# Efficient Underground Target Detection of Urban Roads in Ground-Penetrating Radar Images Based on Neural Networks

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## Abstract

**:**

## 1. Introduction

## 2. Theory and Method

#### 2.1. Detection Model of GPR

#### 2.2. Detection Method

#### 2.2.1. Preprocessing

_{1}-norm of the matrix (the sum of the absolute values of matrix entries), $\lambda $ is a positive regularization parameter, and s.t. is the abbreviation of “subject to”.

#### 2.2.2. Feature Extraction of A-Scan Signals

- (1)
- Mean absolute deviation

- (2)
- Standard deviation

- (3)
- Fourth root of the fourth moment

#### 2.2.3. Target Horizontal Region Recognition

_{k}is the number of neurons in the kth layer, $f(\u2981)$ is the activation function, ${w}_{ij}$ is the weight, and ${b}_{k,j}$ is the bias.

- Training set construction. Km1 A-scan signals with target reflections and kn1 A-scan signals without target reflections are selected from the B-scan images for training, and three features of each selected A-scan signal are extracted. Then, the features are normalized to construct the training set TR1, including km1 positive samples and kn1 negative samples. The output of the positive sample is set to [1 0], and the output of the negative sample is set to [0 1].
- Network training. The training set TR1 is used to train the designed BP neural network, and the network model NET1 is obtained.
- Horizontal region recognition. The three features of all A-scan signals in the test B-scan image are extracted and normalized to construct the test set TE1. Then, the model NET1 is used to classify the samples in TE1. Assuming that K1 samples are identified as positive samples, the corresponding A-scan signals can be written as ${x}_{i}\left({i=i}_{1},{i}_{2},\cdots ,{i}_{K1}\right)$. Then, the target horizontal regions can be denoted as $H1=\left\{{i}_{k}\Delta d,1\le k\le K1\right\}$, where $\Delta d$ is the trace interval.

#### 2.2.4. Optimization of Target Horizontal Regions

- Fusion processing. Fusion processing refers to further judgment for non-target A-scan signals between two adjacent target regions, which aims to reduce the false negative rate (missing detection). The judgment can be expressed as$$\{\begin{array}{l}{x}_{i}is{\mathit{the}\mathit{target}\mathit{signal},\hspace{1em}\hspace{1em}\hspace{1em}1i}_{k+1}-{i}_{k}\le dth/\Delta d\\ {x}_{i}is\mathit{the}\mathit{non}-\mathit{target}\mathit{signal},\mathit{else}\end{array}$$

- 2.
- Deletion processing. Deletion processing further judges the target horizontal regions after fusion processing, which aims to decrease the false positive rate (false detection). The judgment can be represented as$$\{\begin{array}{l}{x}_{i}is{\mathit{the}\mathit{non}-\mathit{target}\mathit{signal},\hspace{1em}i}_{k}-{i}_{1}=k-1\le wth/\Delta d\\ {x}_{i}is\mathit{the}\mathit{target}\mathit{signal},\hspace{1em}\hspace{1em}\hspace{1em}else\end{array}$$

