Convex source support and its application to electric impedance tomography. (English) Zbl 1179.35345
Summary: The aim in electric impedance tomography is to recover the conductivity inside a physical body from boundary measurements of current and voltage. In many situations of practical importance, the investigated object has known background conductivity but is contaminated by inhomogeneities. In this work, we try to extract all possible information about the support of such inclusions inside a two-dimensional object from only one pair of measurements of impedance tomography. Our noniterative and computationally cheap method is based on the concept of the convex source support, which stems from earlier works of Kusiak, Sylvester, and the authors. The functionality of our algorithm is demonstrated by various numerical experiments.
MSC:
35R30 | Inverse problems for PDEs |
65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
78A48 | Composite media; random media in optics and electromagnetic theory |