A Data-driven Edge-preserving D-bar Method for Electrical Impedance Tomography
Format of Original
American Institute of Mathematical Sciences
Inverse Problems and Imaging
Original Item ID
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.
Hamilton, Sarah J.; Hauptmann, Andreas; and Siltanen, Samuli, "A Data-driven Edge-preserving D-bar Method for Electrical Impedance Tomography" (2014). Mathematics, Statistics and Computer Science Faculty Research and Publications. 242.
Inverse Problems and Imaging, Vol. 8, No. 4 (November 2014): 1053-1072. DOI.