TY  - INPR
A1  - Bauer, Frank
A1  - Pereverzev, Sergei
T1  - Regularization without Preliminary Knowledge of  Smoothness and Error Behavior
N2  - The mathematical formulation of many physical problems results in the task of inverting a compact operator. The only known sensible solution technique is regularization which poses a severe problem in itself. Classically one dealt with deterministic noise models and required both the knowledge of smoothness of the solution function and the overall error behavior. We will show that we can guarantee an asymptotically optimal regularization for a physically motivated noise model under no assumptions for the smoothness and rather weak assumptions on the noise behavior which can mostly obtained out of two input data sets. An application to the determination of the gravitational field out of satellite data will be shown.
T3  - Schriften zur Funktionalanalysis und Geomathematik - 13 
KW  - Regularisierung
KW  - Inverses Problem
KW  - Weißes Rauschen
KW  - Satellitengradiogravimetrie
KW  - Regularization
KW  - severely ill-posed inverse problems
KW  - Gaussian random noise
KW  - satellite gravity gradiometry
Y1  - 2004
UR  - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1585
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-13526
ER  -