TY  - JOUR
A1  - Jahn, Tim Nikolas
T1  - A modified discrepancy principle to attain optimal convergence rates under unknown noise
T2  - Inverse problems
N2  - We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right-hand side are available. A natural approach is to take the average of the measurements as an approximation of the right-hand side and to estimate the data error as the inverse of the square root of the number of measurements. We calculate the optimal convergence rate (as the number of measurements tends to infinity) under classical source conditions and introduce a modified discrepancy principle, which asymptotically attains this rate.
KW  - statistical inverse problems
KW  - discrepancy principle
KW  - convergence
KW  - optimality
KW  - spectral cut-off
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63183
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-631838
SN  - 1361-6420
VL  - 37
IS  - 9, art. 095008
SP  - 1
EP  - 23
PB  - Inst.
CY  - Bristol [u.a.]
ER  -