A Physics-Constrained Deep Learning-Based Image Reconstruction for Electrical Capacitance Tomography

The image reconstruction in Electrical Capacitance Tomography (ECT) is a typical nonlinear ill-posed inverse problem. Traditional methods struggle to fit this nonlinear mapping adequately, resulting in image distortion or blur. Although deep learning-based methods considerably enhance reconstruction, they suffer from issues such as overfitting, poor generalization ability and extensive computational cost. In this paper, we propose a dual-deep-neural-network method that utilizes physical information as constraint for ECT image reconstruction, thereby achieving superior reconstruction performance. Specifically, we train a highly accurate network to solve the forward problem of ECT (i.e., calculating capacitance values from the permittivity distribution) and use it as a physical constraint to guide the solution of the inverse problem. This approach ensures a more accurate and physically consistent solution. Both simulation and experimental results demonstrate that our method substantially outperforms baseline methods in terms of image reconstruction performance while maintaining a low computational cost that meets ECT’s real-time imaging requirements. More importantly, due to the incorporation of physical constraint, our method demonstrates a significant advantage in reconstructing flow regimes not present in the training set, which implies its remarkable generalization ability and great potential for practical applications.