| Electrical Impedance Tomography (EIT) is a new type of medical imaging technique. In EIT an array of electrodes is attached around the object and small alternating currents are injected via these electrodes and resulting voltages are measured. Using different current injections and voltage measurements, an approximation for the spatial distribution of impedance (or conductivity) within the object can be reconstructed. The principal potential applications of EIT lie in biomedical imaging, whose biological basis is to acquire the information of physiology and pathology, via injecting electrical current on the periphery of cross section of a human body. The impedance of biological tissue represents some information from function or disease of organs. Depending on the electrical impedance property of tissue, EIT can provide a kind of non-invasive tomography.The advantages are that the technique is inexpensive, portable, and safe. It has the potential for widespread use in medicine for continuous monitoring at the bedside, in the intensive care unit, or in remote medical facilities. In medicine, its accuracy has been demonstrated in imaging lung, heart, stomach and brain hematoma. Moreover,the technique can be used not only in imaging anatomical structures , but also in imaging functional structures. This is most helpful for preventing and diagnosing disease, prior to disease happened. Theoretically EIT is an inverse problem of low frequency electric current field calculation, whose core is reconstruction algorithm. The reconstruction algorithm of EIT is not perfect so far, because it is very difficult in mathematics. As an Inverse Problem of Mathematical Physics, how to solve it involves Partial Differential Equations, Finite Element Method, Numerical Analysis, Matrix Theory, Nonlinear Equations, Error Analysis, Ill-posed Problem, etc.At first, this thesis expatiates on the inverse problem of mathematic physics in details, which is involved by EIT, and points out that, as a representation, all kinds of difficulties focus on ill-posed problem. Withal this thesis gives the quantitative data to measure the degree of ill-posed problem, which demonstrates the problem ofEIT is ill posed badly.Secondly, in this thesis new approaches of EIT image reconstruction are proposed. Four novel methods are developed. The first one, Quasi-Newton method, considers the effect from all of parameters in the cross section of an object. Thus, the ill-posed nature and the precision of solution are all improved, due to the greater sensitivity between boundary potentials and interior conductivities. The second proposed method is extrapolation method, which makes it possible to improve the reconstruction computing velocity. Even though the Quasi-Newton method is a powerful method to solve nonlinear equations, it suffers from a high computational cost while employing fine mesh systems. Extrapolation method can reduce the computing load, besides improving calculating precision. The third method is Continuation method, which is proposed in Electrical Impedance Tomography. Since there is a great difference in physiological parameters between different objects, between varieties of ill cases, and different tissues, it is important to loosen the limits of initial values of reconstruction algorithm. Simulating calculation results are given to validate the approach. The last one is Local Area Accelerating Convergence (LAAC) method, which is based on prior known information of the conductivity distribution. LAAC dramatically reduces the accumulated calculation error into a small number, and also improves computation speed greatly.Thirdly, the technique is applied to real-time monitoring for brain hematoma. Due to the special demands for these cases, such as non-moving, fast variety of states of illness, etc, real-time monitoring is necessary. In this thesis simulation research describes the whole process of dynamic variety of brain hematoma case with EIT. A series of reconstruction images show that it is successful to apply EIT...
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