Journal article ยท Preprint article
Distinguishability Revisited: Depth Dependent Bounds on Reconstruction Quality in Electrical Impedance Tomography: Depth dependent bounds on reconstruction quality in electrical impedance tomography
The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the measurement boundary but better resolution near the measurement boundary. The observation can be quantified by the concept of distinguishability of inclusions.
This paper provides mathematically rigorous results supporting the intuition. Indeed, for a model problem lower and upper bounds on the distinguishability of an inclusion are derived in terms of the boundary data. These bounds depend explicitly on the distance of the inclusion to the boundary, i.e. the depth of the inclusion.
The results are obtained for disk inclusions in a homogeneous background in the unit disk. The theoretical bounds are veried numerically using a novel, exact characterization of the forward map as a tridiagonal matrix.
Language: | English |
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Publisher: | Society for Industrial and Applied Mathematics |
Year: | 2017 |
Pages: | 697-720 |
ISSN: | 1095712x and 00361399 |
Types: | Journal article and Preprint article |
DOI: | 10.1137/16M1072991 |
ORCIDs: | Knudsen, Kim |