Dynamic reconstruction algorithm for electrical capacitance tomography based on the proper orthogonal decomposition

Due to the vivid visualizations obtained of the spatial material distributions of inaccessible objects, electrical capacitance tomography (ECT) is considered to be a promising method for the monitoring and control of various industrial processes in which image reconstruction algorithms play important roles in practical applications. In this study, the proper orthogonal decomposition (POD) method is used to derive a low-dimensional model for ECT imaging problems. We propose a POD-based dimensionality reduction dynamic imaging model, which incorporates the time-varying properties of dynamic imaging objects and prior knowledge obtained from previous measurements, other sensors, or numerical simulation results to simultaneously improve the accuracy and speed of image reconstruction. In the framework of this POD-based low-dimensional imaging model, we propose a new objective functional that integrates additional prior information related to imaging objects to convert the ECT image reconstruction task into an optimization problem. The split Bregman iteration (SBI) method is employed to search for the optimal solution to the proposed objective functional. Unlike standard pixel-based imaging methods, the proposed low-dimensional imaging model is obtained by projecting the original unknown variables onto subspaces spanned by a set of orthogonal basis vectors, where the unknown images are reconstructed indirectly by estimating a low-dimensional coefficient vector. Our theoretical study and numerical simulation results validate the superior performance of the proposed imaging method in alleviating the ill-posedness of the ECT image reconstruction problem, as well as increasing the imaging quality, decreasing the computational cost, improving the reconstruction speed, and enhancing robustness.