Solving inverse problem for electrical impedance tomography using topological derivative and level set method

In this paper, mathematical methods based on level set method, shape and topological derivatives for solving inverse problems were presented in electrical impedance tomography. The topological derivative measures the sensitivity of the functional shape when the domain is disturbed by small inclusions, defects or cracks inside the tested object. The derivative of the shape, on the other hand, measures the sensitivity of the border perturbation. Combining the level set function, shape and topological derivative, we get an algorithm that is more flexible in shape change and is less sensitive to the local minimum.