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We propose a new type of regularization functional for images calledoscillation total generalized variation (TGV) which can represent structuredtextures with oscillatory character in a specified direction and scale. Theinfimal convolution of oscillation TGV with respect to several directions andscales is then used to model images with structured oscillatory texture. Suchfunctionals constitute a regularizer with good texture preservation propertiesand can flexibly be incorporated into many imaging problems. We give a detailedtheoretical analysis of the infimal-convolution-type model with oscillation TGVin function spaces. Furthermore, we consider appropriate discretizations ofthese functionals and introduce a first-order primal-dual algorithm for solvinggeneral variational imaging problems associated with this regularizer. Finally,numerical experiments are presented which show that our proposed models canrecover textures well and are competitive in comparison to existingstate-of-the-art methods.

Infimal convolution of oscillation total generalized variation for the recovery of images with structured texture