Research Of Mixture Regularization Methods For EIT Inverse Problem

Through analysis and processing of ground data, electrical impedance tomography can objectively reflect some basic characteristics of the geological body, and provide effective foundation for solving practical problems. The main principle of resistivity imaging is that:according to different internal structures in the measured area and different conductivity, the injected current signal and data obtained through measuring the different directions are used to reconstruct the resistivity distribution image within the region.Firstly, this paper reviews the domestic and international development of electrical impedance tomography problem, and establishes the basic direct current electric field equation for electrical impedance tomography problem and boundary equation that the problem must satisfy. Then, the finite element subdivision of the EIT forward problem is developed. Furthermore, for the inverse problem of electrical impedance tomography, Tikhonov regularization method, variation regularization method and mixture of regularization method that is a linear combination of Tikhonov regularization method and variation regularization method are respectively used for solving. With regard to electrical impedance imaging model, numerical examples are carried out, and the results of these three kinds of regular methods are compared for analysis. The results reveal that when using Tikhonov regularization, though objective functions can achieve convergence in iterative process, the boundaries between target area and background area are fuzzy and imaging effects are not so good. Variation regularization method can effectively improve over-smooth of boundary values, but its solution is unstable. Compared with Tikhonov regularization method, constructed image obtained through variation regularization method has a steeper resistivity distribution in the targeting area, and a more obvious difference with background area. Mixture of regularization method retains the convergence property of Tikhonov regularization method, and high accurate reconstruction of variation regularization method, and finally, it can obtain a high contrast and sharpness of reconstructed image so that obtain more ideal reconstruction results.