The Application Of Tikhonov Regularization-homotopy Method Based On Fast Algorithm In EIT

In recent decades,Electrical Impedance Tomography has become a new direction of medical imaging technique.By injecting current into the surface of the electric object and then measuring the voltage value on the surface on the conducting object,it uses image reconstruction algorithm to image the electrical impedance distribution or changes in the object.According to the different imaging targets,EIT imaging methods include dynamic imaging methods and static imaging methods.The imaging target of static imaging methods is the absolute value of electrical impedance,so it can reflect the specific distribution of electrical impedance.Static imaging has always been the focus of EIT research.Nonlinear least square method is a clas-sical method in EIT static imaging methods,and the Tikhonov regularization method is the most typical regularization method.The main research contents of this paper include:In the first chapter,the electrical impedance tomography imaging technol-ogy is introduced,including its definition,method classification,the domestic and foreign research status and its advantages and technical difficulties.The second chapter discusses the positive problem of EIT.Firstly,the theoretical basis of EIT is given.On the basis,the mathematical model of the positive problem of EIT is further derived.Finally,the positive problem of EIT is solved by finite element method.The third chapter explores the inverse problem of EIT.The contents of this chapter are divided into three parts,and the latter two are the core of this paper.Firstly,the evaluation index of imaging inversion algorithm is giv-en.Secondly,using the homotopy method to further improve the Tikhonov reg-ularization method,so the Tikhonov regularization-homotopy method is pro-posed,and then the iterative formula is derived.Finally,a fast 4-th order con-vergence algorithm is adopted to obtain the regularization parameters by solv-ing the Morozov discrepancy equation,which further improves the convergence speed of the regularization parameters.