Inverse Anisotropic Conductivity from Power Densities in Dimensionn ≥ 3
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Publication:2855208
DOI10.1080/03605302.2013.787089zbMath1314.35210arXiv1208.6029OpenAlexW2964312073MaRDI QIDQ2855208
Guillaume Bal, François Monard
Publication date: 24 October 2013
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1208.6029
Runge approximationanisotropic tensorscoupled-physics imagingexplicit reconstructionshybrid methods inverse conductivity
Boundary value problems for second-order elliptic equations (35J25) Biomedical imaging and signal processing (92C55) Inverse problems for PDEs (35R30) Second-order elliptic equations (35J15) Composite media; random media in optics and electromagnetic theory (78A48)
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Cites Work
- Unnamed Item
- Inverse diffusion problems with redundant internal information
- Reconstructions for some coupled-physics inverse problems
- Synthetic focusing in ultrasound modulated tomography
- Elliptic partial differential equations of second order
- Current density impedance imaging
- 2D and 3D reconstructions in acousto-electric tomography
- Magnetic Resonance Electrical Impedance Tomography (MREIT)
- Inverse anisotropic diffusion from power density measurements in two dimensions
- Stabilizing inverse problems by internal data
- Imaging by Modification: Numerical Reconstruction of Local Conductivities from Corresponding Power Density Measurements
- A stability theorem for solutions of abstract differential equations, and its application to the study of the local behavior of solutions of elliptic equations
- Electrical Impedance Tomography by Elastic Deformation
- Impedance-Acoustic Tomography
- Calderóns' Inverse Problem for Anisotropic Conductivity in the Plane
- Injectivity can fail for higher-dimensional harmonic extensions
