MUSIC Imaging and Electromagnetic Inverse Scattering of Multiple-Scattering Small Anisotropic Spheres

The Foldy-Lax equation is used to derive a multiple scattering model for the multiple-scattering small anisotropic spheres. By this model, if the number of the non-zero singular values of the multistatic response (MSR) matrix is smaller than the number of the antennas, the range space of the MSR matrix is found to be spanned by the background Green's function vectors corresponding to the $x, y$ and $z$ components of the electric and magnetic dipoles induced in each scatterer, which indicates that the multiple signal classification (MUSIC) method could be implemented to obtain the locations of the scatterers. After estimating the positions of the scatterers, a non-iterative analytical method is proposed for retrieving the polarization strength tensors as well as the orientations of the principle axes of each scatterer. Two numerical simulations show that, the MUSIC method and the non-iterative method are efficacious for the nonlinear inverse scattering problem of determining the locations and polarization strength tensors of multiple-scattering small anisotropic spheres. Such methods could also be applied to the inversion of small isotropic spheres or extended to the inversion of small bianisotropic spheres.