Image Denoising And Image Inpainting Based On The Normal Vector Jacobian

Image processing uses computer technology to operate and analyze images to get results that people need.Variational method is one of the primary methods to achieve image processing,which has strong mathematical theory foundation.The clssical first-order variational model has some defects in the process of image processing,such as the stair effect.High-order variational models can overcome shortcomings of first-order model and has outstanding performance in image smoothing.However,various high-order models exhibit different characteristics in the process of image processing.The research of high-order variational models has been a hot topic in recent years.It is of great significance to analyze the feature preservation of high-order models.Summarizing and analyzing the feature preserving properties of existing variational models in image processing,new variational models are proposed.This paper focuses on the basic problems of denoising and repairing in the field of image processing.The research contents and innovation points are as follows:(1)The characteristics of higher-order regularizer terms in the variational models are analyzed.Firstly,a bounded Hessian model with Jacobian of normals is extended to bounded Hessian model.Secondly,on the basis of the total generalized variation model,a total generalized variation model with Jacobian of normals is proposed.Finally,alternative direction multiplier method(ADMM)are designed to optimize the energy functional of models by setting penalty parameters and introducing a series of auxiliary variables and Lagrange multiplier.(2)The proposed model is applied to image denoising.Then,a large number of experiments are designed to compare with the classical second-order variational model.The corresponding qualitative and quantitative analysis shows that our proposed model has obvious advantages in the aspects of edge,smoothness,contrast and corner preserving.(3)The model proposed in this paper is applied to the field of image restoration.Experiments verifies that the total generalized variation model Jacobian of normals can effectively repair the large scale damaged area of the image.At the same time,it can take into account the linear structure and boundary information of the image as well as reduce the fuzzy area of the boundary.The model in this paper not only improves the accuracy of restoration,but also recovers more damaged image information.