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Electrical Impedance Tomography(EIT) is a developing technology for medical imaging these years, which is to calculate the changes of conductivity of biomedical tissues. Compared to the current imaging technology, such as X-ray, Computed Tomography, and Magnetic Resonance Imaging, EIT has its own advantages, e.g. functional imaging, low-cost, non-invasion and portability. And these features make it become a hot point for study and discussion in biomedical engineering area.Based on the theory of two-dimensional(2D) EIT, the thesis describes the hardware system, and gives a new model for EIT system. The emphases of the paper is the software realization of EIT. First, through the establishment of 2D model of EIT, the article realizes the dissection of the finite element based on Matlab, derives the Laplace-equation and create the finite element equation of the forward problem of EIT. Second, it studies the image reconstruction algorithms of the inverse problem, derives the iteration process of the modified Newton-Raphson algorithm(MNR), and put forward a new image reconstruction algorithm, Newton-Raphson iteration algorithm based on total variation. Third, it gets the reconstruction image with the modified Newton-Raphson iteration algorithm based on Matlab, discusses the result of reconstruction under the condition of one and two imaging object and the influence that different parameters brings. The result shows that a clearer image could be obtained based on the modified Newton-Raphson iteration algorithm with the modified finite element model, and the regularization parameter and iteration times have a great affect on image resolution. Finally, the reconstruction image is obtained with the experimental data according to the MNR.
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