Beyond the Bakushinkii veto: regularising linear inverse problems without knowing the noise distribution
- This article deals with the solution of linear ill-posed equations in Hilbert spaces. Often, one only has a corrupted measurement of the right hand side at hand and the Bakushinskii veto tells us, that we are not able to solve the equation if we do not know the noise level. But in applications it is ad hoc unrealistic to know the error of a measurement. In practice, the error of a measurement may often be estimated through averaging of multiple measurements. We integrated that in our anlaysis and obtained convergence to the true solution, with the only assumption that the measurements are unbiased, independent and identically distributed according to an unknown distribution.
Download full text files
Additional Services
| Author: | Bastian von HarrachORCiDGND, Tim Nikolas Jahn, Roland Potthas |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-637798 |
| DOI: | https://doi.org/10.1007/s00211-020-01122-2 |
| ISSN: | 0945-3245 |
| Parent Title (German): | Numerische Mathematik |
| Publisher: | Springer |
| Place of publication: | Berlin ; Heidelberg |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2020/05/26 |
| Date of first Publication: | 2020/05/26 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2022/06/28 |
| Volume: | 145 |
| Issue: | 3 |
| Page Number: | 23 |
| First Page: | 581 |
| Last Page: | 603 |
| Note: | Open Access funding provided by Projekt DEAL. |
| HeBIS-PPN: | 505146169 |
| Institutes: | Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J22 Inverse problems |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - Namensnennung 4.0 |
