A data-driven edge-preserving D-bar method for electrical impedance tomography

Sarah Jane Hamilton; Andreas Hauptmann; Samuli Siltanen

doi:10.3934/ipi.2014.8.1053

Article Contents

2014, Volume 8, Issue 4: 1053-1072. Doi: 10.3934/ipi.2014.8.1053

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A data-driven edge-preserving D-bar method for electrical impedance tomography

1.
Department of Mathematics, Statistics, and Computer Science, Marquette University, Milwaukee, WI 53233
2.
Department of Mathematics and Statistics, University of Helsinki, Helsinki, 00014
3.
University of Helsinki, Department of Mathematics and Statistics, FI-00014 Helsinki

Received: November 30, 2013

Revised: September 30, 2014

Published: October 2014

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Abstract

In Electrical Impedance Tomography (EIT), the internal conductivity of a body is recovered via current and voltage measurements taken at its surface. The reconstruction task is a highly ill-posed nonlinear inverse problem, which is very sensitive to noise, and requires the use of regularized solution methods, of which D-bar is the only proven method. The resulting EIT images have low spatial resolution due to smoothing caused by low-pass filtered regularization. In many applications, such as medical imaging, it is known a priori that the target contains sharp features such as organ boundaries, as well as approximate ranges for realistic conductivity values. In this paper, we use this information in a new edge-preserving EIT algorithm, based on the original D-bar method coupled with a deblurring flow stopped at a minimal data discrepancy. The method makes heavy use of a novel data fidelity term based on the so-called CGO sinogram. This nonlinear data step provides superior robustness over traditional EIT data formats such as current-to-voltage matrices or Dirichlet-to-Neumann operators, for commonly used current patterns.

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Mathematics Subject Classification: Primary: 65N21; Secondary: 94A08.

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