Monotonicity based shape reconstruction in electrical impedance tomography
For practitioners of EIT, this provides a simple and direct method for inclusion detection without iterative optimization.
The authors solve the shape reconstruction problem in electrical impedance tomography by using a converse monotonicity relation, enabling detection of conductivity anomalies by comparing measurements to test regions.
Current-voltage measurements in electrical impedance tomography can be partially ordered with respect to definiteness of the associated self-adjoint Neumann-to-Dirichlet operators (NtD). With this ordering, a point-wise larger conductivity leads to smaller current-voltage measurements, and smaller conductivities lead to larger measurements. We present a converse of this simple monotonicity relation and use it to solve the shape reconstruction (aka inclusion detection) problem in EIT. The outer shape of a region where the conductivity differs from a known background conductivity can be found by simply comparing the measurements to that of smaller or larger test regions.