I. Introduction
Microwave tomography (MWT) is a modality that has shown potential in various biomedical imaging applications such as breast cancer detection and monitoring [1], as well as in extremity imaging [2]. Several challenges confront the quantitative inverse scattering algorithms associated with the fully nonlinear biomedical imaging problem. One of the biggest challenges is that most biomedical objects of interest (OIs) are highly inhomogeneous with respect to the complex relative permittivity profile that is to be reconstructed. The range of permittivity values corresponding to human tissues is large, and sometimes two tissues of interest differ by only a few percent [3]. Adjacent tissues of widely differing permittivity may also shadow each other with respect to the interrogating microwave energy. This is the case, for example, when an adipose layer surrounds muscle tissue, each having a complex relative permittivity of and , respectively, at 1 GHz. Add to the possible shadowing effects the large amount of multiple scattering inherent in such highly inhomogeneous regions, and it becomes clear why the nonlinear inverse scattering problem is so difficult to solve.