Research On Electrical Impedance Endotomography Inverse Problem Based On Total Variation Regularization

Electrical impedance endotomography(EIE) is a new developing technology on the basis of the electrical impedance tomography(EIT) which is a functional imaging technology. In EIE, the impedance measuring electrodes placed at the centre of the catheters are inserted directly into the organs, the safe currents are injected and the potentials on the surface of interest are measured with the electrodes. Based on the inverse problem solving algorithm, the electrical impedance distribution of the organ is reconstructed.In this thesis, the current research of EIE is reviewed and the principle of EIE imaging is summarized firstly. And the calculation principle of EIE imaging is also overviewed. Then the boundary element method(BEM) for EIE forward problem is studied. The BEM for multilayer homogeneous mediums is deduced. The concentric circles model of BEM is established, and the forward problem is calculated which lays a foundation for the inverse problem solution. Finally, Newton-Raphson method based on total variation(TV) regularization is studied to solve the inverse problem. Concretely, single step conductivity reconstruction is used to make the initial estimate. On the basis of appropriate initial estimate, the convergence is guaranteed to a certain extent, and the convergence speed is also improved. Furthermore, the parameterized theory is employed, and the conductivity reconstruction problem is turned to objective boundary reconstruction problem. Total variation regularization method is introduced to overcome the ill-posedness of the inverse problem, and the parametric reconstruction of two-dimensional model is completed. The results show that the reconstructed images are accordant with the initial target images, which achieve the purpose of lesion localization.