We introduce an output least-squares method for impedance tomography p
roblems that have regions of high conductivity surrounded by regions o
f lower conductivity. The high conductivity is modelled on network app
roximation results from an asymptotic analysis and its recovery is bas
ed on this model. The smoothly varying part of the conductivity is rec
overed by a linearization process as is usual. We present the results
of several numerical experiments that illustrate the performance of th
e method.