Some stability results for electric impedance tomography under elastic deformation

Eric Bonnetier (1) , Guillaume Bal (2) , François Monard (3) , Faouzi Triki (1)

1 EDP - Equations aux Dérivées Partielles
2 APAM - Department of Applied Physics and Applied Mathematics [New York]
3 Columbia University [New York]

We consider electric impedance tomography under elastic perturbations, where one tries to determine the conductivity in a bounded domain from the knowledge of pairs of Dirichlet and Neumann data and from their associated internal energy densities. In 2D, using a result of Alessandrini and Nesi, one can show the injectivity and stability of the map that associates the conductivity to the internal data corresponding to 2 diffeomorphic imposed currents. In 3D, the situation is more complex, and we only obtain a local result of uniqueness and stability.

Domaines: Equations aux dérivées partielles [math.AP]

Eric Bonnetier, Guillaume Bal, François Monard, Faouzi Triki. Some stability results for electric impedance tomography under elastic deformation. Conference on Mathematics of Medical Imaging, Jun 2011, Toronto, Canada. ⟨hal-00750501⟩