Abstract:  In previous work [Analysis \& PDE 11 (2018), no. 8, 1901-1943], we exploited a propagation of singularities implicit in the 2D Calder\’on conductivity problem 

to form the basis for the promising imaging modality of Virtual Hybrid Edge Detection. (Hybrid or `two-physics’ imaging typically combines two types of waves,

allowing the high contrast sensitivity of one, typically modeled by an elliptic PDE such as the conductivity equation, to be paired to the high resolution of the other, modeled by a hyperbolic or real principal type PDE.) 

We showed in 2D that the voltage/current measurements of an electrical field can be combined with microlocal and complex analysis, rather than a second kind of physical wave, to obtain (to some extent) the improved resolution of hybrid imaging. In preliminary results, we now extend this to 3D, and I will describe some of the microlocal geometry and analysis of the problem. 

This is joint work with Matti Lassas, Samuli Siltanen and Gunther Uhlmann (and Matteo Santacesaria for the earlier collaboration in 2D).