Research On Reconstruction Algorithm For PET Images Based On Alternating Direction Method Of Multipliers

Positron Emission Tomography(PET)is a vital role in the development of nuclear medicine nowadays,which has a great contribution to many areas,including cancer diagnosis and treatment,cardiovascular disease diagnosis,neurological diseases and new drug development.The key techniques contained in PET imaging are as follows:PET labeling technology with targeted specificity,Pharmacokinetic analysis of drugs after entering the body,double photon coincidence detection technology to measure annihilation reaction,research on the correction algorithm of the scattering and attenuation of photons in human body,graphic processing system to reconstruction and display images.Among them,the quality of the image reconstruction determines the quality of the system directly,and can influence the clinical diagnosis and treatment.The paper discusses the reconstruction of Positron Emission Tomography,based on the Alternating Direction Method of Multipliers(ADMM),which is applied to the Weighted Least Squares(WLS),Expectation Maximization Algorithm(EM),Conjugate Gradient algorithm(CG),LandWeber algorithm(PL)and solving the classical Lasso problem.ADMM can decompose the scale optimization problem into multiple sub-problems,and obtain the global solution of the original problem by optimizing the distribution.The main contents of this paper are as follows:First of all.we discuss the basic classification of the PET reconstruction algorithm,which is mainly contains analytical method and iterative method.The key point of the analytical method is the filtered back projection method,while the iterative reconstruction method mainly has minimum mean square error criterion,maximum likelihood image reconstruction and the maximum posterior probability method.Secondly,introduce the knowledge of classic ADMM optimization algorithm,and in the basis of the Augmented Lagrange algorithm,decomposing the original problem,the image reconstruction with noise,into sub-problems for local optimization solution.Thirdly,for the PET reconstruction problem with noise,using iterative method mainly,through applied the ADMM algorithm to the weighted least squares.Expectation Maximization algorithm,Conjugate Gradient algorithm,Land Weber algorithm.The article performs iterative update step by step respectively,to reconstruct these iterative algorithm,thereby establishing the objective function.Finally,in the light of the ADMM improved algorithm proposed in the paper,using the maximum mean absolute error(MAE),the cost function and the relative difference of pixel between the reconstructed image and the original image as standards,analyzed the performance of image reconstruction,tested and produced the most appropriate penalty parameter values.