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

TL;DR

This paper introduces a novel regularization method called oscillation TGV and its infimal convolution for improved image reconstruction of textured images, supported by theoretical analysis and numerical experiments.

Contribution

It proposes a new oscillation TGV regularizer and its infimal convolution, with theoretical analysis and an efficient primal-dual algorithm for textured image recovery.

Findings

Effective texture preservation demonstrated in numerical experiments.

Competitive performance compared to state-of-the-art methods.

Flexible incorporation into various imaging problems.

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.