#### 2.2.5. Feature Extraction of Segmented A-Scan Signals

- (1)
- Mean absolute deviation

- (2)
- Standard deviation

- (3)
- Fourth root of the fourth moment

#### 2.2.6. Target Vertical Region Recognition

- Training set construction. Km2 segments with target reflections and kn2 segments without target reflections are selected from the segmented A-scan signals for training, and three features of each selected segment are extracted. Then, the features are normalized to construct the training set TR2, including km2 positive samples and kn2 negative samples. The output of the positive sample is set to [1 0], and the output of the negative sample is set to [0 1].
- Network training. The training set TR2 is used to train the BP neural network, and the network model NET2 is obtained.
- Vertical region recognition. The three features of all segments in the optimized horizontal regions H3 of the test B-scan image are extracted and normalized to form the test set TE2. Then, the model NET2 is used to classify the samples in TE2. Assuming that ${J}_{i}$ samples are identified as positive samples in the A-scan signal ${x}_{i}\left(i={i}_{1},{i}_{2},\cdots ,{i}_{K3}\right)$, the corresponding segments can be written as $x{s}_{i}{}_{,r}\left(r={r}_{1},{r}_{2},\cdots ,{r}_{{J}_{i}}\right)$. Then, the target vertical regions in the A-scan signal ${x}_{i}$ can be denoted as $V{1}_{i}=\left\{\left[\left(({r}_{p}-1)\mathit{ml}+1\right)\Delta t,{r}_{p}\mathit{ml}\Delta t\right],1\le p\le {J}_{i}\right\}$.
- The recognized segments are arranged in the two-dimensional image, and then the final target regions can be obtained.

## 3. Results

#### 3.1. Numerical Simulations

#### 3.2. Field Experiments

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**Clutter suppression results of two methods for the simulated GPR image: (

**a**) PCA (SCR = 4.4 dB); (

**b**) RPCA (SCR = 6.6 dB).

**Figure 9.**Three features of all A-scan signals in the test image: (

**a**) mean absolute deviation; (

**b**) standard deviation; (

**c**) fourth root of the fourth moment.

**Figure 10.**Target horizontal region recognition results for the simulated GPR image: (

**a**) original horizontal regions; (

**b**) optimized horizontal regions.

**Figure 11.**Confusion matrices of target horizontal region recognition for the simulated GPR image: (

**a**) original horizontal regions; (

**b**) optimized horizontal regions.

**Figure 12.**Three features of segments in one A−scan signal: (

**a**) A−scan signal; (

**b**) mean absolute deviation; (

**c**) standard deviation; (

**d**) fourth root of the fourth moment.

**Figure 13.**Target recognition results for the simulated GPR image: (

**a**) traditional segmentation recognition method based on BP neural network; (

**b**) traditional segmentation recognition method based on SVM; (

**c**) proposed method.

**Figure 14.**Confusion matrices of the three methods for the simulated GPR image: (

**a**) traditional segmentation recognition method based on BP neural network; (

**b**) traditional segmentation recognition method based on SVM; (

**c**) proposed method.

**Figure 15.**Real GPR image: (

**a**) original image (SCR = 0.6 dB); (

**b**) image after clutter suppression (SCR = 17.5 dB).

**Figure 16.**Target horizontal region recognition results for the real GPR image: (

**a**) original horizontal regions; (

**b**) optimized horizontal regions.

**Figure 17.**Confusion matrices of target horizontal region recognition for the real GPR image: (

**a**) original horizontal regions; (

**b**) optimized horizontal regions.

**Figure 18.**Target recognition results for the real GPR image: (

**a**) traditional segmentation recognition method based on BP neural network; (

**b**) traditional segmentation recognition method based on SVM; (

**c**) proposed method.

**Figure 19.**Confusion matrices of the three methods for the real GPR image: (

**a**) traditional segmentation recognition method based on BP neural network; (

**b**) traditional segmentation recognition method based on SVM; (

**c**) proposed method.

Parameter | Value |
---|---|

Antenna central frequency | 400 MHz |

Excitation waveform | Ricker wavelet |

Time window | 20 ns |

Number of time samples | 848 |

Trace interval | 0.02 m |

Number of traces | 590 |

Model Number | Void | Metal Pipe | PVC Pipe | ||||||
---|---|---|---|---|---|---|---|---|---|

Depth | Lateral Distance | Radius | Depth | Lateral Distance | Radius (Outer/Inner) | Depth | Lateral Distance | Radius (Outer/Inner) | |

1 | 0.30 m | 3 m | 0.10 m | 0.30 m | 6 m | 0.10 m/0.05 m | 0.30 m | 9 m | 0.10 m/0.05 m |

2 | 0.50 m | 3 m | 0.10 m | 0.50 m | 6 m | 0.10 m/0.05 m | 0.50 m | 9 m | 0.10 m/0.05 m |

