Some Study Of The Numerical Solution Of The Problem Of Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) is a functional imaging technology, whichcan text body's interior tissue properties. It is a new type of image reconstruction tech-nology. EIT has merits of no radiation, security, no damage to the object, it can be usedrepeatedly, simply and low cost. So EIT has important applying prospect in some fields ofbiomedical, geology explore and nondestructive text (NDT). At present, EIT technologyhad caused extensive concern of the domestic and international researchers. In this article,we mainly consider Cauchy mathematical problem in EIT and its numerical algorithms.This article structure is as follows:In the first chapter, we mainly introduce the historical background, the domestic andforeign research present status and development trend of EIT and MREIT, and list severaltypical image reconstruction algorithms of EIT and MREIT.In the second chapter, we sketched introduce the basic knowledge of dealing withill-posed problems regularization methods and the theoretical means of single-layer po-tential and double-layer potential, provide the theory basis for the following chapters andsegments.In the third chapter, firstly, we deduce the mathematical model of EIT by Maxwellequations, secondly, finite element method (FEM) is applied to solve the direct problemof EIT, which is the base of inverse problem of EIT.In the fourth chapter, we firstly introduce the formulation and the mathematicalmodel of EIT inverse problem, then, we propose a numerical algorithm based on thenonlinear integral equations with piecewise constant conductivities.