Iterative Reconstruction Algorithm for Electrical Capacitance Tomography Based on Calderon’s Method

In this paper, the closed-loop control strategy was facilitated to iteratively reconstruct images of high quality for electrical capacitance tomography (ECT). The classical direct reconstruction algorithm, e.g., Calderon’s method, was first used to roughly estimate the permittivity distributions. The yielded distributions were subsequently utilized to generate the mutual capacitances between different electrodes. A fast capacitance extraction method with constraints of equal potential on all nodes in each electrode was also introduced for the first time to calculate the mutual capacitances in terms of the discretized Dirichlet-to-Neumann map. In the method, only the stiffness matrix in the finite-element model was involved to calculate the capacitances between electrodes regarded as floating potentials, and the consumption time can be dramatically reduced. The calculated capacitances from the reconstructed distributions were then compared with the measured data from the ECT sensor. The deviations were used to correct the reconstructed distributions. A proportional-integral-derivative controller was introduced to perform a closed-loop control strategy for image correction. Similar to the classical feedback control systems, Calderon’s method was treated as the control object to generate an output. The output of the retrieved distributions passes the capacitance calculation and the capacitances are used as the negative feedback. In addition, the invariant property of the conformal transformation was strictly proved for the first time for the ECT sensor with a cross-section of any simply-connected region. As a result, the proposed iterative reconstruction algorithm can be promoted to the cases of any non-circular ECT sensors, e.g., square sensor. Simulated data contaminated with and without noises and real data from the experiments were used to demonstrate the feasibility and effectiveness of the proposed iterative reconstruction algorithm for ECT.