Reduced forward models in electrical impedance tomography with probe geometry

Abstract

One possible technique to monitor sedimentation and froth flotation processes is electrical impedance tomography (EIT). When EIT is used in these applications, the measurements are usually conducted using a probe sensor that is positioned inside the process vessel. Full three-dimensional reconstruction is possible, however, it leads to time-consuming reconstructions. For simplifying the reconstruction procedure and reducing the computation time, two different reduced forward models are proposed. In the first model, the conductivity is considered to be rotationally symmetric, that is, the conductivity and the potential do not change in the angular direction. This model is accurate as far as the given assumptions are fulfilled. In the second model, the conductivity is considered to be invariant also in the radial direction. This one-dimensional (1D) forward model is highly approximative and therefore the reconstructed conductivity profile is useless with conventional reconstruction approach. The approximation error approach is applied to compensate the errors due to forward model reduction. The proposed approximative forward models are evaluated through computer simulations of phase interface detection showing feasible reconstructions and significant reduction in reconstruction time without compromising reconstruction accuracy.

Keywords:

• electrical impedance tomography
• probe sensor
• cylindrical symmetry
• 1D model
• approximation error

Acknowledgments

The work was supported by the TEKES projects 2172/31/2010 and 2180/31/2011. Furthermore, this work was supported by the Academy of Finland (project 250215 Finnish Centre of Excellence in Inverse Problems Research). D. Sbarbaro also acknowledges the partial support of Fondecyt Project 1100272.