This document summarizes research on edge-preserving image reconstruction methods for electrical impedance tomography (EIT) applied to lung imaging. It presents three main contributions: 1. A level set-based reconstruction algorithm that was tested on clinical EIT data from lung patients, showing improved results over conventional methods. 2. An algorithm using level sets and L1 norms that better preserves edges and is more robust to noise and outliers. 3. A generalized inverse problem formulation using weighted L1 and L2 norms on data and regularization terms, improving robustness. Evaluation of the methods showed they produced more accurate shapes and were more robust to uncertainties compared to traditional techniques. Future work is proposed on combining level