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.
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Received May 28, 2001 / Revised version received March 15, 2002 / Published online July 18, 2002
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ID="⋆" Supported by the Deutsche Forschungsgemeinschaft (DFG) under grant HA 2121/2-3
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ID="⋆⋆" Supported by the National Science Foundation under grant DMS-0072556
Mathematics Subject Classification (2000): 65N21, 35R30, 35C20
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Brühl, M., Hanke, M. & Vogelius, M. A direct impedance tomography algorithm for locating small inhomogeneities. Numer. Math. 93, 635–654 (2003). https://doi.org/10.1007/s002110200409
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DOI: https://doi.org/10.1007/s002110200409