Total size estimation and identification of multiple anomalies in the inverse conductivity problem

We consider the inverse problem of determining multiple anomalies within a homogeneous medium occupied in a region Ω⊂Rⁿ, n = 2 or 3 from the measurement of voltage response to an injected current on the boundary ∂Ω. We propose a new method of finding the total size of multiple anomalies from the boundary measurement. This algorithm works within a real time and gives a quite precise total size of the anomalies. Next, we present asymptotic formulae which are useful to develop a reconstruction algorithm. Numerical experiments based on the size estimation and asymptotic formulae indicate its efficiency.