A Deep Learning Compensated Back Projection for Image Reconstruction of Electrical Capacitance Tomography

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.