Reconstruction of permittivity profile from boundary capacitance data

We present numerical methods of reconstructing permittivity profile of material flow from data collected in electrical capacitance tomography (ECT). Based on a formula for the sensitivity maps from a partial differential equation model, we propose a unified framework of iterative algorithms using updated sensitivity maps to properly incorporate the nonlinear nature of the problem and a regularization mechanism to address the ill-posedness. For two- and three-phase flows, the total variation (TV) regularization method is shown to be effective in reconstructing the permittivity profiles accurately in a few iterations, without any a priori knowledge of the unknown permittivity values.