3 | 0.70 m | 3 m | 0.10 m | 0.70 m | 6 m | 0.10 m/0.05 m | 0.70 m | 9 m | 0.10 m/0.05 m |

4 | 0.35 m | 3 m | 0.15 m | 0.35 m | 6 m | 0.15 m/0.10 m | 0.35 m | 9 m | 0.15 m/0.10 m |

5 | 0.55 m | 3 m | 0.15 m | 0.55 m | 6 m | 0.15 m/0.10 m | 0.55 m | 9 m | 0.15 m/0.10 m |

6 | 0.75 m | 3 m | 0.15 m | 0.75 m | 6 m | 0.15 m/0.10 m | 0.75 m | 9 m | 0.15 m/0.10 m |

7 | 0.40 m | 3 m | 0.20 m | 0.40 m | 6 m | 0.20 m/0.15 m | 0.40 m | 9 m | 0.20 m/0.15 m |

8 | 0.60 m | 3 m | 0.20 m | 0.60 m | 6 m | 0.20 m/0.15 m | 0.60 m | 9 m | 0.20 m/0.15 m |

9 | 0.80 m | 3 m | 0.20 m | 0.80 m | 6 m | 0.20 m/0.15 m | 0.80 m | 9 m | 0.20 m/0.15 m |

Method | Accuracy | FPR | FNR |
---|---|---|---|

BP neural network | 87.6% | 13.8% | 8.6% |

BP neural network + FAD | 97.1% | 3.0% | 2.5% |

Method | Accuracy | FPR | FNR |
---|---|---|---|

Traditional segmentation recognition method based on BP neural network | 95.1% | 4.4% | 15.5% |

Traditional segmentation recognition method based on SVM | 96.6% | 2.6% | 20.6% |

Proposed method | 98.7% | 0.4% | 18.9% |

Method | Processing Time (s) | ||
---|---|---|---|

Clutter Suppression | Target Recognition | Total | |

Traditional segmentation recognition method based on BP neural network | 0.38 | 0.63 | 1.01 |

Traditional segmentation recognition method based on SVM | 0.38 | 0.65 | 1.03 |

Proposed method | 0.38 | 0.44 | 0.82 |

Method | Accuracy | FPR | FNR |
---|---|---|---|

BP neural network | 87.1% | 10.8% | 18.4% |

BP neural network + FAD | 94.4% | 0.8% | 18.4% |

Method | Accuracy | FPR | FNR |
---|---|---|---|

Traditional segmentation recognition method based on BP neural network | 96.8% | 2.8% | 23.3% |

Traditional segmentation recognition method based on SVM | 97.7% | 1.8% | 26.8% |

Proposed method | 99.1% | 0.3% | 28.4% |

Method | Processing Time (s) | ||
---|---|---|---|

Clutter Suppression | Target Recognition | Total | |

Traditional segmentation recognition method based on BP neural network | 0.54 | 0.93 | 1.47 |

Traditional segmentation recognition method based on SVM | 0.54 | 0.91 | 1.45 |

Proposed method | 0.54 | 0.74 | 1.28 |

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## Share and Cite

**MDPI and ACS Style**

Xue, W.; Chen, K.; Li, T.; Liu, L.; Zhang, J.
Efficient Underground Target Detection of Urban Roads in Ground-Penetrating Radar Images Based on Neural Networks. *Remote Sens.* **2023**, *15*, 1346.
https://doi.org/10.3390/rs15051346

**AMA Style**

Xue W, Chen K, Li T, Liu L, Zhang J.
Efficient Underground Target Detection of Urban Roads in Ground-Penetrating Radar Images Based on Neural Networks. *Remote Sensing*. 2023; 15(5):1346.
https://doi.org/10.3390/rs15051346

**Chicago/Turabian Style**

Xue, Wei, Kehui Chen, Ting Li, Li Liu, and Jian Zhang.
2023. "Efficient Underground Target Detection of Urban Roads in Ground-Penetrating Radar Images Based on Neural Networks" *Remote Sensing* 15, no. 5: 1346.
https://doi.org/10.3390/rs15051346