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Eigenstructure of the linearized electrical impedance tomography problem under radial perturbations
Markus Hirvensalo
We analyze the Fréchet derivative , that maps a perturbation in conductivity to the linearized change in boundary measurements governed by the conductivity equation. The domain…
Infinite-dimensional Lipschitz stability in the Calderón problem and general Zernike bases
Henrik Garde, Markus Hirvensalo, Nuutti Hyvönen
Calderón's inverse conductivity problem has, so far, only been subject to conditional logarithmic stability for infinite-dimensional classes of conductivities and to Lipschitz stab…
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…
Linearised Calderón problem: Reconstruction of unbounded perturbations in 3D
Henrik Garde, Markus Hirvensalo
Recently an algorithm was given in [Garde & Hyvönen, SIAM J. Math. Anal., 2024] for exact direct reconstruction of any perturbation from linearised data in the two-dimensiona…