Image Reconstruction for Electrical Capacitance Tomography Through Redundant Sensitivity Matrix

Moura, Hector Lise de; Pipa, Daniel Rodrigues; Wrasse, Aluísio do Nascimento; Silva, Marco J. da

doi:10.1109/jsen.2017.2719003

Cited by 17 publications

(7 citation statements)

References 35 publications

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“…The conventional approach to obtain the electrical permittivity distribution in electrical tomography is solving the inverse problem by processing the measured capacitance aiming to obtain a reconstructed image of the investigated area. In spite the fact that the previously mentioned problem is nonlinear, it is commonly approximated as a linearized model as follows [18]…”

Section: B Parametric Vortex Reconstructionmentioning

confidence: 99%

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Multichannel Capacitive Imaging of Gas Vortex in Swirling Two-Phase Flows Using Parametric Reconstruction

et al. 2020

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Swirl-based inline phase separation is a promising approach in the process industry with potential application in oil and gas separation in petroleum industry. To increase the efficiency of the separation, the process may be controlled. In this direction, the position and the diameter of the gas vortex are two parameters that can be used in the control loop, provided that they can be non-intrusively estimated. This article presents a capacitive sensor-based imaging method to extract these geometrical parameters. The proposed method consists in obtaining high-temporal resolution capacitance measurements at the pipe boundary of a test rig, which in turn are used in a reconstruction and extracting the targeted parameters of the gas vortex. The calculated parameters are then used to visually present the swirling flow. The measurement system was evaluated quantitatively by performing experiments with different phantoms of known diameters and positions in the sensing area. Dynamic measurements were also performed in a test rig for liquid-gas swirling flow. The capacitive imaging system is capable of detecting characteristics of the flow for a wide range of gas and liquid flow rates. A qualitative analysis was also carried out by comparing time series of the capacitive images with high-speed camera recording. The geometrical parameters obtained by the proposed approach presents a good agreement with the real data, with a root mean square deviation of 0.76mm for diameter and 0.88mm for vortex position. It can be utilized in future work as an alternative or complementary input for the controlled inline liquid-gas separation system. INDEX TERMS Swirling two-phase flows, capacitive sensor, grid search, parameter extraction.

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Section: B Parametric Vortex Reconstructionmentioning

confidence: 99%

“…the sensitivity of each electrode to each defined position inside the pipe and f is a vector of the permittivity distribution inside the pipe. For TPS, sensitivity matrix is obtained by means of electric field simulations and details can be found elsewhere [18], [19].…”

Section: B Parametric Vortex Reconstructionmentioning

confidence: 99%

Multichannel Capacitive Imaging of Gas Vortex in Swirling Two-Phase Flows Using Parametric Reconstruction

et al. 2020

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“…Since the relationship between the capacitance measurements and the permittivity of each voxel is nonlinear, the Jacobian matrix is used to linearize the relationship. To establish the relationship between the permittivity distribution and the capacitance measurements, a sensitivity matrix S is built according to the following equation [ 11 , 12 , 13 , 14 ]:

…”

Section: Image Reconstruction Principlesmentioning

confidence: 99%

Redundancy Analysis of Capacitance Data of a Coplanar Electrode Array for Fast and Stable Imaging Processing

Wen

Zhang

et al. 2017

Sensors

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A coplanar electrode array sensor is established for the imaging of composite-material adhesive-layer defect detection. The sensor is based on the capacitive edge effect, which leads to capacitance data being considerably weak and susceptible to environmental noise. The inverse problem of coplanar array electrical capacitance tomography (C-ECT) is ill-conditioning, in which a small error of capacitance data can seriously affect the quality of reconstructed images. In order to achieve a stable image reconstruction process, a redundancy analysis method for capacitance data is proposed. The proposed method is based on contribution rate and anti-interference capability. According to the redundancy analysis, the capacitance data are divided into valid and invalid data. When the image is reconstructed by valid data, the sensitivity matrix needs to be changed accordingly. In order to evaluate the effectiveness of the sensitivity map, singular value decomposition (SVD) is used. Finally, the two-dimensional (2D) and three-dimensional (3D) images are reconstructed by the Tikhonov regularization method. Through comparison of the reconstructed images of raw capacitance data, the stability of the image reconstruction process can be improved, and the quality of reconstructed images is not degraded. As a result, much invalid data are not collected, and the data acquisition time can also be reduced.

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“…Calculating the sensitivity matrix improves the nonlinearity of the model by definition. In addition to computation by single pixel points, compressed sensing methods that use pixel blocks of multiple pixels [17][18][19] and redundant dictionaries [20] as sparse bases improve the robustness of the algorithm. Still, these algorithms require a large amount of iterative computation.…”

Section: Introductionmentioning

confidence: 99%

Image reconstruction for ECT based on high-order approximate sensitivity matrix

Yang

Liu

2023

Meas. Sci. Technol.

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Electrical capacitance tomography (ECT), widely used for industrial measurements, reflects the permittivity distribution of the imaging region by measuring capacitance. The image reconstruction method is a crucial factor in determining image quality. Normally, the ECT image is reconstructed by sensitivity matrix. To alleviate the effects of the soft field property of the traditional sensitivity matrix, we propose an ECT reconstruction method based on the high-order approximate sensitivity matrix. The high-order approximate sensitivity matrices with four different nonlinearities, including a traditional sensitivity matrix, are derived through electromagnetic field analysis. Both numerical simulation and experiment are implemented for four sensitivity matrices using the Tikhonov regularisation algorithm and Landweber algorithm. Sensitivity evaluation indicators, image evaluation metricises, and capacitance matching correlation coefficients are used to compare the performance of sensitivity matrices. The results show that the high-order approximate sensitivity matrix with suitable nonlinearities improves image reconstruction quality. In different flow regimes, the sensitivity matrix with proper linearity has obvious advantages for regimes with high nonlinearity. The high-order approximate sensitivity matrix leads to shorter calculation time and can be used by various algorithms to enhance image reconstruction quality.

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Image Reconstruction for Electrical Capacitance Tomography Through Redundant Sensitivity Matrix

Cited by 17 publications

References 35 publications

Multichannel Capacitive Imaging of Gas Vortex in Swirling Two-Phase Flows Using Parametric Reconstruction

Multichannel Capacitive Imaging of Gas Vortex in Swirling Two-Phase Flows Using Parametric Reconstruction

Redundancy Analysis of Capacitance Data of a Coplanar Electrode Array for Fast and Stable Imaging Processing

Image reconstruction for ECT based on high-order approximate sensitivity matrix

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