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The purpose of this paper is to investigate the achievable improvement in reconstruction accuracy in electrical tomography through the incorporation of physical bound constraints as prior knowledge in the inverse problem solution.

The structure of the nonlinear least squares inverse problem formulation and the importance of prior knowledge are addressed. Several different methods for the incorporation of bound constraints are discussed. The methods are compared by means of reconstructions from simulated and measured data and the computational demands.

The inclusion of bound constraints on the material values in the inverse problem solution results in a considerable improvement of the reconstructions. The occurrence of artefacts and blurring can be reduced. Among the investigated constraint handling methods, the logarithmic parameter reconstruction approach can be implemented with minimal additional computational effort.

The study is performed with discrete two‐phase material distributions as occurring in industrial problems. A further step would be the extension to multiple phases.

The logarithmic transform method is a novel approach for the incorporation of bound constraints in tomography. It outperforms other constraint handling approaches and may be of interest for electrical tomography systems in various applications.

As one of the tomographic imaging techniques, electrical capacitance tomography (ECT) is widely used in many industrial applications. While most ECT sensors have electrodes placed around a cylindrical chamber, the planar ECT sensor has been investigated for depth and defect detection. However, the planar ECT sensor has limited height and depth sensing capability due to its single-sided assessment with the use of only a single-plane design. The purpose of this paper is to investigate a dual-plane miniature planar 3D ECT sensor design using the 3 × 3 matrix electrode array.

The sensitivity map of dual-plane miniature planar 3D ECT sensor was analysed using 3D visualisation, the singular value decomposition and the axial resolution analysis. Then, the sensor was fabricated for performance analysis based on 3D imaging experiments.

The sensitivity map analysis showed that the dual-plane miniature planar 3D ECT sensor has enhanced the height sensing capability, and it is less ill-posed in 3D image reconstruction. The dual-plane miniature planar 3D ECT sensor showed a 28% improvement in reconstructed 3D image quality as compared to the single-plane sensor set-up.

The 3 × 3 matrix electrode array has been proposed to use only the necessary electrode pair combinations for image reconstruction. Besides, the increase in number of electrodes from the dual-plane sensor setup improved the height reconstruction of the test sample.

This paper aims to investigate the usability of the non-iterative monotonicity approach for electrical capacitance tomography (ECT)-based object detection. This is of particular importance with respect to object detection in robotic applications.

With respect to the detection problem, the authors propose a precomputed threshold value for the exclusion test to speed up the algorithm. Furthermore, they show that the use of an inhomogeneous split-up strategy of the region of interest (ROI) improves the performance of the object detection.

The proposed split-up strategy enables to use the monotonicity approach for robotic applications, where the spatial placement of the electrodes is constrained to a planar geometry. Additionally, owing to the improvements in the exclusion tests, the selection of subregions in the ROI allows for avoiding self-detection. Furthermore, the computational costs of the algorithm are reduced owing to the use of a predefined threshold, while the detection capabilities are not significantly influenced.

The presented simulation results show that the adapted split-up strategies for the ROI improve significantly the detection performance in comparison to the traditional ROI split-up strategy. Thus, the monotonicity approach becomes applicable for ECT-based object detection for applications, where only a reduced number of electrodes with constrained spatial placement can be used, such as in robotics.

The purpose of this paper is to consider the optimization of an 8‐electrode cylindrical electrical capacitance tomography (ECT) sensor. The aim is to obtain maximum uniformity and value of the sensitivity distribution of the sensor, while keeping the mutual capacitances between the electrodes above a predefined level.

The optimization methods that have been used are response surface methodology, genetic algorithm and a combination of both.

As results, optimum dimensions for the gap, mounting pipe, shield and insulation are determined, which ensure more uniform distribution of sensitivity in the sensing area.

The optimization strategies used – RSM and the combined RSM+GA – make the optimization of ECT sensors feasible. The results show the effectiveness of the RSM+GA strategy which could also be used for optimization of 3D multilayer ECT sensors.

The paper aims to present an innovative solution for evaluation study of the dampness level of walls and historical buildings.

Electrical tomography enables one to obtain a distribution pattern of wall dampness. The application of modern tomographic techniques in conjunction with topological algorithms will allow one to perform very accurate spatial assessment of the dampness levels of buildings. The proposed application uses the total variation, Gauss–Newton and level set method to solve the inverse problem in electrical tomography.

Research shows that electrical tomography can provide effective results in damp buildings. This method can provide 2D/3D moisture distribution pattern.

The impact of this technique will be limited to inspection of the facility after floods or assessment of historical buildings.

The presented method could eventually lead to a much more effective evaluation of moisture in the walls.

