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Titel
Infimal convolution of oscillation total generalized variation for the recovery of images with structured texture
Verfasser/ VerfasserinGao, Yiming ; Bredies, Kristian
KörperschaftFonds zur Förderung der Wissenschaftlichen Forschung
Enthalten in
SIAM Journal on Imaging Sciences, Universitätsbibliothek, 2018, 11 (2018), 3, Seite 2021-2063
ErschienenGraz : Universitätsbibliothek, 2018
VersionAccepted version
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)oscillation total generalized variation / infimal-convolution-type regularization / texture modeling / cartoon / texture decomposition / image denoising / image inpainting / undersampled magnetic resonance imaging
URNurn:nbn:at:at-ubg:3-12757 
DOI10.1137/17M1153960 
Fördergeber
Fonds zur Förderung der Wissenschaftlichen Forschung
Projekt-/Reportnummer: P29192
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Abstract

We propose a new type of regularization functional for images called oscillation total generalized variation (TGV) which can represent structured textures with oscillatory character in a specified direction and scale. The infimal convolution of oscillation TGV with respect to several directions and scales is then used to model images with structured oscillatory texture. Such functionals constitute a regularizer with good texture preservation properties and can flexibly be incorporated into many imaging problems. We give a detailed theoretical analysis of the infimal-convolution-type model with oscillation TGV in function spaces. Furthermore, we consider appropriate discretizations of these functionals and introduce a first-order primal-dual algorithm for solving general variational imaging problems associated with this regularizer. Finally, numerical experiments are presented which show that our proposed models can recover textures well and are competitive in comparison to existing state-of-the-art methods.

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