The Research On The Image Denoising Algorithm Based On The Variational Method

With the rapid development of information technology,digital image has become an important medium for people to acquire information,perceive nature and understand the world.In the process of acquisition,transmission and storage,digital images will inevitably be contaminated by noise signals.Signals can hinder people's correct understanding of image information,and at the same time have a great impact on the subsequent processing of images(feature extraction,edge detection,etc.).Therefore,image denoising,as one of the image preprocessing operations,is of great importance and is essential for subsequent processing of images.This paper mainly studies the variational-based image denoising algorithm.Firstly,several classical variational denoising models are mainly studied.Secondly,aiming at the disadvantages of second-order generalized variational denoising model that is easy to blur small structure and small texture,a new model that combines the Kirsch edge detection operator with a second-order generalized variational denoising model is proposed,and the advantages of this model are analyzed theoretically.Finally,simulation experiments are carried out to verify the model.The main work of this paper is as follows:(1)Several classical variational denoising models are introduced.This paper introduces several classical variational denoising models in detail,and theoretically analyzes the denoising mechanism of these models as well as their advantages and disadvantages in the process of denoising.And the simulation experiment is carried out to verify it.(2)A denoising model combining the Kirsch edge detection operator with a second order generalized variational model is proposed.First,the Kirsch edge detection operator is used to extract the local texture feature information of the image,and then an adaptive regular term edge indicator function g(x)and an adaptive data fidelity term parameter?(x)are constructed based on the information.Finally,the edge indicator function g(x)and data fidelity term parameters ?(x)are introduced into the second order generalized variational denoising model,where g(x)guides the variational denoising model adaptively diffusion,?(x)guides the variational denoising model adaptively image constraints.The model can effectively remove noise,improve the performance of edge preserving and restrain "staircase effect".(3)Simulation experiment verification.Based on Matlab software platform,the first-order primal-dual algorithm is used to solve the total variational model,the second-order generalized variation model and the proposed denoising model.The denoising performance of the models is evaluated from the several aspects,including visual effect,PSNR,mean square error and structural similarity.The experimental results show that,compared with the other two models,the denoising model proposed in this paper can better remove noise,maintain the edge texture details of the image and overcome the "staircase effect".