# Image Reconstruction Using Supervised Learning in Wearable Electrical Impedance Tomography of the Thorax

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## Abstract

**:**

## 1. Introduction

#### The Aim of the Work

## 2. Machine Learning Approach in CCEIT

#### 2.1. Model of the Human Thorax

#### 2.2. Measurement Simulation in Electrical Capacitively Coupled Electrical Impedance Tomography

#### 2.3. Training Dataset

- The training set contained 9375 samples from each class and 44,000 samples with random ellipses, for a total of 194,000 samples. During training, this set was randomly split on the fly into learning and validation subsets with a ratio of 75:25.
- The test set contained 2500 samples from each class and 2500 samples with random ellipses, for a total of 42,500 samples.

#### 2.4. ANN Architecture Used

#### 2.5. Reconstruction Quality Assessment

#### 2.6. Image Diagnostical Value Evaluation Using ANN Classifier

## 3. Results

- The linear back projection (LBP) given by$$\epsilon ={\epsilon}_{min}+{\tilde{S}}^{T}{c}_{n},$$
- The pseudoinverse with Tikhonov regularization (TPINV) given by$$\epsilon ={\left({S}^{T}S+\alpha I\right)}^{-1}{S}^{T}{c}_{n}.$$

^{−9}to achieve the best possible results.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Model of a transversal slice of a human thorax with lungs, heart, aorta (A), and spine (S) (

**a**). Model of both lungs regionally affected by pneumothorax (

**b**), pleural effusion (

**c**), and hydropneumothorax (

**d**). Pneumothorax and pleural effusion regions are shown, respectively, in blue and red.

**Figure 2.**Dataset samples: capacitance measurements (log scale), normalized capacitance measurements (linear scale), and corresponding conductivity distribution.

**Figure 5.**cGAN generator architecture: K—convolutional block, DK—deconvolutional block, CV—convolutional layer, L—linear layer.

**Figure 6.**cGAN discriminator architecture: K—convolutional block, CV—convolutional layer, L—linear layer.

**Figure 9.**Conductivity in a thorax slice: (

**a**) healthy lungs; (

**b**) both lungs affected by pneumothorax; (

**c**) both lungs affected by pleural effusion; (

**d**) lungs affected by hydropneumothorax; (

**e**) random ellipses in the thorax. From left to right: ground truth image; image reconstructed by FCNN, cGAN, LBP, and TPINV.

**Figure 10.**Conductivity in a thorax slice reconstructed by FCNN for different level of noise added to measurements in training and testing datasets.

**Figure 11.**Conductivity in a thorax slice reconstructed by cGAN for different level of noise added to measurements in training and testing datasets.

**Figure 12.**Distribution of the image quality norm for the elements of the testing dataset: (

**a**) RMSE, (

**b**) PSNR, (

**c**) SSIM, and (

**d**) 2D correlation. Image reconstruction methods: FCNN (red dashed line), cGAN (blue solid line), LBP (black dotted line), pseudoinverse with Tikhonov regularization (TPINV) (magenta dashed-dotted line).

**Figure 13.**“One-versus-rest” integral ROC curves representing the classifier performance: (

**a**) training and testing without noise, (

**b**) training and testing with noise introduction.

Healthy Lungs | Pneumothorax | Pleural Effusion | ||
---|---|---|---|---|

Inspiration | Expiration | |||

Relative permittivity | 31.6 | 67.1 | 1 | 70 |

Conductivity, S/m | 0.306 | 0.559 | 10^{−15} | 1.4 |

Component | Permittivity | Conductivity |
---|---|---|

Electrodes (metal) | 1 | 0.0643 |

Isolation (plastic) | 2 | 10^{−21} |

Spine | 10.53 | 0.0643 |

Heart, Aorta | 90.8 | 0.733 |

Fat | 12.7 | 0.068 |

**Table 3.**Image quality norms (RMSE—root-mean-square error; PSNR—peak signal-to-noise ratio; SSIM—structural similarity index; CC—2D correlation coefficient; DV—diagnostic value) for the testing dataset. SNR = 60 dB. The mean value of the norm, the median, and the standard deviation for the elements of the testing dataset.

