Regularization Algorithm Research Of Static Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) is a new type of medical imaging technique. In EIT, an array of electrodes attached around an object, small alternating currents injected via these electrodes, and resulting voltages are measured. With those measurements, an approximation of the spatial impedance (or conductivity) distribution of the object been reconstructed. The advantage of EIT is non-invasive, inexpensive, portable, secure and so on. It has the potential to widespread in medicine. This technique can be used as display not only the anatomical structures, but also the function structures. This is most helpful for preventing and diagnosing disease, prior to disease happed.In this thesis, on the base of expatiating on fundamental theory of biomedicine, discussed the research status quo of EIT, the regularization algorithm of EIT is focused on. First, the electrode model of EIT in the forward problem is dealed with complete electrode model, which considered the size and the contact resistance of real electrode. Then, an attention put to both sides of speed and precision of EIT problem, and a dense and sparse FEM model is proposed. Secondly, two new regularization algorithms been proposed to research the inverse problem of EIT. The first one is variation regularization algorithm, which imported a variation function as regularization penalty team to improve the contrast of restored image. The second one is mixed regularization algorithm, which imported both variation function and Tikhonov function as the regularization penalty teams, to improve both sides of contrast and precision of restored image. Moreover, a fast algorithm of Jacobi matrix, based on differential principle, is been proposed to improve computational speed and precision of the matrix, which is significative to utilize EIT technique. Further, the mixed regularization algorithm is used to some applications research, especially, the reconstructed of brain hematoma and human breast cases. The comparison with Tikhonov algorithm shows the new algorithm has powerful reconstruction capability and more medical treatment worth. Finally, noise affection for mixed regularization algorithm is studied, and an acceptable noise level be proposed for the algorithm, which is useful to the data collection in EIT, and some laboratory experiments made to validate the mixed regularization algorithm. The result validates the veracity and validity of the proposed algorithm.