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Electrical impedance tomography (EIT) is a developing imaging modality that is beginning to show promise for detecting and characterizing tumors in the breast. At Rensselaer Polytechnic Institute, we have developed a combined EIT-tomosynthesis system that allows for the coregistered and simultaneous analysis of the breast using EIT and X-ray imaging. A significant challenge in EIT is the design of computationally efficient image reconstruction algorithms which are robust to various forms of model mismatch. Specifically, we have implemented a scaling procedure that is robust to the presence of a thin highly-resistive layer of skin at the boundary of the breast and we have developed an algorithm to detect and exclude from the image reconstruction electrodes that are in poor contact with the breast. In our initial clinical studies, it has been difficult to ensure that all electrodes make adequate contact with the breast, and thus procedures for the use of data sets containing poorly contacting electrodes are particularly important. We also present a novel, efficient method to compute the Jacobian matrix for our linearized image reconstruction algorithm by reducing the computation of the sensitivity for each voxel to a quadratic form. Initial clinical results are presented, showing the potential of our algorithms to detect and localize breast tumors.