k$ denoting the iteration numbers. Numerical tests on the Fredholm integral equation and 2D image deblurring show that it outperforms the widely used $L^2$ and $l^2$ norms, producing stable accurate solutions consistently converging when the noise level decays. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalable iterative data-adaptive RKHS regularization Li, Haibo Feng, Jinchao Lu, Fei Numerical Analysis 47A52, 65F22, 65J20 We present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method, for solving ill-posed linear inverse problems. The method searches for solutions in subspaces where the true solution can be identified, with the data-adaptive RKHS penalizing the spaces of small singular values. At the core of the method is a new generalized Golub-Kahan bidiagonalization procedure that recursively constructs orthonormal bases for a sequence of RKHS-restricted Krylov subspaces. The method is scalable with a complexity of $O(kmn)$ for $m$-by-$n$ matrices with $k$ denoting the iteration numbers. Numerical tests on the Fredholm integral equation and 2D image deblurring show that it outperforms the widely used $L^2$ and $l^2$ norms, producing stable accurate solutions consistently converging when the noise level decays. |
| title | Scalable iterative data-adaptive RKHS regularization |
| topic | Numerical Analysis 47A52, 65F22, 65J20 |
| url | https://arxiv.org/abs/2401.00656 |