<p>In this thesis, a 3D microwave imaging method is developed for a microwave imaging system with an arbitrary background medium. In the previous study on the breast cancer detection of our research group, a full wave inverse method, the Diagonal Tensor approximation combined with Born Iterative Method (DTA-BIM), was proposed to reconstruct the electrical profile of the inversion domain in a homogenous background medium and a layered background medium. In order to evaluate the performance of the DTA-BIM method in a realistic microwave imaging system, an experimental prototype of an active 3D microwave imaging system with movable antennas is constructed. For the objects immersed in a homogenous background medium or a layered background medium, the inversion results based on the experimental data show that the resolution of the DTA-BIM method can reach finely to a quarter of wavelength of the background medium, and the system's signal-noise-ratio (SNR) requirement is 10 dB. Moreover, the defects of this system make it difficult to be implemented in a realistic application. Thus, another active 3D microwave imaging system is proposed to overcome the problems in the previous system. The new system employs a fix patch antenna array with electric switch to record the data. However, the antenna array makes the inversion system become a non-canonical inhomogeneous background. The analytical Greens' functions used in the original DTA-BIM method become unavailable. Thus, a modified DTA-BIM method, which use the numerical Green's functions combined with measured voltage, is proposed. This modified DTA-BIM method can be used to the inversion in a non-canonical inhomogeneous background with the measured voltages (or $S_{21}$ parameters). In order to verify the performance of this proposed inversion method, we investigate a prototype 3D microwave imaging system with a fix antenna array. The inversion results from the synthetic data show that this method works well with a fix antenna array, and the resolution of reconstructed images can reach to a quarter wavelength even in the presence of a strongly inhomogeneous background medium and antenna couplings. A time-reversal method is introduced as a pre-processing step to reduce the region of interest (ROI) in our inversion. In addition, a Multi-Domain DTA-BIM method is proposed to fit the discontinue inversion regions. With these improvements, the size of the inversion domain and the computational cost can be significantly reduced, and make the DTA-BIM method more feasible for rapid response applications.</p> / Dissertation