Analysis and Probability seminar

Abstract: Electrical impedance tomography (EIT) is an imaging technique aimed at determining the electrical conductivity of a medium from knowledge of the current and potential on its boundary. This is an ill-posed nonlinear inverse problem known as the Calderón problem. In this joint work with E. Duse and E. Thorén, a new algorithm for the two-dimensional case is presented. We use an explicit formula for approximating the Dirichlet-to-Neumann map, and through an expansion of the conductivity in a finite basis rephrase the task as a polynomial optimization problem. The algorithm does not make use of any complex geometric optics solutions and can be easily adapted to accommodate a priori information. Our numerical implementation demonstrates strong robustness to measurement errors, and yields highly accurate reconstructions of both smooth and piecewise constant conductivities.