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Recovering multiple small inclusions in a three-dimensional domain using a single measurement

We present and test an effective algorithm to recover multiple small heterogeneities inside arbitrary three-dimensional bounded regions. In applications of electrical impedance tomography, such heterogeneities might represent tumours inside the body, weaknesses or cracks in a solid material or subterranean mineral deposits. The algorithm determines the location of all heterogeneities using a single boundary measurement. The only non-linear step in the algorithm is to find roots of a single polynomial of degree . The efficacy of this method is demonstrated by full numerical computation of the three-dimensional forward problem. In addition, the methods employed can give information regarding the shape of irregular heterogeneities.