An image reconstruction algorithm based on the regularized total least squares method for electrical capacitance tomography

Abstract

Electrical capacitance tomography (ECT) is a non-invasive imaging technology that is aimed at the visualization of the cross-sectional permittivity distribution of a dielectric object based on the measured capacitance data. ECT image reconstruction is a typical ill-posed problem and its solution is unstable, that is, the solution is highly sensitive to noise in the input data. 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 that considers the errors in both sensitivity field matrix and capacitance values based on the regularized total least squares method for electrical capacitance tomography is presented. The image reconstruction problem is transformed into an optimization problem. In addition, the Newton algorithm is employed to solve the objective function. Numerical simulations indicate that the algorithm is efficient and overcomes the numerical instability of ECT image reconstruction. For the cases of the reconstructed objects considered in this paper the spatial resolution of the reconstructed images obtained using the proposed algorithm is enhanced; and the artifacts in the reconstructed images can be eliminated effectively. As a result an efficient method for ECT image reconstruction is introduced.