In recent years, active microwave breast imaging is increasingly being viewed as a promising complementary imaging modality for cancer detection. In this paper, we present a novel deformable reflector microwave tomography technique for noninvasive characterization of the breast tissue. In contrast to conventional multitransceiver designs, the proposed technique utilizes a continuously deformable reflector with metallic coating to acquire field measurements for imaging. Computational feasibility of the proposed technique to image heterogeneous dielectric tissue property is evaluated using simplified 2-D breast models. The robustness of the deformable reflector-based tomography technique in imaging the spatial distribution of the tissue dielectric property in the presence of measurement noise is investigated using first-order Tikhonov regularization. Preliminary results obtained for the 2-D breast models appear promising and indicate further investigation of the new microwave tomography technique for breast imaging.