Convex Source Support and Its Application to Electric Impedance Tomography

In this talk we extend the concept of the convex scattering support to the case of electrostatics in a bounded domain. Furthermore, we apply this approach to devise a new reconstruction algorithm in electric impedance tomography. The convex scattering support was developed by Stephen Kusiak and John Sylvester, cf. [3],[4], and is meant to be the smallest convex set that contains a scattering source compatible with some given data of the scattered wave. To transfer this concept to the case of electrostatics, we consider the Poisson equation in a bounded domain D ⊂ R2 with a natural boundary condition, i.e., ∆u = F in D, ∂u ∂ν = 0 on ∂D, ∫