Image Reconstruction Algorithm For Electrical Capacitance Tomography Research Articles

Image Reconstruction of Electrical Capacitance Tomography Based on an Efficient Sparse Bayesian Learning Algorithm

Image reconstruction is the main research problem of electrical capacitance tomography (ECT). In this article, a novel ECT image reconstruction algorithm based on an efficient sparse Bayesian learning (ESBL) algorithm is presented. This algorithm takes the Gaussian-scale mixture model as the prior distribution of the parameters to increase the flexibility of the model. Then, a surrogate function is used to replace the Gaussian likelihood function to reduce the computational complexity of the algorithm. Finally, the original cost function is equivalently converted into a concave–convex optimization problem through logarithm, and the block coordinate descent (BCD) method is used to solve the problem under the majorization–minimization (MM) framework. In order to verify the effectiveness of this algorithm, the Laplace distribution and the Student’s T distribution are used as the prior distribution of the parameters to achieve two specific implementations of this algorithm, and simulation and experiments are carried out. Compared with the sparse Bayesian learning (SBL) algorithm, the Laplace prior-based Bayesian compress sensing (LPBCS) algorithm, the total variation (TV) algorithm, and the Landweber algorithm, the presented EBSL algorithm with the Laplace prior distribution has better image quality and fairly good real-time performance.

Image Reconstruction of Electrical Capacitance Tomography Based on Adaptive Support Driven Bayesian Reweighted Algorithm

Image reconstruction of electrical capacitance tomography (ECT) is a nonlinear and ill-posed inverse problem. Therefore, how to introduce an effective algorithm to reduce the ill conditioned degree of ECT imaging, thereby improving the imaging accuracy is an important subject of ECT algorithm research. In order to further study the subject, a novel ECT image reconstruction algorithm based on an adaptive support driven Bayesian reweighted (ASDBR) algorithm was proposed in this paper. The great advantage of this algorithm is that it can accurately extract the main features of the flow pattern and remove redundant information. This algorithm transforms the original problem into a series of subproblems with iteratively reweighted weights, and solves these subproblems by the iterative shrinkage-thresholding algorithm (ISTA). Comparisons are made among the ASDBR algorithm, the Landweber iterative algorithm, the sparse Bayesian learning (SBL) algorithm, and Lasso. Both simulation and experiment results show that the proposed new method considerably enhances the quality of the reconstructed image.

ECT Attention Reverse Mapping algorithm: visualization of flow pattern heatmap based on convolutional neural network and its impact on ECT image reconstruction

The flow pattern is one of the most basic characteristic parameters of oil–gas two-phase flow, and it has a great influence on the accurate measurement of other parameters of two-phase flow. Over the past decade, the convolutional neural network (CNN) algorithm has been widely used in flow pattern research. Unfortunately, the flow pattern research based on the CNN algorithm is more on model structure optimization, and there is still little insight into the relationship between the CNN algorithm and the physical meaning of the flow pattern. Thus, in this paper, inspired by the neural network visualization gradient-based class activation mapping (Grad-CAM) method, we propose the electrical capacitance tomography (ECT) Attention Reverse Mapping algorithm (EARM) to explore the relationship between the physical meaning of flow patterns and the CNN algorithm. Specifically, the Grad-CAM method is used to obtain heatmaps of flow patterns, and the EARM algorithm combines the hotspot information of the flow pattern heatmap with the ECT image reconstruction principle, which deeply explores the relationship between the CNN flow pattern identification and the ECT image reconstruction algorithm. Furthermore, we conduct prediction experiments based on the parameters of the flow pattern hotspot capacitance data, and the experimental results are compared with the ECT original capacitance data parameter prediction. The prediction accuracy of oil–gas two-phase flow parameters has been improved by more than 50% on average, and experiments have verified the correctness of the visualization of CNN network flow pattern identification.

Planar capacitive imaging for composite delamination damage characterization

The objective of this study is to develop and validate a noncontact, nondestructive inspection and imaging method for rapidly assessing the subsurface condition of carbon fiber-reinforced polymer (CFRP) composite structures. The method works on the principle of planar electrical capacitance tomography (ECT). Unlike conventional ECT systems, electrodes are arranged on a rectangular planar surface in the form of a grid. The volume on one side of the electrode plane is interrogated with an electric field, and the mutual capacitances between the electrodes are measured. The volumetric electrical permittivity distribution of the interrogated region is then reconstructed from the measured capacitance responses. In this work, an ECT image reconstruction algorithm was implemented, and a customized planar capacitive imaging system was prototyped. First, different objects were placed near the electrode array, and the corresponding volumetric change in electrical permittivity was successfully captured. Second, the planar ECT system was employed for detecting artificially introduced subsurface defects in 3D-printed objects. Third, CFRP specimens with different sizes of single-layer delamination were fabricated and subjected to ECT interrogation. The results confirmed that the planar ECT system could detect the location and size of delamination in CFRP panels. The accuracy and resolution of the planar ECT prototype were also characterized.

