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 dataset consisting of 40000 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 dataset, 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.

The linear back projection (LBP) algorithm is often used for real-time online image reconstruction of electrical capacitance tomography (ECT) due to its high speed. However, due to the fact that the image reconstruction of ECT is a nonlinear ill-posed inverse problem, reconstructed images obtained by the LBP algorithm that simplifies ECT image reconstruction as a linear problem, tend to have distortion and can only be used for qualitative observation. In this paper, a deep fully-connected neural network, which improves the imaging quality of the LBP algorithm by compensating its imaging results is proposed. Instead of simplifying the ECT image reconstruction as a linear problem, our proposed compensated LBP algorithm uses a deep neural network to map the nonlinear relationship from capacitance to permittivity distribution. Furthermore, the difference between the capacitance regarding the permittivity distribution reconstructed by the LBP algorithm and the actual capacitance is used as the input of the network while the difference between the reconstructed permittivity distribution and the actual permittivity distribution is used as the output of the network. The results of the network can be used to compensate the image reconstruction results of the LBP. This strategy makes the ECT image reconstruction need only to deal with a support interval significantly smaller than that of the original ECT image reconstruction problem and is helpful to suppress the nonlinearity to be trained. Both the training and testing results based on simulation data instances and experimental data show that the proposed compensation network has a great improvement on image reconstruction results of the LBP algorithm. In addition, the computation load is comparable to the original LBP algorithm.

Electrical Capacitance Tomography (ECT) image reconstruction has developed for decades and made great achievements, but there is still a need to find a new theoretical framework to make it better and faster. In recent years, machine learning theory has been introduced in the ECT area to solve the image reconstruction problem. However, there is still no public benchmark dataset in the ECT field for the training and testing of machine learning-based image reconstruction algorithms. On the other hand, a public benchmark dataset can provide a standard framework to evaluate and compare the results of different image reconstruction methods. In this paper, a benchmark dataset for ECT image reconstruction is presented. Like the great contribution of ImageNet that transformed machine learning research, this benchmark dataset is hoped to be helpful for society to investigate new image reconstruction algorithms since the relationship between permittivity distribution and capacitance can be better mapped. In addition, different machine learning-based image reconstruction algorithms can be trained and tested by the unified dataset, and the results can be evaluated and compared under the same standard, thus, making the ECT image reconstruction study more open and causing a breakthrough.