Research On The Model And Algorithm In Three-dimensional Electrical Impedance Tomography

Electrical impedance tomography (EIT) is a novel noninvasive imaging techniquewhich obtains the electrical properties of biological tissue via a series of electrodesplaced on its surface. Typically, some safe excitations (current or voltage) are injectedinto the body through the electrodes. As a functional imaging modality, it is low-costand non-invasion，as well as it’s helpful for the early detection and prediction ofabnormalities. Thus, EIT becomes one of the significant research projects inbiomedicine engineering. So far, there are several challenges to deal with thereconstruction problem of EIT.①building a properly model. The current diffuses in thethree-dimensioned space, so it is necessary to model a reasonable3-D model;②starveof information.The amount of information is limited by the number of electrodes;③huge computational cost. Computation exponentially increases with the number of finiteelement mesh;④poorly conditioned. Minor changes in the boundary voltage bring out agreat influence on the reconstructed images. In order to get around the problems, a3Dmodel is established. Based on this model, the parameters in Tikhonov regularizationand NOSER are been optimized to improve the ill-posed property of the inverseproblem. In addition, the preconditioning iteration technique is also analysed toovercome the problem of huge computation.The main contents of the dissertation are as follows:①Based on the mathematical model of EIT in the electromagnetic problem，thehemispherical model has been established, whose surface is encircled uniformly byfour layers of electrodes. Obviously, this constitution can make the current distributeequally. At the same time, it can improve the exploration depth, widen the range ofmeasurement and increase the information of the imaging region.②The traditional Tikhonov regularization algorithm is introduced first.Then anovel approach, which is based on the product of the residual norm and the solutionnorm(PRS), is presented to optimize the regularization parameter. In theory, thismethod can reduce the condition number of Jacobian matrix and improve the accuracyof the reconstructed images.③The principle of Newton’s One-Step Error Reconstructor(NOSER) isdemonstrated to study the inverse problem of EIT. Secondly，the U-curve method isapplied to reconstruct images. And then the NOSER regularization parameter is chosen by the modified U-curve method. This method can improve the ill-posed property ofthe inverse problem through the derivation.④Due to huge computation and large iterations in the image reconstruction of3DEIT, the principle of conjugate gradient method and preconditioning have beenintroduced briefly. The equation has been preconditioned simply by the Jacobianmatrix.In addition, some threshold have been set to enhance the sparsity of thecoefficient matrix.⑤Some simulations and the corresponding agar experiments have been carriedout. Based on the reconstructed3D images, several evaluation indices are given toestimate the image quality. The results of the indicators verify the feasibility andeffectiveness of the proposed methods.At last, this paper summarizes the major work and research achievements, aswell as the existing problems at present. Meanwhile, some improvements and thefurther researches on this topic have been proposed.