An ECT image reconstruction algorithm based on object-and-background adaptive regularization

Electrical capacitance tomography (ECT) image reconstruction is an ill-posed inverse problem. Regularization methods are generally employed to solve the ill-posed problem, and the reconstructed image quality is seriously influenced by the selection of the regularization parameter. At present, a same regularization parameter is generally adopted for the whole reconstruction region, but the object region and the background region have different requirements on the regularization parameter, so it is difficult to obtain high-quality reconstruction images. In order to solve this problem, an image reconstruction algorithm based on object-and-background adaptive regularization, the OABAR algorithm for short, is proposed in this paper. The basic idea of the proposed OABAR algorithm is to dynamically divide the reconstructed region into object and background regions according to the reconstructed gray values. This is followed by iteratively reducing the regularization parameter values corresponding to the object region on the one hand to improve the detail reconstruction ability of the object region. On the other hand, a fixed regularization parameter value larger than the initial regularization parameter is provided for the background region to improve the smoothing ability of the background region. The iterative process is terminated when the change trend of capacitance residual norm first reverses or the number of iterations reaches the preset maximum value. If the change trend of capacitance residual norm does not reverse within the preset maximum number of iterations, the reconstructed result with the minimum capacitance residual norm is taken as the final result. Simulation and experimental tests were carried out and the results verify the effectiveness of the proposed algorithm on improving ECT image reconstruction quality.

Application of Barzilai-Borwein gradient projection for sparse reconstruction algorithm to image reconstruction of electrical capacitance tomography

Electrical capacitance tomography (ECT) is one kind of two/three-phase flow parameter visualization measurement technique. Image reconstruction of ECT is an ill-posed problem. Among the two-phase flow regimes, there are such distribution situations as objects being in the centre, objects being rather small or many objects being close to each other, the accuracy of reconstructed images is relatively poor. Based on the fact that the permittivity distribution of these flow regimes satisfies the priori condition of sparsity, the ECT image reconstruction algorithm based on Barzilai-Borwein gradient projection for sparse reconstruction (GPSR-BB) was presented in this paper. Simulation and experimental tests were carried out for the sparse distribution phantoms and experimental results show that the quality of reconstructed images can be enhanced obviously.

An Autoencoder-Based Image Reconstruction for Electrical Capacitance Tomography

Electrical capacitance tomography (ECT) image reconstruction has developed decades and made great achievements, but there is still a need to find new theory framework to make image reconstruction results better and faster. Recent years, deep learning, which is based on different series of artificial neural networks good at mapping complicated nonlinear functions, is flourishing and adopted in many fields. In this paper, a supervised autoencoder neural network is proposed to solve the image reconstruction problem of ECT, which has an encoder network and a decoder network. A simulation-based data set consisting of 40 000 pairs of instances, of which each pair of sample has a capacitance vector and corresponding permittivity distribution vector, is used to train and test the performance of the autoencoder by 10-fold cross validation. Furthermore, data with artificial noise, data regarding flow pattern not in training data set, and experimental data from a practical ECT system, are used to test the generalization ability and practicability of the network, respectively. The preliminary results show that the proposed autoencoder-based image reconstruction algorithm for ECT is of providing better reconstruction results.

Sparsity-inspired image reconstruction for electrical capacitance tomography

We present a new image reconstruction method for Electrical Capacitance Tomography (ECT). ECT image reconstruction is generally ill-posed because the number of measurements is small whereas the image dimensions are large. Here, we present a sparsity-inspired approach to achieve better ECT image reconstruction from the small number of measurements. Our approach for ECT image reconstruction is based on Total Variation (TV) regularization. We apply an efficient Split-Bregman Iteration (SBI) approach to solve the problem. We also propose three metrics to evaluate image reconstruction performance, i.e., a joint metric of positive reconstruction rate (PRR) and false reconstruction rate (FRR), correlation coefficient, and a shape and location metric. The results on both synthetic and real data show that the proposed TV-SBI method can better preserve the edges of images and better resolve different objects within reconstructed images, as compared to a representative state-of-the-art ECT image reconstruction algorithm, Projected Landweber Iteration with Linear Back Projection initialization (LBP-PLI).

Image Reconstruction for Electrical Capacitance Tomography Based on Sparse Representation

Image reconstruction for electrical capacitance tomography (ECT) is a nonlinear problem. A generalized inverse operator is usually ill-posed (unbounded) and ill-conditioned (with a large norm). Therefore, the solutions for ECT are not unique and highly sensitive to the measurement noise. To improve the image quality, a new image reconstruction algorithm for ECT based on sparse representation is proposed. An unconventional basis, i.e., an extended sensitivity matrix consisting of some normalized capacitance vectors corresponding to the base permittivity elements is designed as an expansion frame. The permittivity distributions to be reconstructed can have a natural sparse representation based on the new basis and can be represented as a linear combination of the base elements. Another sparsity regularization method-the standard Landweber iteration with a threshold is also conducted for comparison. The proposed algorithm has been evaluated by both simulation (with and without noise) and experimental results for different permittivity distributions.

