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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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Volume 22, Issue 6


Regularization of linear inverse problems with total generalized variation

Kristian Bredies / Martin Holler
Published Online: 2014-02-26 | DOI: https://doi.org/10.1515/jip-2013-0068


The regularization properties of the total generalized variation (TGV) functional for the solution of linear inverse problems by means of Tikhonov regularization are studied. Considering the associated minimization problem for general symmetric tensor fields, the well-posedness is established in the space of symmetric tensor fields of bounded deformation, a generalization of the space of functions of bounded variation. Convergence for vanishing noise level is shown in a multiple regularization parameter framework in terms of the naturally arising notion of TGV-strict convergence. Finally, some basic properties, in particular non-equivalence for different parameters, are discussed for this notion.

Keywords: Linear ill-posed problems; total generalized variation; multiple parameter regularization; symmetric tensor fields; spaces of bounded deformation; a-priori parameter choice

MSC: 65L09; 65F22; 65L20; 46G05; 46B26

About the article

Received: 2013-11-20

Published Online: 2014-02-26

Published in Print: 2014-12-01

Funding Source: Austrian Science Fund (FWF)

Award identifier / Grant number: SFB-F32

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 22, Issue 6, Pages 871–913, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2013-0068.

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