An image reconstruction algorithm based on new objective functional for electrical capacitance tomography

摘要

Electrical capacitance tomography (ECT) is considered one of the promising process tomography technologies. Its successful application depends greatly on the precision and speed of the image reconstruction algorithm. ECT image reconstruction belongs to the category of ill-posed problems, and its solution is unstable. Methods that impose stability while retaining certain desired features of a solution should be used to deal with the ill-posed problem. In this paper, a novel algorithm for electrical capacitance tomography is presented. On the basis of analyzing the standard Tikhonov regularization method, a new objective functional was established using the l(p) norm and a robust estimation according to the ill-posed characteristics of ECT, which transformed the image reconstruction problem into an optimization problem. In addition, the Newton algorithm is used to solve the objective functional. Numerical simulations indicate that the proposed algorithm is effective for enhancing the spatial resolution of the reconstructed images. In the cases of the reconstructed objects in this paper, the quality of the reconstructed images obtained using the proposed algorithm is better than that of other image reconstruction algorithms such as linear back projection (LBP), the standard Tikhonov regularization method and the projected Landweber iteration algorithm. Furthermore, the computation of the algorithm is direct, simple, and does not involve complex techniques.