Electrical impedance tomography is a modern biomedical imaging method. Its goal is to image the electrical properties of human tissues. This approach is safe for the patient's health, is non-invasive and has no known hazards. However, the approach suffers from low accuracy. Linear inverse solvers are commonly used in medical applications, as they are strongly robust to noise. However, linear methods can give only an approximation of the solution that corresponds to a linear perturbation from an initial estimate. This paper proposes a novel reconstruction process. After applying a linear solver, the conductivity distribution is post-processed with a nonlinear algorithm, with the aim of reproducing the abrupt change in conductivity at the boundaries between tissues or organs. The results are used to compare the proposed method with three other widely used methods. The proposed method offers higher quality images and a higher robustness to noise, and significantly reduces the error associated with image reconstruction.