Otared Kavian
(Versaille, France)

Remarks on Inverse Problems arising from Electrical Impedance Tomography

In this talk we present a few inverse problems related to the technique known as Electrical Impedance Tomography, which has important applications in medical imaging. In particular we shall present some results recently published in joint paper with Y. Capdeboscq, J. Fehrenbach, F. de Gournay. In that paper, we discuss the reconstruction of the impedance from the local power density. This study is motivated by a new imaging principle which allows to recover interior measurements of the energy density by a non invasive method. We discuss the theoretical feasibility in two dimensions, and propose numerical algorithms to recover the conductivity in two and three dimension. The efficiency of this approach is documented by several numerical simulations.