Electrical capacitance tomography exhibits great potentials in the visualization measurement of industrial processes, and high-precision images are of great significance for the reliability and usefulness of measurement results. In this paper, we propose a deep learning-based inversion method to ameliorate the reconstruction accuracy. With the aid of the deep learning methodology, the prior from the images reconstructed by a certain imaging technique to the true images is abstracted and stored in the deep extreme learning machine. A new cost function is constructed to encapsulate the prior from the proposed deep learning model and the domain expertise about imaging targets, and the split Bregman algorithm and the fast iterative shrinkage thresholding technique are combined into a new numerical method to effectively solve it to get the final reconstruction. The numerical and experimental results validate that the inversion method proposed in this paper reduces the reconstruction artifacts and deformations and leads to the much improvement in the imaging quality.

Fast reconstruction of the temperature field from the partial temperature measurement data is highly desirable in the field of thermal engineering, in which reconstruction algorithms play a crucial role in real applications. Based on the gappy proper orthogonal decomposition technique, a promising approach that integrates the numerical simulation information and the measurement information is proposed in this study for the temperature field reconstruction from the partial measurement data, where the original reconstruction problem is formulated into an optimisation problem. An objective functional, which simultaneously considers the outliers in the measurement data and the model approximation distortions, is presented. Based on the split Bregman iteration technique, an iterative scheme is developed for solving the proposed objective functional. Numerical simulations are implemented to demonstrate the feasibility and effectiveness of the proposed algorithm.