Electrical capacitance tomography: image reconstruction along electrical field lines

For image reconstruction in electrical capacitance tomography (ECT) various implementations of the linear backprojection (LBP) algorithm and iterative reconstruction techniques have become the standard in most applications. Most implementations suffer from a smoothing effect and lack of accuracy due to their smooth sensitivity maps and the so-called 'soft' field problem in ECT, respectively. Therefore it is usually difficult in capacitance tomography to reconstruct objects with sharp contours. In the present paper a novel reconstruction model based on a finite-element-method (FEM) calculation is introduced. The model is derived directly from linear (x-ray) tomography, wherein weighting matrices along the rays are calculated. By analogy, weighting matrices in ECT are calculated numerically along the paths of the electrical field lines, which are influenced by the distribution of the various permittivities in the measurement plane. Finally the image reconstruction is done by implementing these new weighting matrices within standard iteration techniques (ART and LBP). With the new algorithm even objects with sharp contours can be reconstructed. The results are more detailed and accurate tomograms.