The possibility of reconstructing the distribution of the dielectric characteristics of unknown inhomogeneous dielectric objects contained inside a fixed investigation volumeV, where the scatterers can be placed at arbitrary positions is considered. It is assumed that the localisation of the scatterers and the determination of their surface shapes can be accomplished through the reconstruction of the equivalent current density, following a previously proposed approach. The method is based on an inverse-scattering formulation, and makes use of the moment method, together with a pseudoinversion algorithm, to face the problems associated with ill-conditioning. The approach does not require any plane-wave illumination or first-order approximations. It can potentially be used even in the case of strong scatterers. The advantages of using suitable thresholds for the reconstruction of the equivalent current density is considered. The capabilities and limitations of the approach have been assessed by means of numerical computer simulations, for which even data strongly affected by Gaussian noise have been used.