In this dissertation, the inverse technique, which was exploited for the reconstruction of complex permittivity profiles by the moment method, is modified to be applicable in the spectral domain. The merit of this scheme is that contributions from several involved variables such as the basis function, cell geometry, and measurement location are separated explicitly. This separation helps us to diagnose the actual mechanism on the ill-posedness as the evanescent behavior of the spectral domain Green's function for higher spectral frequency than the wavenumber in the surrounding homogeneous medium. Therefore, the ill-posedness may be interpreted as the inaccurate restoration of the induced source distribution from the significantly noise-contaminated data for the higher spectral components of the scattered field. In order to reduce this ill-posed characteristics, two regularization approaches may be proposed intuitively.
One involves discretization of objects, in which each cell size is taken large enough to disregard the contribution of the evanescent components to the reconstructed profiles.
The second approach may be the modification of the inverse form of the spectral domain Green's function by multiplying a low-pass filter. Since regularization is considered a compromise on degradation of it's resolution with improvement of the ill-posedness, selection of a suitable low-pass filter is very sensitive not only to reduction of the noise effect but also to sustenance of the acceptable resolution. In this paper, the low-pass filter is implemented by taking the same form as the absolute value of the exponentially decaying term in the spectral domain Green's function, where the wavenumber in the surrounding medium is changed arbitrary as a control factor. A number of numerical simulations are performed for a simple test geometry, and those results show the validity of the low-pass filter in reducing the noise effect.
