Microwave Imaging: Inversion of Scattered Near-Field Measurements

In this paper, the problem of reconstructing the electromagnetic properties of unknown scatterers is treated by means of a spatial-domain technique. This technique combines the finite-element method and the Polak–Ribière nonlinear conjugate gradient optimization algorithm. The forward scattering problem is solved via the finite-element method, while the inversion is implemented by minimizing a cost function. This function consists of a standard error term and a regularization term. The first one is related to the scattered near-field measurements, which are obtained by illuminating the scatterer with plane waves from various directions of incidence. The regularization term is introduced in order to cope with the ill-posedness of the inversion. A sensitivity analysis, which is performed by an elaborate finite-element procedure, provides the direction required for updating the estimate of the scatterer profile. Significant reduction of the computation time is obtained by applying the adjoint-state-vector methodology.