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Prof. Allan Greenleaf

Department of Mathematics, University of Rochester, Rochester, NY, USA

Propagation and recovery of singularities in the inverse conductivity problem

The Calderon conductivity problem is the exemplar of an ill-posed inverse problem. Its exponential ill-posedness is responsible for the poor spatial resolution of Electrical Impedance Tomography (EIT) and has been an impetus for the development of hybrid imaging techniques, which compensate for this lack of resolution by coupling with a second type of physical wave, typically modeled by a hyperbolic PDE. Here we show that the inverse conductivity problem already contains within itself a mechanism for efficient, high resolution propagation of interior singularities of the conductivity to the boundary. Preliminary numerical simulations indicate that this approach, which we call Virual Hybrid Edge Detection (VHED), is effective for detecting and resolving complex inclusions in the interior using only EIT data.