Infimal convolution of oscillation total generalized variation for the recovery of images with structured texture
For image processing researchers, this provides a new regularizer that improves texture preservation in variational imaging problems.
The paper introduces oscillation total generalized variation (TGV) as a new regularization functional for images with structured textures, and uses infimal convolution across directions and scales to model such textures. Numerical experiments show the method recovers textures well and is competitive with state-of-the-art methods.
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.