A NONLINEAR ESTIMATION METHOD IN TOMOGRAPHIC IMAGING

A nonlinear estimation approach to solving the inverse scattering prob lem, and reconstructing the space-varying complex permittivity of unkn own objects is considered. The bilinear operator equations governing t he scattering are approximated into finite dimensional spaces on the b asis of the finite degrees of freedom of data, and on the simple conce pt that one cannot expect to reconstruct an arbitrary function from a finite number of independent equations. As a consequence, a discrete m odel, well suited to numerical inversion, is developed, The particular bilinear nature of the equations, and a suitable choice of contrast a nd field unknowns allows the functional adopted in the estimation to b e minimized in an accurate and numerically efficient manner, Numerical experiments show how the method is capable, when a proper number of s earched unknowns is adopted, to manage the possible convergence to loc al minima (which is a typical question in nonlinear inverse problems), and validate the effectiveness of the proposed approach.