An iterative numerical method for inverse scattering problems

In this paper an inverse scattering method for reconstructing the constitutive 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 distribution of the inverse of the relative complex permittivity is estimated, iteratively, by minimizing an error function. This minimization procedure is based on a nonlinear conjugate gradient optimization technique. The error function is related to the difference between the measured and estimated scattered magnetic field data. Moreover, an additional term, which is associated with the Tikhonov regularization theory, is introduced to the error function in order to cope with the ill-posedness of the inverse problem. For an estimate of the scatterer profile the direct scattering problem is solved 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 analysis scheme. The latter is enhanced by introducing the adjoint state vector methodology. This approach reduces dramatically the computational burden. The capabilities of the proposed method are investigated by applying it to synthetic field measurements, which are affected by additive noise. Different levers of the regularization are also examined.