A quadratic approach for the reconstruction of conductivity profiles using eddy currents

This paper proposes a new method for the reconstruction of conductivity profiles in the low frequency limit. The method is based on second order expansion of the operator that maps the unknown conductivity profile into the scattered electric field. The solution of the inverse problem corresponds to the global minimum of an error functional whose geometric properties are highlighted leading to an effective minimisation algorithm. Some simple numerical examples are reported showing the main features of the proposed approach