A novel effective model for solving 3D non-linear inverse scattering problems in a homogeneous background

A reformulation of the contrast source-extended Born method, recently introduced with respect to the 2D scalar case, is proposed for the solution of vectorial 3D inverse scattering problems. In particular, a suitable auxiliary function is defined in order to preserve the scalar nature of the unknown of the problem (i.e., the permittivity profile). The developed inversion procedure is based on an iterative conjugate gradient scheme in which ill-posedness of the problem is dealt with through a proper representation of the unknowns in terms of spatial Fourier harmonics. Numerical examples confirm effectiveness of the proposed method, which, in addition, favorably compares with other methods previously known in the literature.