Total size estimation and identification of multiple anomalies in the inverse conductivity problem. (English) Zbl 0972.35188
Summary: We consider the inverse problem of determining multiple anomalies within a homogeneous medium occupied in a region \(\Omega\subset \mathbb R^n\), \(n= 2\) or \(3\) from the measurement of voltage response to an injected current on the boundary \(\partial\Omega\). 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.
MSC:
35R30 | Inverse problems for PDEs |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |