101201 517Implementation of the Newton （101201 517牛顿的实现）.pdfVIP

International Journal of Bioelectromagnetism Vol. 12, No. 1, pp. 12 -20, 2010 Implementation of the Newton-Raphson and Admittance Methods for EIT D. Romano, S. Pisa, E. Piuzzi Dept. of Electronic Engineering, Sapienza University of Rome, Italy Correspondence: D. Romano, Dept. of Electronic Engineering, Via Eudossiana, 18, 00184 Rome, Italy. E-mail: romano@die.uniroma1.it, phone +39 06 fax +39 06 4742647 Abstract. Electrical Impedance Tomography (EIT) is an imaging technique which aims to the reconstruction of the spatial electrical conductivity distribution of a section of the human body. In this paper, in order to solve the EIT forward and inverse problems, a finite difference approach to the solution of Maxwell’s equations, namely the admittance method, and the Newton-Raphson algorithm have been employed, respectively. The Jacobian matrix involved in the Newton-Raphson (NR) algorithm has been computed by using both the admittance matrix of the forward problem and the so- called sensitivity matrix. The reconstruction problem has been solved using the standard Tikhonov regularization with various choices of the regularization matrix. The obtained results, for three thorax models of increasing complexity, approximating a section of the human chest, show that the lowest reconstruction errors are usually obtained by choosing as regularization matrix a discrete form of the Laplacian operator. Keywords: EIT; forward problem; inverse problem; admittance method; Newton-Raphson algorithm; sensitivity matrix; regularization techniques. 1. Introduction Electrical impedance to