Electrical capacitance tomography: image reconstruction alongelectrical field lines

Abstract

For image reconstruction in electrical capacitance tomography (ECT)various implementations of the linear backprojection (LBP) algorithm anditerative reconstruction techniques have become the standard in mostapplications. Most implementations suffer from a smoothing effect and lack ofaccuracy due to their smooth sensitivity maps and the so-called `soft' fieldproblem in ECT, respectively. Therefore it is usually difficult in capacitance tomography to reconstruct objects with sharp contours. In the present paper a novel reconstruction modelbased on a finite-element-method (FEM) calculation is introduced. The model isderived directly from linear (x-ray) tomography, wherein weighting matricesalong the rays are calculated. By analogy, weighting matrices in ECT arecalculated numerically along the paths of the electrical field lines, whichare influenced by the distribution of the various permittivities in themeasurement plane. Finally the image reconstruction is done by implementingthese new weighting matrices within standard iteration techniques (ART andLBP). With the new algorithm even objects with sharp contours can bereconstructed. The results are more detailed and accurate tomograms.