Microwave imaging (MWI) is an emerging tool for medical diagnostics, potentially offering unique advantages such as the capability of providing quantitative images of the inspected tissues. This involves, however, solving a challenging nonlinear and ill-posed electromagnetic inverse scattering problem. This paper presents a robust method for quantitative MWI in medical applications where very little, if any, a priori information on the imaging scenario is available. This is accomplished by employing a distorted Born iterative method and a regularization by projection technique, which reconstructs the tissue parameters using a wavelet basis expansion to represent the unknown contrast. This approach is suited for any microwave medical imaging application where the requirement for increased resolution dictates the use of higher frequency data and, consequently, a robust regularization strategy. To demonstrate the robustness of the proposed approach, this paper presents reconstructions of highly heterogeneous anatomically realistic numerical breast phantoms in a canonical 2-D configuration.