Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces
| Autor: | Weidling, Frederic, Sprung, Benjamin, Hohage, Thorsten |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We show order optimal rates of convergence for finitely smoothing operators and for the backwards heat equation for a range of Besov spaces using variational source conditions. We also derive order optimal rates for a white noise model with the help of variational source conditions and concentration inequalities for sharp negative Besov norms of the noise. |
| Databáze: | arXiv |
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