An innovative methodology is proposed to solve quantitative three-dimensional microwave imaging problems formulated within the contrast source framework. The introduced technique is based on the combination of an efficient iterative multiscaling strategy aimed at mitigating local minimum issue arising in inverse scattering problems, and a local search algorithm based on the subspace-based optimization method (SOM) devoted to effectively retrieving both the "deterministic" and the "ambiguous" parts of the unknown contrast currents. To achieve this goal, a nested iteration process is adopted in which the outer loop iteratively refines the region of interest (ROI) where the scatterers are detected, while the inner loop retrieves the dielectric properties of the scatterers within the ROIs. Selected numerical examples are also given to show the validity and robustness of the proposed algorithm in comparison with state-of-the-art techniques.