 
Summary: AN ACCURATE FORMULA FOR THE RECONSTRUCTION OF CONDUCTIVITY
INHOMOGENEITIES
HABIB AMMARI x AND JIN KEUN SEOz
Abstract. We carefully derive accurate asymptotic expansions of the steadystate voltage potentials
in the presence of a nite number of diametrically small inhomogeneities with conductivities dierent
from the background conductivity. We then apply these accurate asymptotic formulae for the purpose of
identifying the location and certain properties of the shape of the conductivity anomaly. Our designed
realtime algorithm makes use of constant current sources. It is based on the observation in both the
near and far eld of the pattern of a simple weighted combination of the input currents and the output
voltages. The mathematical analysis provided in this paper indicates that our algorithm is with a very
high resolution and accuracy.
1. Introduction
Electrical Impedance Tomography (EIT) is designed to produce images of conductivity distribution
of conducting objects by means of several currentvoltage relations captured on its surface: the current
voltage pairs are usually obtained by applying currents through electrodes attached on the surface and
measuring the resultant voltage potentials. Due to several merits of EIT such as safe, low cost, real time
monitoring, EIT has received considerable attention for the last two decades. However, insensitivity of
boundary measurements to any change of innerbody conductivity values has hampered EIT for providing
accurate static conductivity images. In practice the capturing data, currentvoltage pairs, must be limited
by the number of electrodes attached on the surface of the body, which conne the resolution of the image.
