Journal article
Electrical Impedance Tomography: 3D Reconstructions using Scattering Transforms
Department of Informatics and Mathematical Modeling, Technical University of Denmark1
Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark2
Applied functional analysis, Department of Mathematics, Technical University of Denmark3
Department of Mathematics, Technical University of Denmark4
In three dimensions the Calderon problem was addressed and solved in theory in the 1980s. The main ingredients in the solution of the problem are complex geometrical optics solutions to the conductivity equation and a (non-physical) scattering transform. The resulting reconstruction algorithm is in principle direct and addresses the full non-linear problem immediately.
In this paper a new simplication of the algorithm is suggested. The method is based on solving a boundary integral equation for the complex geometrical optics solutions, and the method is implemented numerically using a Nystrom method. Convergence estimates are obtained using hyperinterpolation operators.
We compare the method numerically to two other approximations by evaluation on two numerical examples. In addition a moment method for the numerical solution of the forward problem is given.
| Language: | English |
|---|---|
| Publisher: | Taylor & Francis Group |
| Year: | 2012 |
| Pages: | 737-755 |
| Journal subtitle: | An International Journal |
| ISSN: | 10267360 , 00036811 and 1563504x |
| Types: | Journal article |
| DOI: | 10.1080/00036811.2011.598863 |
| ORCIDs: | Hansen, Per Christian and Knudsen, Kim |
