A Novel Excitation Pattern And Image Reconstruction Algorithms For Electrical Impedance Tomography

Electrical impedance tomography (EIT) is a technique for reconstructing conductivity distribution of an inhomogeneous medium, usually by injecting a current at the periphery of an object and measuring the resulting changes in voltage. Mathematically, the EIT reconstruction problem is a non-linear and ill-posed inverse problem, the solution of which necessitates the use of regularization methods.In this thesis, two new approaches of EIT image reconstruction and a novel excitation pattern are proposed, all of which aim at meeting the main challenges of EIT techniques. The first one, adaptive multigrid method, adopts the adaptive mesh refinement and multigrid method into both the forward and inverse problem. In the forward problem, the potential distribution of the sensitive field can be obtained with improved accuracy and efficiency by adaptive multigrid method. Adaptive mesh refinement used in the inverse problem can improve the spatial resolution of reconstructed images.The second proposed image reconstruction algorithm is the Schur conjugate gradient (Schur CG), a variant of conjugate gradient (CG) method. It is based on the principle that the solution space is divided into two subspaces and the main part of solution lies in the coarse subspace, which can be calculated directly and its corresponding correction term with a small norm can be solved in the Schur complement subspace. Compared with conventional CG method and preconditioned CG method, the Schur CG has even higher convergence rate and additionally it can reconstruct images more accurately.The proposed excitation pattern is based on Walsh function which can be used as the applied currents for EIT system. In the implementation, Walsh currents are applied to the object and the resulting voltages are collected. Then the voltage responses to the optimal current pattern can be synthesized by the linear combination of the voltage responses to Walsh currents. Through the use of Walsh function as the injected currents, the same signal to noise ratio (SNR) as the optimal current pattern can be realized only with simplified hardware configuration. At the end of thesis, the exciting results of monitoring human lung ventilation, achieved in our biomedical EIT group, are described. Both the visualization results and characteristic curves, which reflect the lung respiration, are given.