An image reconstruction algorithm based on the extended Tikhonov regularization method for electrical capacitance tomography

Electrical capacitance tomography (ECT) attempts to image the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. Successful applications of ECT depend on the speed and precision of the image reconstruction algorithms. Image reconstruction for ECT is a typical ill-posed problem, methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. In this paper, an image reconstruction algorithm for ECT is presented. The standard Tikhonov regularization method is extended using a combination estimation method and an extended stabilizing item according to the ill-posed characteristics of ECT. The image reconstruction problem is transformed into an optimization problem and the Newton algorithm is employed to solve the objective function. The proposed algorithm is tested by the noise-free capacitance data and the noise-contaminated capacitance data. Numerical simulations indicate that the proposed algorithm is efficient and can overcome the numerical instability of ECT image reconstruction. In the cases of the reconstructed objects considered in this paper, the reconstruction results show much improvement in the accuracy. The spatial resolution of the reconstructed images by the proposed algorithm is enhanced and the artifacts in the reconstructed images can be eliminated effectively. In addition, the reconstruction results from the noise-contaminated capacitance data also show a good robustness to noise. As a result, an efficient method for ECT image reconstruction is introduced.