Three-Dimensional Scattering and Inverse Scattering from Objects With Simultaneous Permittivity and Permeability Contrasts

There has been increasing efforts in enhanced biomedical and geophysical imaging in the recent years exploring the magnetic contrast agent. The handling of both dielectric and magnetic contrasts adds on difficulties to the forward and inverse scattering problems. In this paper, the 3-D scattering and the inverse scattering from objects having simultaneous electric and magnetic contrasts are presented, where the permittivity, conductivity, and permeability of the objects can all be different from the background. To cope with the challenging high computation cost in the 3-D scattering problem, we formulate the combined field volume integral equations and extend the stabilized biconjugate gradient method and fast Fourier transform (BCGS-FFT) method to compute the electromagnetic field incorporating both the electric and magnetic contrasts. The variational Born iterative method for electrical contrast inversion in axisymmetric media is generalized to 3-D and to the simultaneous reconstruction of objects with electric and magnetic contrasts. The BCGS-FFT method provides the predicted scattered field from the 3-D heterogeneous objects and the Fréchet derivatives in the inverse scattering problem. The efficient forward solver also dramatically reduces the computation time of the inverse problem. Numerical results are presented to validate the forward solver and to demonstrate the effectiveness of the inverse scattering method.