Journal
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
Volume 22, Issue 6, Pages 871-913Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/jip-2013-0068
Keywords
Linear ill-posed problems; total generalized variation; multiple parameter regularization; symmetric tensor fields; spaces of bounded deformation; a-priori parameter choice
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Funding
- Austrian Science Fund (FWF) [SFB-F32]
- Austrian Science Fund (FWF) [F 3203] Funding Source: researchfish
- Austrian Science Fund (FWF) [W1244] Funding Source: Austrian Science Fund (FWF)
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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.
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