Research Of Numerical Methods For Duality-type CT Image Reconstruction Problem

The study of models and their corresponding algorithms in CT image reconstruction is an important research topic in the field of image reconstruction.This paper proposes a dual-type alternating direction multiplier method based on the classical total variation reconstruction model.That is,the primal problem is transformed into its equivalent dual problem through the definition of conjugate function.Since this problem is an equali-ty constraint concave optimization problem,it will be transformed into a saddle point problem by augmented lagrangian function and use the alternating direction multiplier method to solve.Simultaneously,the dual problem is a concave problem.Therefore,the convergence of the algorithm can be guaranteed.In addition,the total variation recon-struction problem of the primal problem is transformed into a smooth convex optimization problem by the smoothing method-Huber function.Then use the primal dual method to solve and can guarantee the convergence of the algorithm theoretically.For the above two types of algorithms,numerical experiments verify the rationality and effectiveness of the model and algorithm.The paper is arranged as follows.Firstly,this paper introduces the background and research status of CT image re-construction.At the same time,the basis for the selection of this paper and the augment-ed lagrangian function associated with it are introduced.The primal dual algorithm,common theoretical background knowledge such as CT image reconstruction algorithm;Secondly,a dual algorithm based on augmented lagrangian is derived based on the ba-sic nonsmooth optimization problem and give convergence analysis.The dual algorithm and other methods(such as:filtered back projection algorithm,tikhonov regularization,primal dual algorithm)for analysis and comparison in image reconstruction experiments.Experimental results show that the augmented lagrangian dual algorithm reconstructs the image with higher quality presented in this paper.In addition,this paper proposes an improved model based on the total variation and applied to the CT image reconstruction.In the numeric experiment,we use the two models of TV-L2 with or without negative constraints as the reference model.Experimental results show that the improved model proposed in this paper has higher reconstruction performance.At last,summarize this work and give further research work.