Method | RMSE | PSNR | SSIM | CC | DV | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

µ | M | σ | µ | M | σ | µ | M | σ | µ | M | σ | AUC | |

FCNN | 14.61 | 14.49 | 5.49 | 20.37 | 20.55 | 2.92 | 0.78 | 0.79 | 0.05 | 0.96 | 0.97 | 0.05 | 0.99 |

cGAN | 8.86 | 8.17 | 4.13 | 27.06 | 27.39 | 3.07 | 0.87 | 0.87 | 0.03 | 0.98 | 0.99 | 0.03 | 0.99 |

LBP | 54.37 | 53.94 | 14.4 | 12.45 | 12.52 | 1.23 | 0.11 | 0.12 | 0.02 | 0.68 | 0.68 | 0.06 | 0.82 |

TPINV | 57.22 | 57.48 | 18.16 | 12.93 | 12.73 | 1.97 | 0.19 | 0.19 | 0.02 | 0.62 | 0.63 | 0.1 | 0.77 |

**Table 4.**Image quality norms (RMSE—root-mean-square error; PSNR—peak signal-to-noise ratio; SSIM—structural similarity index; CC—2D correlation coefficient; DV—diagnostic value) for the testing dataset with Gaussian noise added to measurements during training and testing. The mean value of the norm, the median, and the standard deviation for the elements of the testing dataset.

Method | RMSE | PSNR | SSIM | CC | DV | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

µ | M | σ | µ | M | σ | µ | M | σ | µ | M | σ | AUC | |

Training—no noise, Testing—30 dB SNR | |||||||||||||

FCNN | 14.84 | 14.76 | 5.53 | 20.44 | 20.66 | 3.02 | 0.78 | 0.79 | 0.05 | 0.96 | 0.97 | 0.05 | 0.99 |

cGAN | 9.45 | 8.96 | 4.37 | 26.9 | 27.17 | 2.96 | 0.87 | 0.87 | 0.03 | 0.98 | 0.99 | 0.03 | 0.99 |

Training—no noise, Testing—10 dB SNR | |||||||||||||

FCNN | 62.51 | 61.18 | 14.17 | 11.2 | 11.22 | 1.83 | 0.48 | 0.48 | 0.05 | 0.68 | 0.7 | 0.13 | 0.79 |

cGAN | 18.00 | 17.36 | 7.37 | 21.67 | 22.01 | 3.67 | 0.81 | 0.82 | 0.04 | 0.95 | 0.96 | 0.06 | 0.97 |

Training—30 dB SNR, Testing—30 dB SNR | |||||||||||||

FCNN | 15.01 | 14.92 | 5.52 | 20.28 | 20.5 | 2.97 | 0.77 | 0.79 | 0.05 | 0.96 | 0.97 | 0.05 | 0.99 |

cGAN | 9.58 | 9.07 | 4.43 | 26.8 | 27.06 | 2.98 | 0.87 | 0.87 | 0.03 | 0.98 | 0.99 | 0.03 | 0.99 |

Training—30 dB SNR, Testing—10 dB SNR | |||||||||||||

FCNN | 27.55 | 27.13 | 6.61 | 14.96 | 15.12 | 2.38 | 0.64 | 0.65 | 0.06 | 0.89 | 0.91 | 0.08 | 0.94 |

cGAN | 17.54 | 16.86 | 7.29 | 22.03 | 22.41 | 3.74 | 0.82 | 0.82 | 0.04 | 0.95 | 0.97 | 0.06 | 0.97 |

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## Share and Cite

**MDPI and ACS Style**

Ivanenko, M.; Smolik, W.T.; Wanta, D.; Midura, M.; Wróblewski, P.; Hou, X.; Yan, X.
Image Reconstruction Using Supervised Learning in Wearable Electrical Impedance Tomography of the Thorax. *Sensors* **2023**, *23*, 7774.
https://doi.org/10.3390/s23187774

**AMA Style**

Ivanenko M, Smolik WT, Wanta D, Midura M, Wróblewski P, Hou X, Yan X.
Image Reconstruction Using Supervised Learning in Wearable Electrical Impedance Tomography of the Thorax. *Sensors*. 2023; 23(18):7774.
https://doi.org/10.3390/s23187774

**Chicago/Turabian Style**

Ivanenko, Mikhail, Waldemar T. Smolik, Damian Wanta, Mateusz Midura, Przemysław Wróblewski, Xiaohan Hou, and Xiaoheng Yan.
2023. "Image Reconstruction Using Supervised Learning in Wearable Electrical Impedance Tomography of the Thorax" *Sensors* 23, no. 18: 7774.
https://doi.org/10.3390/s23187774