  In this paper, we will discuss the use of a Sampling Method to reconstruct
impenetrable inclusions from Electrostatic Cauchy data. We consider the case of
a perfectly conducting and impedance inclusion. In either case, we show that
the Dirichlet to Neumann mapping can be used to reconstruct impenetrable
sub-regions via a sampling method. We also propose a non-iterative method based
on boundary integral equations to reconstruct the impedance parameter using the
reconstructed boundary of the inclusion from the knowledge of multiple Cauchy
pairs which can be computed from Dirichlet to Neumann mapping. Some numerical
reconstructions are presented in two space dimensions.
