A direct impedance tomography algorithm for locating small inhomogeneities

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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