Inverse Problems and Imaging (IPI)

Localized potentials in electrical impedance tomography

Pages: 251 - 269, Volume 2, Issue 2, May 2008      doi:10.3934/ipi.2008.2.251

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Bastian Gebauer - Institut für Mathematik, Johannes Gutenberg-Universität Maint, 55099 Mainz, Germany (email)

Abstract: In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of a domain and low energy on another. We show that such potentials exist for general $L^\infty_+$-conductivities in almost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability result for the famous Calderón problem with partial data. We also show how to construct such potentials numerically and use a connection with the factorization method to derive a new non-iterative algorithm for the detection of inclusions in electrical impedance tomography.

Keywords:  Electrical impedance tomography, Calderon problem, factorization method.
Mathematics Subject Classification:  35J25, 35R05, 35R30.

Received: January 2008;      Revised: March 2008;      Available Online: April 2008.