Numerische Mathematik

, Volume 93, Issue 4, pp 635–654

A direct impedance tomography algorithm for locating small inhomogeneities

  • Martin Brühl
  • Martin Hanke
  • Michael S. Vogelius

DOI: 10.1007/s002110200409

Cite this article as:
Brühl, M., Hanke, M. & Vogelius, M. Numer. Math. (2003) 93: 635. doi:10.1007/s002110200409

Summary.

 Impedance tomography seeks to recover the electrical conductivity distribution inside a body from measurements of current flows and voltages on its surface. In its most general form impedance tomography is quite ill-posed, but when additional a-priori information is admitted the situation changes dramatically. In this paper we consider the case where the goal is to find a number of small objects (inhomogeneities) inside an otherwise known conductor. Taking advantage of the smallness of the inhomogeneities, we can use asymptotic analysis to design a direct (i.e., non-iterative) reconstruction algorithm for the determination of their locations. The viability of this direct approach is documented by numerical examples.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Martin Brühl
    • 1
  • Martin Hanke
    • 1
  • Michael S. Vogelius
    • 2
  1. 1.Fachbereich Mathematik, Johannes Gutenberg-Universität Mainz, 55099 Mainz,Germany; e-mail: bruehl,hanke@math.uni-mainz.deDE
  2. 2.Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA; e-mail: vogelius@math.rutgers.eduUS