Recovering an obstacle and its impedance from Cauchy data
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We consider the inverse problem of recovering the shape, location and surface properties of an object where the surrounding medium is both conductive and homogeneous. It is assumed that the physical situation is modeled by harmonic functions u and the boundary condition on the obstacle is one of impedance type. We measure {u,u/u that is, Cauchy data, on an accessible part of the exterior boundary. Given sets of Cauchy data pairs we wish to recover both the shape and location of the unknown obstacle together with its impedance. We give a local injectivity result and use two different algorithms to investigate numerical reconstructions. The setting is in 2 , but indications of possible extensions (and difficulties) to 3 are provided. 2008 IOP Publishing Ltd.
