Colloquium: Propagation of singularities in Calderón's inverse conductivity problem
Title: Propagation of singularities in Calderón's inverse conductivity problem.
The ill-posedness of the Calderón inverse problem is responsible for the poor resolution of Electrical Impedance Tomography - the imaging of a conductivity distribution inside a region via voltage-current measurements at the boundary. In the applied realm, this has been an impetus for the development of hybrid imaging techniques, which compensate for this lack of resolution by coupling electrostatics with a second type of physical wave, typically modeled by a hyperbolic PDE. I will describe how the inverse conductivity problem in 2D already contains within itself, without coupling to a second kind of physics, a mechanism for efficient transmission of interior singularities of the conductivity to the boundary, based on propagation of singularities for complex principal type operators. This approach involves certain multilinear singular Radon transforms. I will describe the underlying problem and some of the analysis involved.
This is joint work with Matti Lassas, Mateo Santacesaria, Samu Siltanen and Gunther Uhlmann.
Contact Name: Matthew Blair