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Applied and Computational Math Seminar

Reconstruction of inclusions in the inverse conductivity problem

Henrik Garde (Aarhus University, Denmark)

Location:  Hill 705
Date & time: Tuesday, 28 March 2023 at 11:00AM - 12:00PM

I will discuss the inverse conductivity problem on recovering interior information about the electrical conductivity of an object/body from exterior electrical measurements. I will show how one can reconstruct the exact shape and position (called inclusions) of very general inhomogeneities from a known conductivity coefficient, using the monotonicity in terms of the conductivity coefficient of the associated Neumann-to-Dirichlet map. The inhomogeneities can be of several different types, with parts that are finite positive and negative perturbations, parts that are superconducting or insulating, and parts originating from a Muckenhoupt weight (e.g. leading to degenerate or singular problems). If time permits it, I will also discuss how to handle more practical electrode models and noisy measurements in a rigorous way.