Fully non-linear 3D reconstruction method for the Calderón problem
The Calderón problem concerns the determination and stable reconstruction of a conductivity distribution in a bounded domain from knowledge of Cauchy data on the boundary; it is a mathematical model for Electrical Impedance Tomography. There is a rich theory for the problem, and several reconstruction methods have been suggested. Among them is the method based on the so-called complex geometrical optics (GCO) solutions to the governing equations.
The CGO method computes in principle the unique solution to the inverse problem. Even though the theory was established in 1987-88, only recently a numerical algorithm following the same approach was developed. In this talk we will present this numerical algorithm and discuss its benefits and challenges. Moreover, we will describe a rigorous regularization method based on the approach.
This work is joint with Fabrice Delbary, University of Genoa.