This chapter is devoted to a description of quantitative deterministic reconstruction methods, that is, to procedures aimed at retrieving the values of the electromagnetic parameters of an investigation region by means of deterministic algorithms.
Such approaches attempt to solve the equations describing the scattering phenomena that were introduced in Chapters 2 and 3 by using algorithms not exploiting randomness for determining the problem solution (see Chapter 7 for stochastic approaches).
Quantitative methods are based on “exact” models, which are theoretically valid for any scatterers, even those with high contrast with respect to the background and to a large extent in terms of wavelength. In principle, they are able to inspect strong scatterers since they take into account the nonlinear nature of the inverse scattering problem, without the approximations used by qualitative methods.
As stated previously, the key relationships for a general inverse scattering problem formulation are equations (3.2.1) and (3.2.2) within the EFIE framework, or equations (3.2.3) and (3.2.4) if the contrast source approach is considered. In both cases, the inverse problem becomes nonlinear and involves two sets of unknowns. Namely, if the EFIE formulation is considered, the electric field inside the investigation domain as well as the dielectric properties of the inspected scatterers are unknown. Within the contrast ...