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Licensed Unlicensed Requires Authentication Published by De Gruyter February 15, 2014

Reconstructing conductivities with boundary corrected D-bar method

  • Samuli Siltanen EMAIL logo 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.

Received: 2013-7-8
Published Online: 2014-2-15
Published in Print: 2014-12-1

© 2014 by De Gruyter

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