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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.

This paper aims to present an approach based on electrical impedance tomography spectroscopy (EITS) for the determination of water and ice fraction in low-power applications such as autarkic wireless sensors, which require a low computational complexity reconstruction approach and a low number of electrodes. This paper also investigates how the electrode design can affect the reconstruction results in tomography.

EITS is performed by using a non-iterative method called optimal first order approximation. In addition to that, a planar electrode geometry is used instead of the traditional circular electrode geometry. Such a structure allows the system to identify materials placed on the region above the sensor, which do not need to be confined in a pipe. For the optimization, the mean squared error (MSE) between the reference images and the obtained reconstructed images was calculated.

The authors demonstrate that even with a low number of four electrodes and a low complexity reconstruction algorithm, a reasonable reconstruction of water and ice fractions is possible. Furthermore, it is shown that an optimal distribution of the sensor electrodes can help to reduce the MSE without any costs in terms of computational complexity or power consumption.

This paper shows through simulations that the reconstruction of ice and water mixtures is possible and that the electrode design is a topic of great importance, as they can significantly affect the reconstruction results.

This paper aims to investigate the optimal placement and/or orientation of individual sensor elements within integrated angular position sensors, in particular magnetic sensors based on the Hall effect or magnetoresistive effects under consideration of random deviations (variations in the production process, environmental influences, noise) and correlations of these influences.

The authors utilize methods from optimal design of experiments to consider random deviations in a system-level model. In this sensor model, they include spatial dependencies of random deviations by means of a Gaussian random field. Based on this, an approach for fast determination of D-optimal designs is presented.

The results show that the intuitive and commonly used distributions of magnetic field sensors are actually optimal for the determination of in-phase and quadrature signals in the presence of spatial correlations, provided that the number of field sensors is higher or equal to three. However, in the uncorrelated case, the intuitive solutions are not the only optimal solutions or even not optimal at all. It is found that a restriction to symmetric designs is not necessary; thus, the design space can be extended to allow for further improvements, e.g. miniaturization, of such angular position sensors.

The proposed approach allows for the fast optimization based on a system model. Correlated random influences are considered by means of a Gaussian random field, which can be obtained either from measurements or from field simulations, e.g. using the finite element method. As this is done before the actual simulation, such evaluations are not needed during the optimization, which allows for very fast solution of the optimization problem. Therefore, the approach is well suited for application-dependent adjustment of sensor designs.

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.

The investigation of the influence of the modeling error on the solution of the inverse problem given uncertain measured data in electrical capacitance tomography (ECT).

The solution of the nonlinear inverse problem in ECT and hence, the obtainable accuracy of the reconstruction result, highly depends on the numerical modeling of the forward map and on the required regularization. The inherent discretization error propagates through the forward map, the solution of the inverse problem, the subsequent calculation of process parameters and properties and may lead to a substantial estimation error. Within this work different finite element meshes are compared in terms of obtainable reconstruction accuracy. In order to characterize the reconstruction results, two error measures are introduced, a relative integral error and the relative error in material fraction. In addition, the influence of the measurement noise given different meshes is investigated from the statistical point of view using repeated measurements.

The modeling error, the degree of regularization, and measurement uncertainties are the determining and limiting factors for the obtainable reconstruction accuracy of electrical tomography systems. The impact of these key influence factors on the calculation of process properties given both synthetic as well as measured data is quantified. Practical implications – The obtained results show that especially for measured data, the variability in calculated parameters strongly depends on the efforts put on the forward modeling, i.e. on an appropriate finite element mesh size. Hence, an investigation of the modeling error is highly recommended when real‐world tomography problems have to be solved.

The results presented in this work clearly show how the modeling error as well as inherent measurement uncertainties influence the solution of the inverse problem and the posterior calculation of certain parameters like void fraction in process tomography.