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Active microwave imaging has attracted significant interests in biomedical applications, in particular for breast imaging. However, the high electrical contrasts in breast tissue also increases the difficulty of forming an accurate image because of the increased multiple scattering. To model such strong three-dimensional (3-D) multiple scattering effects in biomedical imaging applications, we develop a full 3-D inverse scattering algorithm based on the combination of the contrast source inversion and the fast Fourier transform algorithm. Numerical results show that our algorithm can accurately invert for the high-contrast media in breast tissue.