TY  - JOUR
A1  - Harrach, Bastian von
A1  - Jahn, Tim Nikolas
A1  - Potthas, Roland
T1  - Beyond the Bakushinkii veto: regularising linear inverse problems without knowing the noise distribution
T2  - Numerische Mathematik
N2  - 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.
Y1  - 2020
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63779
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-637798
SN  - 0945-3245
N1  - Open Access funding provided by Projekt DEAL.
VL  - 145
IS  - 3
SP  - 581
EP  - 603
PB  - Springer
CY  - Berlin ; Heidelberg
ER  -