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Microwave imaging is a feasible tool for medical imaging owing to the different electric properties of tissues. To this end, it is important to devise inversion procedures capable of achieving a reliable quantitative estimate of the tissues under test. With respect to breast screening, we propose a full-wave inversion method, which takes advantage of the adaptive multiresolution features of the wavelet basis to accommodate the trade off between spatial resolution and inversion stability. As shown through a preliminary numerical assessment on 2D anthropomorphic breast phantoms, the proposed approach is capable of achieving satisfying results without any a priori knowledge of breast shape, as well as of thickness and electric properties of the skin layer.