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CGAN-ECT: Tomography Image Reconstruction from Electrical Capacitance Measurements Using CGANs

Wael Deabes, Alaa E. Abdel-Hakim

TL;DR

Reconstructing cross-sectional permittivity distributions from capacitance measurements is challenging due to the ill-posed inverse problem. The authors propose CGAN-ECT, a conditional GAN framework with a UNet-based generator and a rotation-invariant modulator, trained on a large synthetic dataset of $320k$ pairs to map modulated capacitance matrices to $128×128$ permittivity images. The method achieves average CC above $0.99$ and IE around $0.07$ on simulated tests, demonstrates robustness to noise, generalizes to unseen patterns, and performs well on real data with reconstruction times around $0.062$ s, indicating potential for real-time industrial deployment. These results suggest CGAN-ECT can outperform traditional and some DL-based reconstructions in both accuracy and speed, offering a practical path toward high-quality, fast ECT imaging.

Abstract

Due to the rapid growth of Electrical Capacitance Tomography (ECT) applications in several industrial fields, there is a crucial need for developing high quality, yet fast, methodologies of image reconstruction from raw capacitance measurements. Deep learning, as an effective non-linear mapping tool for complicated functions, has been going viral in many fields including electrical tomography. In this paper, we propose a Conditional Generative Adversarial Network (CGAN) model for reconstructing ECT images from capacitance measurements. The initial image of the CGAN model is constructed from the capacitance measurement. To our knowledge, this is the first time to represent the capacitance measurements in an image form. We have created a new massive ECT dataset of 320K synthetic image measurements pairs for training, and testing the proposed model. The feasibility and generalization ability of the proposed CGAN-ECT model are evaluated using testing dataset, contaminated data and flow patterns that are not exposed to the model during the training phase. The evaluation results prove that the proposed CGAN-ECT model can efficiently create more accurate ECT images than traditional and other deep learning-based image reconstruction algorithms. CGAN-ECT achieved an average image correlation coefficient of more than 99.3% and an average relative image error about 0.07.

CGAN-ECT: Tomography Image Reconstruction from Electrical Capacitance Measurements Using CGANs

TL;DR

Reconstructing cross-sectional permittivity distributions from capacitance measurements is challenging due to the ill-posed inverse problem. The authors propose CGAN-ECT, a conditional GAN framework with a UNet-based generator and a rotation-invariant modulator, trained on a large synthetic dataset of pairs to map modulated capacitance matrices to permittivity images. The method achieves average CC above and IE around on simulated tests, demonstrates robustness to noise, generalizes to unseen patterns, and performs well on real data with reconstruction times around s, indicating potential for real-time industrial deployment. These results suggest CGAN-ECT can outperform traditional and some DL-based reconstructions in both accuracy and speed, offering a practical path toward high-quality, fast ECT imaging.

Abstract

Due to the rapid growth of Electrical Capacitance Tomography (ECT) applications in several industrial fields, there is a crucial need for developing high quality, yet fast, methodologies of image reconstruction from raw capacitance measurements. Deep learning, as an effective non-linear mapping tool for complicated functions, has been going viral in many fields including electrical tomography. In this paper, we propose a Conditional Generative Adversarial Network (CGAN) model for reconstructing ECT images from capacitance measurements. The initial image of the CGAN model is constructed from the capacitance measurement. To our knowledge, this is the first time to represent the capacitance measurements in an image form. We have created a new massive ECT dataset of 320K synthetic image measurements pairs for training, and testing the proposed model. The feasibility and generalization ability of the proposed CGAN-ECT model are evaluated using testing dataset, contaminated data and flow patterns that are not exposed to the model during the training phase. The evaluation results prove that the proposed CGAN-ECT model can efficiently create more accurate ECT images than traditional and other deep learning-based image reconstruction algorithms. CGAN-ECT achieved an average image correlation coefficient of more than 99.3% and an average relative image error about 0.07.
Paper Structure (14 sections, 4 equations, 10 figures, 6 tables, 1 algorithm)

This paper contains 14 sections, 4 equations, 10 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. CGAN-ECT Model Description
  3. Modulator
  4. Generator
  5. CGAN Model
  6. Experimentation
  7. Experimental Setup and ECT Dataset
  8. Evaluation Metrics
  9. Evaluation Results
  10. Qualitative Results on Simulation Test Dataset
  11. Experiments on contaminated data
  12. Results of Nonexistent Flow Patterns in the Training Dataset
  13. Testing with Real Data
  14. Conclusions

Figures (10)

  • Figure 1: ECT sensor with 12 electrodes
  • Figure 2: Architecture of CGAN-ECT model
  • Figure 3: Samples of different flow patterns
  • Figure 4: Training and validation loss curves
  • Figure 5: Box plots of Relative Image Errors (IE)
  • ...and 5 more figures