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arXiv · 2401.00656

Scalable iterative data-adaptive RKHS regularization

Haibo Li·Jinchao Feng·Fei Lu
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Abstract

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.

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Haibo Li, Jinchao Feng, Fei Lu. 2024-01-01. Scalable iterative data-adaptive RKHS regularization. https://arxiv.org/abs/2401.00656

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