Electrical impedance tomography and Calderon's inverse problem: a review
Matteo Santacesaria - University of Genoa
Calderon's inverse conductivity problem consists in the determination of an electrical conductivity distribution inside a body from current and voltage measurements on its boundary. Applications include medical imaging, nondestructive testing and geophysical prospecting. Since its formulation in 1980 it has stimulated a huge amount of research both in pure and applied mathematics. On the theoretical side, the main issue has been to prove uniqueness results, meaning the injectivity of the measurement or forward map, under appropriate assumptions on the regularity of the unknown conductivity, the amount of measurements and the geometry of the domain. Concerning applications, electrical impedance tomography (EIT) has been developed as the main imaging modality modeled by Calderon's problem. EIT faces great numerical hurdles, since errors in the data propagate exponentially to the reconstruction; in order to mitigate the instability (ill-posedness), strategies ranging from regularization methods, compressed sensing or machine learning have been employed. In this talk I will review the main results obtained for this problem and point out some theoretical and numerical challenges that are still open.
Matteo Santacesaria obtained his PhD in applied mathematics at École Polytechnique (France) in 2012. He has held post-doctoral positions at Université Joseph Fourier, University of Helsinki and Politecnico di Milano. He is currenty assistant professor (RTD A) at DIMA, University of Genoa.
2019-04-16 at 2:30 pm (subject to variability)