Image Zooming Model And Fast Algorithm Based On Modified TGV Regularization

In recent years,the application of variational and partial differential equations in numerical computation is flexible and the stability of discretization is good,so the applications of variational and partial differential equations cover the whole image processing field.During the image processing,in order to improve the image quality and visual effect,it is necessary to improve the image resolution(i.e.,image zooming).Based on the total generalized variation(TGV)regularization,several new modified TGV image zooming models are proposed and solved quickly with the primal-dual algorithm.Meanwhile,we also promote our proposed models to the furtherpractical problems(e.g.,astronomical images).The main research contents and innovation points are as follows:1.Firstly,we introduce some classical mathematical models in the field of image processing: PM model,TV model,TGV model,BSCB model,LLT model,etc.At the same time,we introduce the development process of these modelsand compare with each other.Also,some efficient numerical algorithms used in image processing are given.2.A new image zooming model based on weighted TGV is proposed.By take advantages of the TGV regular term andadjusting the weighted funcion reasonably,our proposed model overcomes the disadvantage of the TV model.In the numerical algorithm,we use the primal-dual algorithm to solve the problem efficiently,and compare the obtained experimental results with the standard second-order TGV image zooming model.The results of numerical experiments show that the weighted TGV image zooming model has been greatly improved in the objective evaluation criteria,such as the visual effect and the peak signal to noise ratio.3.Based on the original second-order TGV regularization method,we further adjust the selection of weighted function,construct a convex weight function,and propose a non convex total generalized variation image zooming model,which can obtain the weaker smoothed results at the edge and stronger smoothed results at the other areas.Furthmore,The primal dual algorithm is applied to solve the numerical problem.The analysis of the numerical experiment data shows that the new model can not only preserve the texture information of the image effectively,but also improve the performance index of noise reduction.4.Finally,in views of application,we extend the weighted TGV model and the non convex TGV model proposed in this paper to the actual astronomical images.In this chapter,we compare the numerical results of astronomical images among the second-order TGV model,the weighted TGV model and the non-convex TGV model.Through a series of numerical experiments,we can find that our proposed model and algorithm also have outstanding results in practical problems.