A Data-driven Edge-preserving D-bar Method for Electrical Impedance Tomography

Document Type




Format of Original

20 p.

Publication Date



American Institute of Mathematical Sciences

Source Publication

Inverse Problems and Imaging

Source ISSN


Original Item ID

doi: 10.3934/ipi.2014.8.1053


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.


Inverse Problems and Imaging, Vol. 8, No. 4 (November 2014): 1053-1072. DOI.