Using the unrelated illumination method in the reconstruction of three dimensional dielectric bodies

In the last decade several numerical techniques have been developed for solving the inverse electromagnetic scattering problems and microwave imaging of inhomogeneous dielectric bodies. In particular two approaches have been utilized. The first is the microwave diffraction tomography [1]. This approach is based on the generalization of the classical x-ray computed tomography by taking into consideration the diffraction effects. This method can only handle low contrast dielectric bodies. The second approach aims to solve the exact equation of the electromagnetic inverse scattering problem by numerical methods such as the method of moments (MoM) [2]. In the MoM, the problem solution is reduced to the solution of linear system of algebraic equations. Unfortunately the scattering matrix that governs the external scattered field induced by an internal equivalent current is highly ill-conditioned. Thus any attempt to compute its inverse makes the system ill-posed especially in the presence of noise. Several regularization techniques have been used [3], [4] aiming to reduce the effect of the ill-conditioning. These employ priori information either to select a suitable regularization parameter or to enforce convergence in iterative techniques. Moreover, most of these techniques require the presence of a few number of scatterers and employ multiview illumination and some are only applicable to two-dimensional problems.