Coupled Boundary Element Method and Level Set Function for Solving Inverse Problem in EIT

T. Rymarczyka, J. Sikorab,c, B. Waleskac

aNet-art, Lotnicza 3, Lublin 20-322, Poland

bFaculty of Electrical Engineering and Computer Science, Department of Electronics, LublinUniversity of Technology, Nadbystrzycka 38A,20-618 Lublin, Poland

cElectrotechnical Institute, ul. Po?aryskiego 28, 04-703 Warszawa, Poland

Abstract

The solution for the inverse problem of the identification unknown internal object?s boundary by Electrical Impedance Tomography (EIT) is presented in this paper. Proposed mathematical model is based on the Level Set Method (LSM) and the Boundary Element Method (BEM). The main advantage of BEM and LSM is the fact that both methods are the boundary one. What is more the BEM provide as a primary solution not only the state function but also its normal derivative used together with adjoint variable for boundary (interface) velocity calculation. Experimental results have demonstrated the efficiency of the proposed approach to achieve the solution of the inverse problem.

Keywords: Boundary Element Method; Set Level Methods; Electrical Impedance Tomography; Inverse Problem