The Poisson Image Denoising Research Based On Total Generalized Variation Regularization

In the innovation of science and technology, the digital image processing technology is widely used in people’s daily life, and used in biomedical, aerospace, target recognition and tracking and other important fields. However, in the process of image acquiring, due to the external environment and the limitation of the technology the image degradation often happens when we obtain the image, so how to quickly recover the original image from the degraded image and keep high quality is an important issue in real life.In order to solve the Poisson noise image restoration problem, several kinds of regularization method have been put forward and one of the most famous models is total variation model. Although the total variation model can remove noise and at the same time keep the image detail information, but it also cause staircase effect. It is well known that the total generalized variation as a regularization can effectively eliminate the staircase effect, but because of the existence of higher order derivative term in the image restoration process the image edge detail information cannot keep well. In order to be in the image restoration project, not only effectively eliminate the staircase effect, but also can keep the image edge details, based on this idea, the following two aspects are mainly considered in this article.First, based on second-order total generalized variation we consider plus a Shear let transform as a regularization item, because the Shearlet transform in image restoration can keep the image edge details very well. Therefore, as a starting point in this paper, a new regularization model is put forward.The second point is considering the second order total generalized variation regularization item only have higher derivative, in the process of image restoration cannot effectively maintain image detail information, so we consider adding a whole norm as the regularization to deal with the Poisson noise image. Based on this idea, in this paper we put the second order total generalized variation and full combination of norm put forward a new model for Poisson noise image restoration. The new model uses split Bregman iterative algorithm to solve.The two new proposed model numerical experiments results no matter from the visual, and on the numerical results both show that the new model can maintain the superiority of the image edge details.