Estimation of inhomogeneous permittivity profiles of spherical objects from noisy scattering measurement data

An accurate method for reconstructing inhomogeneous permittivity profiles of spherically shaped objects from the measurement of noisy scattering data is presented. The overall reconstruction is achieved in two basic steps. In the first step, the direct problem is formulated to obtain a nonlinear differential equation involving a frequency dependent reflection coefficient in a spherical coordinate system. The second step involves the inversion of this nonlinear differential equation using our previously proposed renormalization technique to obtain the unknown permittivity profile of spherically shaped objects in terms of a spherical Fourier-Bessel transform of the measured reflection coefficient data. Several higher order TE- and TM-mode illuminations with different noise levels have been considered. A good agreement between the actual and the reconstructed profiles even under high noise conditions shows the validity of our proposed scheme.