Purpose Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost, non-invasive and visualization features. There are two major difficulties in image reconstruction for ECT and ERT: the “soft-field”effect, and the ill-posedness of the inverse problem, which includes two problems: under-determined problem and the solution is not stable, i.e. is very sensitive to measurement errors and noise. This paper aims to summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide reference for further research and application. Design/methodology/approach In the past 10 years, various image reconstruction algorithms have been developed to deal with these problems, including in the field of industrial multi-phase flow measurement and biological medical diagnosis. Findings This paper reviews existing image reconstruction algorithms and the new algorithms proposed by the authors for electrical capacitance tomography and electrical resistance tomography in multi-phase flow measurement and biological medical diagnosis. Originality/value The authors systematically summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide valuable reference for practical applications.

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This paper describes a recently developed digital-based data acquisition system for electrical capacitance tomography (ECT). The system consists of high-capacity field-programmable gate arrays (FPGA) and fast data conversion circuits together with a specific signal processing method. In this system, digital phase-sensitive demodulation is implemented. A specific data acquisition scheme is employed to deal with residual charges in each measurement, resulting in a high signal-to-noise ratio (SNR) at high excitation frequency. A high-speed USB interface is employed between the FPGA and a host PC. Software in Visual C++ has been developed to accomplish operational functions. Various tests were performed to evaluate the system, e.g. frame rate, SNR, noise level, linearity, and static and dynamic imaging. The SNR is 60.3 dB at 1542 frames s−1 for a 12-electrode sensor. The mean absolute error between the measured capacitance and the linear fit value is 1.6 fF. The standard deviation of the measurements is in the order of 0.1 fF. The dynamic imaging test demonstrates the advantages of high temporal resolution of the system. The experimental results indicate that the digital signal processing devices can be used to construct a high-performance ECT system.

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Calderon's method was introduced to electrical capacitance tomography in this paper. It is a direct algorithm of the image reconstruction for low-contrast dielectrics, as no matrix inversion or iterative process is needed. It was implemented through numerical integration. Since the Gauss–Legendre quadrature was applied and can be predetermined, the image reconstruction process was fast and resulted in images of high quality. Simulations were carried out to study the effect of different dielectric contrasts and different electrode numbers. Both simulated and experimental results validated the feasibility and effectiveness of Calderon's method in electrical capacitance tomography for low-contrast dielectrics.

Electrical impedance tomography is a technique that reconstructs the medium distribution in a region of interest through electrical measurements on its boundary. In this paper, an optimized square sensor was designed for electrical impedance tomography in order to obtain maximum information over the cross section of interest, e.g., circulating fluidized beds, in the sense of Shannon information entropy. An analytical model of the sensor was obtained using the conformal transformation. The model indicates that the square sensor possesses calculable property, which allows the calculation of standard values of the sensor directly from a single dimensional measurement that can be made traceable to the SI unit of length. Based on the model, the sensitivity maps and electrical field lines can be calculated in less than a second. Two model based algorithms for image reconstruction, i.e., back projection algorithm based on electrical field lines and iterative Lavrentiev regularization algorithm based on the sensitivity map, were introduced. Simulated results and experimental results validate the feasibility of the algorithms.

Electrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution inside an inhomogeneous distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. A hybrid method is proposed for solving the inverse problem for EIT, which combines the Krylov subspace and the Tikhonov regularization for double levels of regularization to the ill-posed problem. Numerical simulation results using the hybrid method are presented and compared to those from truncated singular value decomposition (TSVD) regularization and the Tikhonov regularization. Experimental results with the hybrid method are also presented, indicating that the hybrid method can reduce the computation time, and improve the resolution of reconstructed images with the regularization parameter automatically chosen by the L-curve method.