A finite element based technique for microwave imaging of two-dimensional objects

In this paper, a microwave imaging technique for estimating the spatial distributions of the permittivity and the conductivity of a scatterer, by post-processing electromagnetic scattered field data, is presented. The proposed technique is based on the minimization of an error function via the Polak-Ribiere algorithm. For the description of the direct scattering problem, the differential formulation is applied. This allows the use of the finite element method. During the inversion, the computation of the derivative of the finite element solution with respect to the parameters, which describe the scatterer, is required. This task is performed by a finite element based sensitivity analysis scheme, which is enhanced by applying the adjoint state vector methodology. The merits of the proposed technique are examined by applying it to both transverse magnetic and transverse electric polarization cases. Finally, the technique is adopted by a frequency-hopping approach to cope with multifrequency inverse scattering problems.