Total Variation Optimization Algorithm And Its Application

With the continuous development of the use of the Internet,people mainly get information from the outside word through images.However,in the process of image acquisition,transmission,processing,storage and output,image degradation will be caused by unrestricted factors.Therefore,it is very important to restore or restore the original image from the blurred noisy image in practical application.This dissertation takes image restoration as the research background,combines total variation regularization and optimization algorithm,and makes a thorough analysis and research on image restoration.Its main work includes the following aspects.(1)Based on the basic knowledge of image restoration,the research background,significance and research status at home and abroad are described in detail.(2)Based on the mathematical model of degenerate image,the discrete process of degenerate model is given.And the types of the degraded function and the noise types of the degraded image are introduced.(3)Based on the total variation regularization method,the theoretical basis of the total variation regularization for image restoration is discussed,and the discrete process of the total variation regularization is deduced.Based on the total variation regularization term,the Newton method of image restoration,the damped Newton method combined with BB algorithm,the primal-dual Newton method and detailed steps are discussed,and carry on the experiments and analysis.By comparing the experimental results of the three optimization algorithms,it is concluded that the primal-dual Newton method is better in image restoration.(4)Based on the total variation regularization term and Huber function regularization term,a new regularization term is proposed for image restoration,and numerical experiments and analysis are carried out.By comparing the experimental results of three regularization terms,the validity and feasibility of the new method are verified.