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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Enhancing linear regularization to treat large noise

1Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.

2Department of Mathematics, University of Applied Sciences Zittau/Görlitz, P. O. Box 1454, 02754 Zittau, Germany.

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 19, Issue 6, Pages 859–879, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2011.052, September 2011

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For solving linear ill-posed problems with noisy data, regularization methods are required. In this paper we study regularization under general noise assumptions containing large noise and small noise as special cases. We derive order optimal error bounds for an extended Tikhonov regularization by using some pre-smoothing. This accompanies recent results by the same authors, Regularization under general noise assumptions, Inverse Problems 27:3, 035016, 2011.

Keywords.: Ill-posed problems; inverse problems; regularization; Hilbert scales; order optimal error bounds; large noise; small noise

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