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.
Author:Bastian von HarrachORCiDGND, Tim Nikolas Jahn, Roland Potthas
Parent Title (German):Numerische Mathematik
Place of publication:Berlin ; Heidelberg
Document Type:Article
Date of Publication (online):2020/05/26
Date of first Publication:2020/05/26
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2022/06/28
Page Number:23
First Page:581
Last Page:603
Open Access funding provided by Projekt DEAL.
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
Licence (German):License LogoCreative Commons - Namensnennung 4.0