Reconstruction of cracks in Calderón's inverse conductivity problem using energy comparisons
arXiv:2305.06870 · doi:10.1137/23M1572416
Abstract
We derive exact reconstruction methods for cracks consisting of unions of Lipschitz hypersurfaces in the context of Calderón's inverse conductivity problem. Our first method obtains upper bounds for the unknown cracks, bounds that can be shrunk to obtain the exact crack locations upon verifying certain operator inequalities for differences of the local Neumann-to-Dirichlet maps. This method can simultaneously handle perfectly insulating and perfectly conducting cracks, and it appears to be the first rigorous reconstruction method capable of this. Our second method assumes that only perfectly insulating cracks or only perfectly conducting cracks are present. Once more using operator inequalities, this method generates approximate cracks that are guaranteed to be subsets of the unknown cracks that are being reconstructed.
arXiv comment16 pages
References in corpus (9)
- Monotonicity based shape reconstruction in electrical impedance tomography
- Resolution Guarantees in Electrical Impedance Tomography
- Uniqueness and Lipschitz stability in Electrical Impedance Tomography with finitely many electrodes
- Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography
- Strong unique continuation for general elliptic equations in 2D
- The regularized monotonicity method: detecting irregular indefinite inclusions
- Reconstruction of piecewise constant layered conductivities in electrical impedance tomography
- Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography
- Reconstruction of singular and degenerate inclusions in Calderón's problem