Reconstructing Images Based on the CG Method with Krylov Subspace for ECT

Abstract

Electrical capacitance tomography (ECT) is considered to be one of the most promising process tomography techniques. The image reconstruction for ECT is an inverse problem to find the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. The conjugate gradient (CG) method is one of the most popular methods applied for image reconstruction, although its convergence rate is low. In this paper, an advanced version of the CG method, i.e. the projected CG method, is proposed to solve the inverse problem for ECT. The solution space is projected onto the Krylov subspace and the ill-posed problem is solved by the CG method in a low-dimensional specific subspace. Simulated results using the projected CG method are presented and compared with the conventional CG method, indicating that the proposed method can reduce the computation time, and improve the resolution of reconstructed images.