A free-discontinuity approach to inverse problems
Seminar Room 1, Newton Institute
AbstractPhase-field methods and length or perimeter penalization have been successfully applied to many imaging problems, such as for instance the Mumford-Shah approach to segmentation and its phase-field counterpart by Ambrosio and Tortorelli.
In this talk we shall illustrate how these techniques may be used also to treat inverse problems where a discontinuous function has to be recovered. As an example we consider the inverse problem of determining insulating cracks or cavities by performing few electrostatic measurements on the boundary. We show the validity of these methods by a convergence analysis and by numerical experiments. The numerical experiments have been performed jointly with Wolfgang Ring (University of Graz, Austria).