A new regularization term based on second order total generalized variation for image denoising problems

Variational models are one of the most efficient techniques for image denoising problems. A variational method refers to the technique of optimizing a functional in order to restore appropriate solutions from observed data that best fit the original image. This paper proposes to revisit the discrete total generalized variation (TGV ) image denoising problem by redefining the operations via the inclusion of a diagonal term to reduce the staircasing effect, which is the patchy artifacts usually observed in slanted regions of the image. We propose to add an oblique scheme in discretization operators, which we claim is aware of the alleviation of the staircasing effect superior to the con ventional TGV method. Numerical experiments are carried out by using the primal-dual algorithm, and numerous real-world examples are conducted to confirm that the new proposed method achieves higher quality in terms of rel ative error and the peak signal to noise ratio compared with the conventional TGV method.