Recent Developments in Inverse Problems - Abstract

Knudsen, Kim

Direct vs. iterative reconstruction methods for Electrical Impedance Tomography

The Calderón problem is the mathematical formulation of the reconstruction problem in Electrical Impedance Tomography. It is a well-studied inverse problem known to be extremely ill-posed. The reconstruction problem has a direct solution using complex geometrical optics solutions for the underlying PDE problem, and this method can also be shown to provide a regularization scheme. Another reconstruction algorithm uses a quite flexible formulation in terms of regularized least squares, which is then solved iteratively. In this talk both of these methods will be discussed with the aim of providing a fair comparison of the two approaches.