Computational Imaging Method with a Learned Plug-and-Play Prior for Electrical Capacitance Tomography

  • J. LeiEmail author
  • Q. B. Liu
  • X. Y. Wang


Electrical capacitance tomography (ECT) is a potent image-based measurement technology for monitoring industrial processes, but low-quality images generally limit its application scope and measurement reliability. To increase the precision of reconstruction, in this study, a data-driven plug-and-play prior abstracted by a deep convolutional neural network (DCNN) and the sparseness prior of imaging objects, in form of regularizers, are jointly leveraged to generate a potent imaging model, in which the L1 norm of the mismatch error acts as a data fidelity term (DFT) to weaken the sensitivity of estimation result to noisy input data. The DCNN is embedded into the split Bregman (SB) technique to generate a powerful computing scheme for solving the built imaging model and the fast iterative shrinkage-thresholding algorithm (FISTA) is applied to solve the sub-problems efficiently. Extensive numerical results verify that the proposed imaging technique has competitive reconstruction ability and better robustness in comparison with the state-of-the-art methods. This study demonstrates the validity and efficacy of the proposed algorithm in reducing reconstruction error. Most importantly, the research outcomes verify that the data-driven plug-and-play prior and the sparseness prior can be jointly embedded into the imaging model, leading to a remarkable decline in reconstruction error.


Image reconstruction Deep convolutional neural network Image prior Data-driven prior Inverse problem Electrical capacitance tomography 


Funding Information

This study was funded by the Fundamental Research Funds for the Central Universities (no. 2017MS012), the National Natural Science Foundation of China (nos. 51206048 and 51576196), and the National Key Research and Development Program of China (no. 2017YFB0903601).

Compliance with Ethical Standards

Ethical Approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Energy, Power and Mechanical EngineeringNorth China Electric Power UniversityBeijingChina
  2. 2.Institute of Engineering ThermophysicsChinese Academy of SciencesBeijingChina
  3. 3.School of Control and Computer EngineeringNorth China Electric Power UniversityBeijingChina

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