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Regularization without Preliminary Knowledge of Smoothness and Error Behavior

  • 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.

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Author:Frank Bauer, Sergei Pereverzev
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (13)
Document Type:Preprint
Language of publication:English
Year of Completion:2004
Year of Publication:2004
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2004/11/09
Gaussian random noise; Regularization; satellite gravity gradiometry; severely ill-posed inverse problems
GND-Keyword:Regularisierung; Inverses Problem; Weißes Rauschen
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011