Paper Info
Title
Exact Shape-Reconstruction by One-Step Linearization in Electrical Impedance Tomography
Abstract
For electrical impedance tomography (EIT), the linearized reconstruction method using the Frechet derivative of the Neumann-to-Dirichlet map with respect to the conductivity has been widely used in the last three decades. However, few rigorous mathematical results are known regarding the errors caused by the linear approximation. In this work we prove that linearizing the inverse problem of EIT does not lead to shape errors for piecewise-analytic conductivities. If a solution of the linearized equations exists, then it has the same outer support as the true conductivity change, no matter how large the latter is. Under an additional definiteness condition we also show how to approximately solve the linearized equation so that the outer support converges toward the right one. Our convergence result is global and also applies for approximations by noisy finite-dimensional data. Furthermore, we obtain bounds on how well the linear reconstructions and the true conductivity difference agree on the boundary of the outer support.
Year
DOI
Venue
2010
10.1137/090773970
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
inverse problems,electrical impedance tomography,linearization,shape reconstruction
Convergence (routing),Linear approximation,Conductivity,Mathematical optimization,Mathematical analysis,Fréchet derivative,Inverse problem,One-Step,Linearization,Mathematics,Electrical impedance tomography
Journal
Volume
Issue
ISSN
42
4
0036-1410
Citations 
PageRank 
References 
11
0.98
11
Authors
2
Name
Order
Citations
PageRank
Bastian Harrach1285.21
Jin Keun Seo237658.65