The solution has commercial potential and could result in more cost-effective monitoring of historical buildings, which have an economic impact on society.

The authors propose a system for imaging spatial moistness of walls and historic buildings based on electrical tomography and consisting of a measuring device, sensors and image reconstruction algorithms.

The purpose of this paper is to present the sensing mechanism, design issues, performance evaluation and applications for planar capacitive sensors. In the context of characterisation and imaging of a dielectric material under test (MUT), a systematic study of sensor modelling, features and design issues is needed. In addition, the influencing factors on sensitivity distribution, and the effect of conductivity on sensor performance need to be further studied for planar capacitive sensors.

While analytical methods can provide accurate solutions to sensors of simple geometries, numerical modelling is preferred to obtain sensor response to different design parameters and properties of MUT, and to derive the sensitivity distributions of various electrode designs. Several important parameters have been used to evaluate the response of the sensors in different sensing modes. The designs of different planar capacitive sensor arrays are presented and experimentally evaluated.

The response features and design guidelines for planar capacitive sensors in different sensing modes have been summarised, showing that the sensor in the transmission mode or the single‐electrode mode is suitable for material characterisation and imaging, while the sensor in the shunt mode is suitable for proximity/displacement measurement. The sensitivity distribution of the sensor depends largely on the geometry of the electrodes. Conductivity causes positive changes for the sensor in the transmission and single‐electrode mode, but negative changes for the sensor in the shunt mode. Experimental results confirm that sensing depths of the sensor arrays and the influence of buried conductor on capacitance measurements are in agreement with simulations.

Experimental verification is needed when a sensor is designed.

This paper provides a comprehensive study for planar capacitive sensors in terms of sensor design, evaluation and applications.

Circular pipelines are mostly used for pneumatic conveyance in industrial processes. For optimum and efficient production in industries that use a pipeline for conveyance, tomographic image of the transport particles is paramount. Sensing mechanism plays a vital role in process tomography. The purpose of this paper is to present a two‐dimensional (2‐D) model for sensing the characteristics of electrostatic sensors for electrical charge tomography system. The proposed model uses the finite‐element method.

The domain is discretized into discrete shapes, called finite elements, by using a MATLAB. Each of these elements is taken as image pixels, on which the electric charges carried by conveyed particles are transformed into equations. The charges' interaction and the sensors installed around the circumference, at the sensing zone of the conveying pipeline are related by the proposed model equations. A matrix compression technique was also introduced to solve the problem of unevenly sensing characteristics of the sensors due to elements' number's concentration. The model equations were used to simulate the modeled electrostatic charge distribution carried by the particles moving in the pipeline.

The simulated results show that the proposed sensors are highly sensitive to electrostatic charge at any position in the sensing zone, thereby making it a good candidate for tomographic image reconstruction.

Tomographic imaging using finite element method is found to be more accurate and reliable compared to linear and filtered back projection method.

The purpose of this paper is to reduce the artifacts in fast Bayesian reconstruction images in electrical tomography. This is in particular important with respect to object detection in electrical tomography applications.

The authors suggest to apply the Box-Cox transformation in Bayesian linear minimum mean square error (BMMSE) reconstruction to better accommodate the non-linear relation between the capacitance matrix and the permittivity distribution. The authors compare the results of the original algorithm with the modified algorithm and with the ground truth in both, simulation and experiments.

The results show a reduction of 50 percent of the mean square error caused by artifacts in low permittivity regions. Furthermore, the algorithm does not increase the computational complexity significantly such that the hard real time constraints can still be met. The authors demonstrate that the algorithm also works with limited observations angles. This allows for object detection in real time, e.g., in robot collision avoidance.

This paper shows that the extension of BMMSE by applying the Box-Cox transformation leads to a significant improvement of the quality of the reconstruction image while hard real time constraints are still met.

Electrical capacitance tomography (ECT) is a technique for reconstructing information about the spatial distribution of the contents of closed pipes by measuring variations in the dielectric properties of the material inside the pipe. In this paper, we propose a method that solves the non‐linear reconstruction problem directly leading to less iterations and higher accuracy than linear back projection algorithms currently in use in most ECT systems.

For the spatial reconstruction of a two phase flow, as it might occur in a pipe, the main problem has always been the blurring of the resulting images.

In this paper, we present a method where blurring is implicitly avoided by the use of level sets. The level set method describes the iteratively evolving interface between different materials. The underlying field problem is solved with the boundary element method formulated in the region, where the degrees of freedom are present and the finite element method in all other regions.

Finally reconstruction results of an electrical capacitance tomography sensor are presented to show the validity of the method.

Presents a method where blurring is avoided by the use of level sets.