Abstract
In this article, we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods, from a statistical point of view. The basic purpose of the paper is to develop adaptive model selection techniques for determining the regularization parameters, i.e., the iteration index. We assume observations are taken over a fixed grid and we consider solutions over a sequence of finite-dimensional subspaces. Based on concentration inequalities techniques, we derive non-asymptotic optimal upper bounds for the mean square error of the proposed estimator.
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The authors would like to thank Projects Agenda Petróleo, Fonacit and Ecos-Nord for their financial support.
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Fermín, A.K., Ludeña, C. A statistical view of iterative methods for linear inverse problems. TEST 17, 381–400 (2008). https://doi.org/10.1007/s11749-006-0038-2
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DOI: https://doi.org/10.1007/s11749-006-0038-2
Keywords
- Ill-posed problem
- Singular value decomposition
- Iterative regularization methods
- Model selection
- Descent methods