Abstract: A system and a method are provided for estimating the average dielectric properties of a plurality of regions in space. The application of this technique is illustrated for determining the average properties of breast tissue. The knowledge of average properties is important when UWB microwave radar signal processing algorithms are used for tumor detection and localization. The method is an extension of a time-domain inverse scattering algorithm based on the finite-difference time-domain method. A hybrid conjugate gradient optimization is used to minimize a cost function defined between a measured and a calculated total electromagnetic field at a series of antennas. The output of the method is an average set of electromagnetic material parameters that describe specific regions of interest in either a non-dispersive heterogeneous medium or a dispersive heterogeneous medium.