The image reconstruction is a crucial step in the electrical capacitance tomography. This paper presents a new methodology for improving the reconstruction accuracy. The prior image induced regularization from the deep convolutional extreme learning machine (DCELM) is introduced, which is integrated with the domain knowledge related to imaging targets to form a more effective mathematical model for reconstruction. A new numerical scheme is developed to train the DCELM more effectively. The fast iterative shrinkage-thresholding method is embedded into the alternating direction method of multipliers (ADMM) to form a new solver for the proposed imaging model. Extensive validations are implemented to evaluate the proposed imaging method. The numerical results demonstrate that the proposed imaging technique outperforms the state-of-the-art reconstruction methods and produces better reconstructions. INDEX TERMS Prior image induced regularization, image reconstruction, inverse problem, deep convolutional extreme learning machine, iterative imaging method, electrical capacitance tomography. QIBIN LIU received the B.Eng. and M.Sc. degrees in engineering thermophysics from Xi'an Jiaotong University, China, in 2002 and 2005, respectively, and the Ph.D. degree in engineering thermophysics from the Institute of Engineering Thermophysics, Chinese Academy of Sciences, China, in 2008. He is currently a Professor with the Institute of Engineering Thermophysics, Chinese Academy of Sciences, China. He has published more than 80 research papers. His research interests include solar energy utilization technologies, energy system integration, electrical capacitance tomography, inverse problems in engineering and science, and computational fluid dynamics.

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The inverse heat conduction problems (IHCP) analysis method provides a promising approach for acquiring the thermal physical properties of materials, the boundary conditions and the initial conditions from the known temperature measurement data, where the efficiency of the inversion algorithms plays a crucial role in real applications. In this paper, an inversion model that simultaneously utilizes the process evolution information of the objects to be estimated and the measurement information is proposed. The original IHCP is formulated into a state-space problem, and the unscented Kalman filter (UKF) method is developed for solving the proposed inversion model. The implementation of the proposed method does not require the gradient vector, the Jacobian matrix or the Hessian matrix, and thus the computational complexity is decreased. Numerical simulations are implemented to evaluate the feasibility of the proposed algorithm. For the cases simulated in this paper, satisfactory results are obtained, which indicates that the proposed algorithm is successful in solving the IHCP.