On the local minima problem in conductivity imaging via a quadratic approach

The nonlinear inverse problem of the reconstruction of the electric conductivity of a cylindrical object embedded in a homogeneous space is addressed by approximating the operator that maps the conductivity into the scattered field at the second order. The problem is stated as the minimization of an error functional that can exhibit local minima. The geometrical properties of the quadratic operator are exploited to avoid the presence of local minima. Numerical results validate the theoretical analysis.