Huaxiang Wang

A high-performance digital system for electrical capacitance tomography

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.

A pre-iteration method for the inverse problem in electrical impedance tomography

In this paper, the relationship between Landweber iteration and the generalized inverse has been analyzed, and it is shown that Landweber iteration is, in fact, a modification of the generalized inverse that is implemented by using the iteration solution. At the same time, a new reconstruction algorithm, termed the pre-iteration method, is proposed, which splits the image reconstruction process into two steps that are the off-line pre-iteration and the on-line one-step reconstruction. The speed of image reconstruction is remarkably increased.

Image reconstruction technique of electrical capacitance tomography for low-contrast dielectrics using Calderon's method

Calderons 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 Calderons method in electrical capacitance tomography for low-contrast dielectrics.

Electrical Capacitance Tomography for Sensors of Square Cross Sections Using Calderon's Method

Calderons method was generalized to electrical capacitance tomography (ECT) for sensors of square cross sections in this paper. It is a direct algorithm of image reconstruction, as neither matrix inversion nor an iterative process is required for image reconstruction. Since the major calculations are implemented in terms of a circular region, complicated calculations required by Calderons method for a noncircular cross section are avoided. A unique conformal transformation was used to establish a map from a circular region to a square. Results were obtained for a sensor of square cross section by using the conformal transformation. Two approximations of the scattering transform used in Calderons method were compared with simulated data. The Gauss-Legendre quadrature was applied to provide a fast-speed and high-quality image reconstruction. The reconstructed results validated the feasibility and effectiveness of the proposed treatment of Calderons method in ECT with a sensor of noncircular cross section.

A Specific Data Acquisition Scheme for Electrical Tomography

Electrical tomography techniques have been developed for monitoring the internal behavior of industrial processes. The electrical tomography offers some advantages over other tomography modalities, such as low cost, no radiation and being non-intrusive. In the past, individual data acquisition systems have been used for tomographic measurement, e.g., for ECT, ERT and EMT, most of which are in analog hardware. Generally, it is difficult to transfer these systems to other modalities. This paper presents a FPGA based data acquisition scheme, which can be used to facilitate the hardware design of electrical tomography. Improvements in system performance are achieved by implementing most functions in digital rather than analog hardware. Currently, individual ECT and ERT data acquisition systems have been used for achieving dual-modality tomography, which will result in poor hardware integration and data combination. With this scheme, multi-modality measurement techniques could be integrated into a system based on a single FPGA chip, providing effective integration. Preliminary results show that the signal to noise ratio is greater than 74 dB.

Electrical capacitance tomography with a non-circular sensor using the dbar method

In this paper, a new treatment of the dbar method for electrical capacitance tomography with a non-circular sensor is presented. It is a direct algorithm of image reconstruction and the gray value at any pixel of the reconstructed image is obtained directly and independently. The major calculations of image reconstruction in the dbar method were implemented in a circular sensor. As a result, complicated calculations of the scattering transform required by a non-circular sensor were avoided. A unique conformal transformation was used to map a circular sensor onto a non-circular sensor, e.g. a square sensor. In the experiments, a square sensor was constructed and the reconstructed results validated the feasibility and effectiveness of the dbar method in electrical capacitance tomography with a non-circular sensor.

A hybrid reconstruction algorithm for electrical impedance tomography

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.

Electrical impedance tomography with an optimized calculable square sensor

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.

An integrated ECT/ERT dual modality sensor

Capacitance and resistance tomography systems have been developed for visualizing the distributions of materials in an industrial process. They offer certain advantages over other tomography modalities, such as low cost, rapid response, no radiation and being non-intrusive. Single modal tomography could provide a satisfactory solution in most process applications. However, in some more complex applications, additional information is required for comprehensive understanding of the process under investigation. ECT and ERT are two most researched electrical tomography techniques. Individual ECT and ERT systems has been combined for dual modal measurement in recent years, however, the two sensors were located at two different cross-sections of the process, resulting in poor sensor integration and data fusion. As a result of the present research an integrated tomography system with capacitive and resistive sensors located at the same cross-section of the process has been developed. In the integrated system the use of both resistive and capacitive electrodes help eliminate mutual interferences between the two modalities. Experimental work with water-gas two-phase flow on vertical and horizontal pipes shows that the integrated system can provide effective dual modal measurements. The reconstructed images together with the stacked images are used to deduce such process parameters as gas holdup and flow velocity.

Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method.

Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing.