6533b858fe1ef96bd12b58a0
RESEARCH PRODUCT
Localized potentials in electrical impedance tomography
Bastian Gebauersubject
Work (thermodynamics)Control and OptimizationMathematical analysisBoundary (topology)510 MathematikConnection (mathematics)Continuation510 MathematicsSimple (abstract algebra)Modeling and SimulationDiscrete Mathematics and CombinatoricsIdentifiabilityPharmacology (medical)Factorization methodElectrical impedance tomographyAnalysisMathematicsdescription
In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of a domain and low energy on another. We show that such potentials exist for general L ∞ -conductivities in almost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability result for the famous Calderon problem with partial data. We also show how to con- struct such potentials numerically and use a connection with the factorization method to derive a new non-iterative algorithm for the detection of inclusions in electrical impedance tomography.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-01-01 | Inverse Problems & Imaging |