International Society for Industrial Process Tomography

Direct methods for image reconstruction in electrical capacitance tomography

Zhang Cao, Lijun Xu

School of Instrumentation and Opto-Electronics Engineering, Beihang University, Beijing 100191, China

email: zh_cao@hotmail.com, lijunxu@buaa.edu.cn

ABSTRACT

Electrical capacitance tomography (ECT) has been investigated extensively during the past decades, as a kind of visible measurement in industry. The task of ECT is to recover the information of cross-sectional material distribution in the form of reconstructed images by using the capacitance measurements on the boundary of the region of interest (ROI) It has several advantages over other tomographic techniques, e.g. low-cost, rapid response, portability, non-invasion and robustness. The main difficulty for ECT sensors is the `soft' field nature of the problem. The core of the ECT technique is to estimate the material property in any position of ROI, which means at least two nonlinear dependent parameter estimations, i.e. estimations of both the location and associated material property, take place simultaneously. In the past, most of the image reconstruction algorithms of ECT were based on the sensitivity theorem given by Geselowitz and Lehr, which is a kind of linearization using the perturbation principle. However, ECT possesses the `soft' field property, as the sensing field is distorted by objects in the imaging area. The sensitivity distribution changes with the spatial permittivity distribution. In recent years, iterative image reconstruction with an updated sensitivity matrix has been investigated, but they are very time-consuming and the property of convergence of the iteration has not been reported. Meanwhile, in the iterative algorithms based on the sensitivity/Jacobi matrix, the permittivity perturbations for the whole domain must be reconstructed simultaneously. In the paper, several direct algorithms, e.g. Calderon’ s method, dbar method and factorization method etc. for image reconstruction in ECT are reviewed and compared. The proposed methods are able to reconstruct only a part of the ROI without information of the other parts. Moreover, the methods can be generalized to the case of sensors of non-circular cross sections by using conformal transformations. Some experimental results are provided.

Keywords electrical capacitance tomography, direct algorithm, Calderon’ s method, dbar method, factorization method, conformal transformation

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