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 (EIT), 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 K heterogeneities using a single boundary measurement. The only nonlinear step in the algorithm is to find K roots of a single polynomial of degree K. 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.