4 papers · 1 filter
Reconstruction of shear modulus inclusions in elastostatics via divergence-free localization
Henrik Garde, Nuutti Hyvönen, Valter Pohjola
We formulate an improved version of the monotonicity method for shape reconstruction in the inverse problem of linear elastostatics. We show that this method can reconstruct inclus…
Continuity of the linearized forward map of electrical impedance tomography from square-integrable perturbations to Hilbert-Schmidt operators
Joanna Bisch, Markus Hirvensalo, Nuutti Hyvönen
This work considers the Fréchet derivative of the idealized forward map of two-dimensional electrical impedance tomography, i.e., the linear operator that maps a perturbation of th…
Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension
Henrik Garde, Nuutti Hyvönen
The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance…
On regularity of the logarithmic forward map of electrical impedance tomography
Henrik Garde, Nuutti Hyvönen, Topi Kuutela
This work considers properties of the logarithm of the Neumann-to-Dirichlet boundary map for the conductivity equation in a Lipschitz domain. It is shown that the mapping from the…