An image reconstruction algorithm based on the extended Tikhonov regularization method for electrical capacitance tomography

Electrical capacitance tomography (ECT) attempts to image the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. Successful applications of ECT depend on the speed and precision of the image reconstruction algorithms. Image reconstruction for ECT is a typical ill-posed problem, methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. In this paper, an image reconstruction algorithm for ECT is presented. The standard Tikhonov regularization method is extended using a combination estimation method and an extended stabilizing item according to the ill-posed characteristics of ECT. The image reconstruction problem is transformed into an optimization problem and the Newton algorithm is employed to solve the objective function. The proposed algorithm is tested by the noise-free capacitance data and the noise-contaminated capacitance data. Numerical simulations indicate that the proposed algorithm is efficient and can overcome the numerical instability of ECT image reconstruction. In the cases of the reconstructed objects considered in this paper, the reconstruction results show much improvement in the accuracy. The spatial resolution of the reconstructed images by the proposed algorithm is enhanced and the artifacts in the reconstructed images can be eliminated effectively. In addition, the reconstruction results from the noise-contaminated capacitance data also show a good robustness to noise. As a result, an efficient method for ECT image reconstruction is introduced.

A hybrid ECT image reconstruction based on Tikhonov regularization theory and SIRT algorithm

Electrical Capacitance Tomography (ECT) image reconstruction is a key problem that is not well solved due to the influence of soft-field in the ECT system. In this paper, a new hybrid ECT image reconstruction algorithm is proposed by combining Tikhonov regularization theory and Simultaneous Reconstruction Technique (SIRT) algorithm. Tikhonov regularization theory is used to solve ill-posed image reconstruction problem to obtain a stable original reconstructed image in the region of the optimized solution aggregate. Then, SIRT algorithm is used to improve the quality of the final reconstructed image. In order to satisfy the industrial requirement of real-time computation, the proposed algorithm is further been modified to improve the calculation speed. Test results show that the quality of reconstructed image is better than that of the well-known Filter Linear Back Projection (FLBP) algorithm and the time consumption of the new algorithm is less than 0.1 second that satisfies the online requirements.

Novel Iterative Image Reconstruction Algorithm for Electrical Capacitance Tomography: Directional Algebraic Reconstruction Technique

Electrical capacitance tomography (ECT) is used to obtain information about the distribution of a mixture of dielectric materials inside a vessel or pipe. ECT has several advantages over other reconstruction algorithms and has found many applications in the industrial fields. However, there are some difficulties with image reconstruction in ECT: The relationship between the permittivity distribution and measured capacitance is nonlinear. And inverse problem is ill-posed so that the inverse solution is sensitive to measurement error. To cope with these difficulties iterative image reconstruction algorithms have been developed. In general, the iterative reconstruction algorithms in ECT have comparatively good-quality in reconstructed images but result in intensive computational burden. This paper presents the iterative image reconstruction algorithm for ECT that can enhance the speed of image reconstruction without degradation in the quality of reconstructed image. The main contribution of the proposed algorithm is new weighting matrices, which are obtained by the interpolation of the grouped electrical field centre lines (EFCLs). Extensive simulation results have demonstrated that proposed algorithm provides improved reconstruction performance in terms of computational time and image quality.

A stable image reconstruction algorithm for ECT

Most image reconstruction algorithms developed for electrical capacitance tomography (ECT) can only reconstruct qualitative images. Stabled quantitative image reconstruction is necessary for many applications. To get stable ECT image, the authors constructed a compressive operator and developed a new iterative algorithm, which can overcome the semi-convergence occurring in the Landweber iteration reconstruction technique. Experimental results showed that the stability and quality of reconstructed images are improved significantly.

Prior-online iteration for image reconstruction with electrical capacitance tomography

Electrical capacitance tomography (ECT) has been developed for imaging dielectric material distributions. While iterative image reconstruction algorithms may produce high-quality images, they are regarded as being time-consuming and currently can only be used offline. This paper describes a new image reconstruction algorithm for ECT. First, a coefficient matrix is generated through an offline iteration process. The matrix is then used for online image reconstruction in the same way as a sensitivity map is used in the popular linear back-projection (LBP) algorithm. This new algorithm can produce similar quality images to the Landweber iteration algorithm, but at the same speed as the LBP. An optimal step-length has been incorporated into the new algorithm for improved convergence. The algorithm has been evaluated by both simulation and experiment.