Electrical impedance tomography, enclosure method \\and machine learning

Electrical impedance tomography (EIT) is a non-destructive imaging method, where a physical body is probed with electric measurements at the boundary, and information about the internal conductivity is extracted from the data. The {\it enclosure method} of Ikehata [J. Inv. Ill-Posed Prob. 8(2000)] recovers the convex hull of an inclusion of unknown conductivity embedded in known background conductivity. Practical implementations of the enclosure method are based on least-squares (LS) fitting of lines to noise-robust values of the so-called {\it indicator function}. It is shown how a convolutional neural network instead of LS fitting improves the accuracy of the enclosure method significantly while retaining interpretability.