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AN ACCURATE FORMULA FOR THE RECONSTRUCTION OF CONDUCTIVITY INHOMOGENEITIES
 

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 steady-state voltage potentials
in the presence of a nite number of diametrically small inhomogeneities with conductivities di erent
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
real-time 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 current-voltage 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 inner-body conductivity values has hampered EIT for providing
accurate static conductivity images. In practice the capturing data, current-voltage pairs, must be limited
by the number of electrodes attached on the surface of the body, which con ne the resolution of the image.

  

Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique

 

Collections: Mathematics