On the tangential cone condition for electrical impedance tomography
Stefan Kindermann
TL;DR
This paper establishes sufficient criteria for the tangential cone condition in electrical impedance tomography, based on Taylor residual estimates and convexity, ensuring the condition holds for conductivities with specific monotonicity properties.
Contribution
It provides new criteria for verifying the tangential cone condition in electrical impedance tomography using Taylor residuals and convexity analysis.
Findings
Criteria established for the tangential cone condition.
Verification for conductivities with certain monotonicity.
Use of Taylor residual estimates and convexity in analysis.
Abstract
We state some sufficient criteria for the tangential cone conditions to hold for the electrical impedance tomography problem. The results are based on an estimate for the first-order Taylor residual for the forward operator and some convexity results in the L\"owner order. As a consequence, for conductivities satisfying certain monotonicity properties, the tangential cone condition is verified.
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Taxonomy
TopicsNumerical methods in inverse problems · Advanced Mathematical Modeling in Engineering · Microwave Imaging and Scattering Analysis