Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems
- In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy data. In this statistical learning setting, we derive the rates of convergence for the regularized solution under certain assumptions on the nonlinear forward operator and the prior assumptions. We discuss estimates of the reconstruction error using the approach of reproducing kernel Hilbert spaces.
| Author details: | Abhishake RastogiORCiD |
|---|---|
| DOI: | https://doi.org/10.3934/cpaa.2020183 |
| ISSN: | 1534-0392 |
| ISSN: | 1553-5258 |
| Title of parent work (English): | Communications on Pure and Applied Analysis |
| Publisher: | American Institute of Mathematical Sciences |
| Place of publishing: | Springfield |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/05/01 |
| Publication year: | 2020 |
| Release date: | 2023/01/05 |
| Tag: | Hilbert Scales; Statistical inverse problem; Tikhonov regularization; minimax convergence rates; reproducing kernel Hilbert space |
| Volume: | 19 |
| Issue: | 8 |
| Number of pages: | 16 |
| First page: | 4111 |
| Last Page: | 4126 |
| Funding institution: | Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG); [SFB1294/1 - 318763901] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Bronze Open-Access |
