An iterative numerical method for inverse scattering problems

In this paper an inverse scattering method for reconstructing the constitut ive parameters of two-dimensional scatterers is proposed. The inversion is based on measurements of the scattered magnetic field component, while the scatterer domain is illuminated by transverse electric waves. The spatial d istribution of the inverse of the relative complex permittivity is estimate d, iteratively, by minimizing an error function. This minimization procedur e is based on a nonlinear conjugate gradient optimization technique. The er ror function is related to the difference between the measured and estimate d scattered magnetic field data. Moreover, an additional term, which is ass ociated with the Tikhonov regularization theory, is introduced to the error function in order to cope with the ill-posedness of the inverse problem. F or an estimate of the scatterer profile the direct scattering problem is so lved by means of the finite element method. On the other hand, the gradient of the error function is computed by a finite element based sensitivity an alysis scheme. The latter is enhanced by introducing the adjoint state vect or methodology. This approach reduces dramatically the computational burden . The capabilities of the proposed method are investigated by applying it t o synthetic field measurements, which are affected by additive noise. Diffe rent levers of the regularization are also examined.