Journal article · Conference paper
A Direct Numerical Reconstruction Algorithm for the 3D Calderón Problem
Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark1
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 Calderón's problem was addressed and solved in theory in the 1980s in a series of papers, but only recently the numerical implementation of the algorithm was initiated. 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 we will outline the theoretical reconstruction method and describe how the method can be implemented numerically. We will give three different implementations, and compare their performance on a numerical phantom.
| Language: | English |
|---|---|
| Publisher: | IOP Publishing |
| Year: | 2011 |
| Pages: | 012003 |
| Proceedings: | International Conference on Inverse Problems |
| ISSN: | 17426596 and 17426588 |
| Types: | Journal article and Conference paper |
| DOI: | 10.1088/1742-6596/290/1/012003 |
| ORCIDs: | Hansen, Per Christian and Knudsen, Kim |
