Inverse scattering using the finite-element method and a nonlinear optimization technique

A new spatial-domain technique for the reconstruction of the complex permit tivity profile of unknown scatterers is proposed in this paper. The techniq ue is based on a combination of the finite-element method (FEM) and the Pol ak-Ribiere nonlinear conjugate gradient optimization algorithm. The direct scattering problem is explicitly dealt with by means of the differential fo rmulation and it is solved by applying the FEM. The inversion methodology i s oriented to minimizing a cost function, which consists of a standard erro r term and regularization term. A sensitivity analysis, which is carried ou t by an elaborate finite-element procedure, results in the determination of the direction required for correcting the profile. Significant reduction o f the computation time its obtained by introducing the adjoint state vector methodology, The efficiency of the presented inversion technique is valida ted by applying it to the inversion of synthetic scattered far-field measur ements, which are corrupted by additive noise.