Abstract
The use of the factorization method for electrical impedance tomography has been proved to be very promising for applications in the case where one wants to find inhomogeneous inclusions in a known background. In many situations, the inspected domain is three dimensional and is made of various materials. In this case, the main challenge in applying the factorization method is in computing the Neumann Green's function of the background medium. We explain how we solve this difficulty and demonstrate the capability of the factorization method to locate inclusions in realistic inhomogeneous three dimensional background media from simulated data obtained by solving the so-called complete electrode model. We also perform a numerical study of the stability of the factorization method with respect to various modelling errors.
Highlights
IntroductionWe choose to follow a classical idea presented in [1], and more recently used in [7] in the Electrical impedance tomography (EIT) context in two dimensions, because it can be extended to three dimensional problems and allows to compute Neumann Green’s functions for non constant conductivities
The factorization method and its regularization have been studied by Lechleiter et al in [16] in the context of the so-called complete electrode model which was shown by Isaacson et al in [5] to be close to real-life experimental devices
The main purpose of this paper is to show that the factorization method can be successfully applied to realistic three dimensional Electrical impedance tomography (EIT) inverse problems
Summary
We choose to follow a classical idea presented in [1], and more recently used in [7] in the EIT context in two dimensions, because it can be extended to three dimensional problems and allows to compute Neumann Green’s functions for non constant conductivities. It consists in splitting the Green’s function into a singular part (which is known) plus a regular part and to compute the regular part which is the solution to a well posed boundary value problem with numerical methods such as finite elements or boundary elements.
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