Calderón’s inverse conductivity problem sparked a general interest in inverse coefficient problems (Calderón-type inverse problems). The problem concerns recovering an interior conductivity distribution of a body from boundary electrical measurements; mathematically, it is the reconstruction of a coefficient in a generalized Laplace equation from knowledge of all possible Dirichlet and Neumann boundary values.

I will show how very general inhomogeneities/obstacles in such a coefficient can be constructively characterized from partial boundary measurements. I will also discuss issues that arise when realistic electrode models are used instead.