The goal of microwave breast imaging is to recover the profile of the dielectric properties of the breast by solving an inverse problem. In this thesis, a novel DBIM algorithm based on the TwIST method is proposed to reconstruct the complex permittivity of 2-D anatomically realistic numerical breast phantoms. A combined optimisation of the algorithm parameters is applied to improve the quality of reconstructions and the robustness of the algorithm. Furthermore, we present new strategies which improve further the performance of the DBIM-TwIST algorithm by refining our previous work on multiple-frequency reconstructions using a single-pole Debye model. Multiple-frequency approaches can combine the stabilizing effects of lower frequencies with enhanced resolution of higher frequencies, thereby overcoming stability and resolution limitations of single-frequency algorithms which tend to be very dependent upon the chosen frequency. And then a novel hybrid frequency approach is proposed to optimise stability and reconstruction accuracy at lower computational cost relative to frequency-hopping techniques. Besides, we propose an innovative two-step reconstruction approach for optimising the initial guess prior to reconstruction. Our approach adds low computational cost to the final breast reconstructions, and improves significantly the reconstruction quality for different breast phantoms. It can then be proposed that an L1 norm regularisation of the TwIST method is based on the Pareto curve, which contributes to de-noising and stabilising the algorithm convergence. At last, we focus on the application of the optimized DBIM-TwIST algorithm to data obtained from an MWI prototype, including direct measured data from MWI experiments, and numerical data from a CAD model emulating the MWI experiments using CST EM software. Based on our new eight-antenna microwave system with a small triangular patch printed monopole, our research demonstrates that the algorithm is able to image cylindrical targets immersed in a background (known) medium despite the model errors due to approximating the real experiment with our 2-D FDTD model. Moreover, a frequency selection method based on correlation analysis is proposed to improve the usage of the frequency information. Finally, we perform image reconstructions using a two-layer medium in order to enhance signal transmission through the imaging domain and at the same time reduce unwanted multi-path signals that do no interact with the interrogated imaging domain.
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