Electrical impedance tomography (EIT) has been introduced as an alternative to classical tomography in medical diagnostics. In EIT the goal is to reconstruct the conductivity in the interior of a body from measurements of currents and potentials on its boundary. It is hoped that this method can contribute to a reduction of both, stress and costs, of physical examinations. The course material (in German) for a lecture course from 2004 may provide an introduction into this fascinating mathematical research area.
In joint work with a former student, Dr. M. Brühl, we developed a new approach (the so-called factorization method) to find discontinuities of the electric conductivity in a very efficient way. This may be particularly useful to find certain anomalies within a human body. A popular scientific presentation (in German) of this method appeared back in 2000 in the Forschungsmagazin of the Johannes Gutenberg University. While the original method is available on the web for interactive tests, the factorization method has found further applications in the meantime. For a survey of these results, we refer to some lecture slides.
Recently, we have focused our attention on reconstruction methods for reduced data sets, such as the so-called backscatter data, that arise if current/voltage measurements are taken with just a single pair of electrodes.