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| Content Provider | Springer Nature Link |
|---|---|
| Author | Staboulis, Stratos Garde, Henrik |
| Copyright Year | 2016 |
| Abstract | The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it was shown that a simple monotonicity property of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity. In this paper we formulate a monotonicity-based shape reconstruction scheme that applies to approximative measurement models, and regularizes against noise and modelling error. We demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected, and under reasonable assumptions, asymptotically exactly characterized. Moreover, we rigorously associate this result with the complete electrode model, and describe how a computationally cheap monotonicity-based reconstruction algorithm can be implemented. Numerical reconstructions from both simulated and real-life measurement data are presented. |
| Ending Page | 1251 |
| Page Count | 31 |
| Starting Page | 1221 |
| File Format | |
| ISSN | 0029599X |
| e-ISSN | 09453245 |
| Journal | Numerische Mathematik |
| Issue Number | 4 |
| Volume Number | 135 |
| Language | English |
| Publisher | Springer Berlin Heidelberg |
| Publisher Date | 2016-08-06 |
| Publisher Place | Berlin, Heidelberg |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | ApplicationMathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics Mathematics Complete electrode model PDEs in connection with optics and electromagnetic theory Electrical impedance tomography Partial differential equations with discontinuous coefficients or data Mathematical Methods in Physics Inverse problems Direct reconstruction methods Monotonicity method Numerical Analysis Numerical and Computational Physics, Simulation Regularization |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Computational Mathematics |
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