A Fractional-Order PID Controlled Iterative Calderon's Method for Electrical Capacitance Tomography

Electrical capacitance tomography (ECT) is a technique that uses image reconstruction algorithms to reconstruct permittivity distributions in the region of interest (ROI) with capacitances measured at the boundary of ROI. In this paper, a closed-loop iterative reconstruction algorithm is proposed, and it aims to eliminate the error between the measured capacitances and recuperative capacitances, and in this way, the quality of the reconstructed images is improved. The proposed algorithm includes three parts, namely, Fractional-order Proportional Integral Derivative (FPID) controller, Calderon's method, and a fast-solving forward method for numerical simulated capacitances in ECT. The error to be eliminated is the difference between measured capacitances and the simulated capacitances and is input to the FPID controller. When the coefficients in the FPID controller are determined, the output of controller is used to reconstruct permittivity distribution in the Calderon's method. Reconstructed image provides simulated capacitances as an updating reference for measured capacitances for the iterative reconstructions. Both noise-free and noisy data are used and verified the feasibility and effectiveness of the proposed algorithm for ECT.