T-Scan electrical impedance imaging system for anomaly detection

We consider an inverse conductivity problem arising in anomaly detections with its mathematical model based on the T-Scan system ( breast cancer detection system). In this model, we try to detect an anomaly D from one or two sets of measured data that are available only on a small portion Gamma of the boundary of the subject Omega. In practice, Omega differs in each subject, so our detection algorithm should not depend much on the global geometry of Omega. The purpose of this work is to provide a mathematical ground for the reconstruction of a rough feature of D which is stable against any measurement noise and any change of geometry partial derivativeOmega. Based on rigorous estimates with a simplified model, we found an approximation that gives a noniterative detection algorithm of finding a useful feature of anomaly. We also present a multifrequency approach to handling the case where the complex conductivity of the background is not homogeneous and is not known a priori.