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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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1569-3945
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Volume 19, Issue 6

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Enhancing linear regularization to treat large noise

Peter Mathé / Ulrich Tautenhahn
  • Department of Mathematics, University of Applied Sciences Zittau/Görlitz, P. O. Box 1454, 02754 Zittau, Germany.
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Published Online: 2011-09-12 | DOI: https://doi.org/10.1515/jiip.2011.052

Abstract

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

About the article

Received: 2011-04-20

Revised: 2011-05-27

Published Online: 2011-09-12

Published in Print: 2011-12-01


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: https://doi.org/10.1515/jiip.2011.052.

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Citing Articles

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[1]
Bernd Hofmann and Peter Mathé
Inverse Problems, 2018, Volume 34, Number 1, Page 015007
[2]
Serena Morigi, Lothar Reichel, and Fiorella Sgallari
Journal of Computational and Applied Mathematics, 2017, Volume 324, Page 142
[3]
Kolyan Ray and Johannes Schmidt-Hieber
Inverse Problems, 2016, Volume 32, Number 6, Page 065003
[4]
Kui Lin, Shuai Lu, and Peter Mathé
Inverse Problems and Imaging, 2015, Volume 9, Number 3, Page 895
[5]
Hanne Kekkonen, Matti Lassas, and Samuli Siltanen
Inverse Problems, 2014, Volume 30, Number 4, Page 045009
[6]
Qinian Jin and Peter Mathé
SIAM/ASA Journal on Uncertainty Quantification, 2013, Volume 1, Number 1, Page 386

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