# Adversarial Resolution Enhancement for Electrical Capacitance Tomography Image Reconstruction

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## Abstract

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## 1. Introduction

- The adversarial resolution enhancement (ARE-ECT) model was developed in the problem of the ECT image reconstruction quality improvement.
- The proposed model aimed to predict enhanced ECT image reconstructions from the lower quality ones.
- Our CGAN-based approach produces qualitative and quantitative improved results in ECT image resolution better than current complex and time-consuming non-linear reconstruction algorithms.

## 2. Problem Statement

## 3. Deep Neural Network Models

#### 3.1. GAN

#### 3.2. CGAN

## 4. ARE-ECT Model

## 5. ECT Dataset

## 6. Experimental Results and Analysis

#### 6.1. Validation Metrics

#### 6.2. Qualitative Results on Simulation Test Dataset

#### 6.3. Testing Results of Non-Existing Phantoms in Training Dataset

#### 6.4. Evaluation Using Experimental Data

#### 6.5. Computational Time Measure

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CT | Computed Tomography |

ECT | Electrical Capacitance Tomography |

ARE-ECT | Adversarial Resolution Enhancement |

ILM | Iterative Landweber Method |

LBP | Linear Back Projection |

ML | Machine Learning |

DNN | Deep Neural Networks |

DL | Deep Learning |

CNN | Convolutional Neural Network |

LSTM | Long Short-Term Memory |

CANN | Capacitance Artificial Neural Network |

GCN | Graph Convolutional Networks |

GAN | Generative Adversarial Network |

CGAN | Conditional Generative Adversarial Network |

LW | Landweber Algorithm |

IE | Image Error |

CC | Correlation Coefficient |

LSTM-IR | Long Short-Term Memory Image Reconstruction |

LETKF | Local Ensemble Transform Kalman Filter |

ECVT | Electrical Capacitance Volume Tomography |

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**Figure 4.**Samples of different flow patterns. (

**a**) Ring, (

**b**) annular, (

**c**) stratified, (

**d**) 1 cir. bar, (

**e**) 2 cir. bars, (

**f**) 3 cir. bars, (

**g**) sq. bar, (

**h**) 2 sq. bars, (

**i**) 3 sq. bars.

**Figure 6.**Box plots of testing criterion. (

**a**) Relative image errors (ie), (

**b**) correlation coefficients (CC).

GAN | CGAN | |
---|---|---|

Input | Latent vector | Random and auxiliary data |

Output | Classify as real or generated | Classify labeled data as real or generated |

Type | Unsupervised | Supervised |

Data | No control over data | Conditional data |

Flow Patterns | Min. IE | Max. IE | Average IE | Min. CC | Max. CC | Average CC |
---|---|---|---|---|---|---|

Annular | 0.0219 | 0.2864 | 0.1160 | 0.9736 | 1.0000 | 0.9921 |

Ring | 0.0562 | 0.3704 | 0.1781 | 0.9165 | 0.9980 | 0.9770 |

Stratified | 0.0000 | 0.1395 | 0.0694 | 0.9907 | 1.0000 | 0.9970 |

Single Cir. Bar | 0.0173 | 0.1276 | 0.0712 | 0.9819 | 1.0000 | 0.9923 |

Multiple Cir. Bars | 0.0308 | 0.2178 | 0.1288 | 0.9639 | 0.9985 | 0.9845 |

Single Sq. Bar | 0.0000 | 0.1329 | 0.0415 | 0.9868 | 1.0000 | 0.9965 |

Multiple Sq. Bars | 0.0000 | 0.2512 | 0.1086 | 0.9390 | 1.0000 | 0.9803 |

Total Average | IE | 0.1019 | CC | 0.9884 |

Flow | LBP | Tikhonov | ILM | CNN | LSTM-IR | ARE-ECT | |
---|---|---|---|---|---|---|---|

Relative Image Error (IE) | Annular | 0.2412 | 0.1950 | 0.3351 | 0.1222 | 0.0561 | 0.0687 |

Ring | 0.3776 | 0.1216 | 0.2984 | 0.2107 | 0.0989 | 0.0941 | |

Stratified | 0.2590 | 0.6953 | 0.3203 | 0.3365 | 0.2032 | 0.1994 | |

Cir. Bar | 0.3923 | 0.6562 | 0.6575 | 0.2224 | 0.1420 | 0.0821 | |

2 Cir. Bars | 0.4568 | 0.6638 | 0.4038 | 0.3274 | 0.1445 | 0.0990 | |

3 Cir. Bars | 0.6083 | 0.7492 | 0.4275 | 0.4765 | 0.2043 | 0.0940 | |

Sq. Bar | 0.3677 | 0.5841 | 0.6575 | 0.2490 | 0.2122 | 0.0991 | |

2 Sq. Bars | 0.4988 | 0.3449 | 0.3294 | 0.3176 | 0.2415 | 0.1653 | |

3 Sq. Bars | 0.5112 | 0.6070 | 0.6909 | 0.4999 | 0.2558 | 0.0528 | |

Correlation Coefficient (CC) | Annular | 0.8701 | 0.8885 | 0.9084 | 0.9590 | 0.9913 | 0.9864 |

Ring | 0.8110 | 0.9792 | 0.9576 | 0.9396 | 0.9857 | 0.9870 | |

Stratified | 0.9126 | 0.4232 | 0.9100 | 0.8200 | 0.9401 | 0.9587 | |

Cir. Bar | 0.6964 | 0.7754 | 0.7974 | 0.8860 | 0.9541 | 0.9850 | |

2 Cir. Bars | 0.6681 | 0.8565 | 0.7963 | 0.8060 | 0.9640 | 0.9823 | |

3 Cir. Bars | 0.5498 | 0.5652 | 0.7625 | 0.7325 | 0.9363 | 0.9862 | |

Sq. Bar | 0.8442 | 0.8264 | 0.6575 | 0.8997 | 0.9277 | 0.9850 | |

2 Sq. Bars | 0.7041 | 0.8326 | 0.8663 | 0.8527 | 0.9161 | 0.9617 | |

3 Sq. Bars | 0.5099 | 0.6361 | 0.5688 | 0.6668 | 0.8707 | 0.9951 |

Phantom | IE | CC |
---|---|---|

1 | 0.2601 | 0.9049 |

2 | 0.1847 | 0.9427 |

3 | 0.2761 | 0.8909 |

4 | 0.2816 | 0.8852 |

LBP | Tikhonov | ILM | LETKF | CNN | LSTM-IR | ARE-ECT |
---|---|---|---|---|---|---|

0.026 | 5.326 | 6.245 | 1.310 | 0.085 | 0.052 | 0.046 |

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**MDPI and ACS Style**

Deabes, W.; Abdel-Hakim, A.E.; Bouazza, K.E.; Althobaiti, H. Adversarial Resolution Enhancement for Electrical Capacitance Tomography Image Reconstruction. *Sensors* **2022**, *22*, 3142.
https://doi.org/10.3390/s22093142

**AMA Style**

Deabes W, Abdel-Hakim AE, Bouazza KE, Althobaiti H. Adversarial Resolution Enhancement for Electrical Capacitance Tomography Image Reconstruction. *Sensors*. 2022; 22(9):3142.
https://doi.org/10.3390/s22093142

**Chicago/Turabian Style**

Deabes, Wael, Alaa E. Abdel-Hakim, Kheir Eddine Bouazza, and Hassan Althobaiti. 2022. "Adversarial Resolution Enhancement for Electrical Capacitance Tomography Image Reconstruction" *Sensors* 22, no. 9: 3142.
https://doi.org/10.3390/s22093142