Reconstructing conductivities with boundary corrected D-bar method
-
Samuli Siltanen
and
Janne P. Tamminen
Abstract
The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed inverse problem and calls for a special regularized algorithm. One such algorithm, the so-called D-bar method, is improved in this work by introducing new computational steps that remove the so far necessary requirement that the conductivity should be constant near the boundary. The numerical experiments presented suggest two conclusions. First, for most conductivities arising in medical imaging, it seems the previous approach of using a best possible constant near the boundary is sufficient. Second, for conductivities that have high contrast features at the boundary, the new approach produces reconstructions with smaller quantitative error and with better visual quality.
Funding source: Tampere University of Technology
Funding source: Pirkanmaan kulttuurirahasto
Funding source: Finnish Centre of Excellence in Inverse Problems Research
Award Identifier / Grant number: CoE-project 213476
During part of the preparation of this work, S. Siltanen worked as professor and J. P. Tamminen worked as an assistant at the Department of Mathematics of Tampere University of Technology. The authors thank Jennifer Mueller for her valuable comments on the manuscript.
© 2014 by De Gruyter
Articles in the same Issue
- Frontmatter
- An inverse problem for the recovery of the vascularization of a tumor
- Estimating the ice thickness of mountain glaciers with a shape optimization algorithm using surface topography and mass-balance
- On the determination of the principal coefficient from boundary measurements in a KdV equation
- Reconstructing conductivities with boundary corrected D-bar method
- Regularization of linear inverse problems with total generalized variation
Articles in the same Issue
- Frontmatter
- An inverse problem for the recovery of the vascularization of a tumor
- Estimating the ice thickness of mountain glaciers with a shape optimization algorithm using surface topography and mass-balance
- On the determination of the principal coefficient from boundary measurements in a KdV equation
- Reconstructing conductivities with boundary corrected D-bar method
- Regularization of linear inverse problems with total generalized variation
