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 Γ of the boundary of the subject Ω. In practice, Ω differs in each subject, so our detection algorithm should not depend much on the global geometry of Ω. 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 ∂Ω. 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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics