Construction Environment Noise Suppression of Ground-Penetrating Radar Signals Based on an RG-DMSA Neural Network

Abstract

Ground-penetrating radar (GPR) is often used to detect targets in a construction environment. Due to the different construction environments, the noise exhibits different characteristics on the GPR signal. When the noise is widely distributed on the GPR signal, and its spectrum and the spectrum of the active signal are aliased, it is difficult to separate and suppress the noise by traditional filtering methods. In this paper, we propose a deep learning GPR image noise suppression method based on a recursive guided and dual multi-scale self-attention mechanism neural network (RG-DMSA-NN), which uses a recursive guidance module and a dual multi-scale self-attention mechanism module to improve the feature extraction ability of the image and enhance the robustness and generalization ability in image noise suppression. Through the application of noise suppression on the synthesized test data and the GPR data actually collected by the Macao Science and Technology Museum, the advantages of this method over the traditional filtering, DnCNN and UNet noise suppression methods are demonstrated.

1. Introduction

Electromagnetic waves can be used for space, surface, and shallow underground target detection. Typical radars for air and surface detection include deep space detection radar, early-warning radar, navigation radar, search radar, and radar satellite SAR. A typical radar for the detection of shallow underground targets is called ground-penetrating radar (GPR). Due to the advantages of high resolution, high efficiency, and non-destructive detection imaging, ground-penetrating radar is widely used in underground engineering target detection or disaster detection assessment [1,2,3,4]. The mainstream ground-penetrating radar adopts the time pulse electromagnetic wave signal transmission and reception mode; the electromagnetic wave signal reflected by the underground target can image the position and geometry of the underground target well on the radar signal profile, and the ground-penetrating radar signal carries the physical property information of the underground medium, which can be inverted and interpreted for the data, and then the physical information of the underground medium is obtained, which is of great value for engineering construction or disaster assessment.

The application scenario of GPR is often in engineering and construction environments. In this environment, the heterogeneity of underground medium, ferromagnetic substances, construction machinery, electronic equipment, and other sensors can interfere with the GPR signal, and the noise generated by the interference is widely distributed and the frequency band is wider, which has a great impact on the quality of the signal, reduces the signal-to-noise ratio, and has a negative impact on the geometric characteristics and physical information of the detection target carried by the signal. In order to improve the signal-to-noise ratio of GPR, noise suppression has always been a difficult point in the field of GPR signal processing.

In terms of background noise suppression technology in GPR, domain filtering is the most commonly used signal noise suppression method that processes stable signals and has a fixed noise spectrum distribution. This method is less effective at suppressing GPR noise for nonlinear and nonstationary signals [5,6]. Techniques such as median filtering, F-K (or F-X) filtering, and wavelet transform filtering have been used to suppress noise on GPR signals, and some progress has been made in local feature filtering compared with the Fourier transform [7,8]. Although these methods overcome the smoothing effect of the Fourier transform on high-frequency signals and protect the high-frequency characteristics of the signal, there are still some shortcomings. For example, the F-K (or F-X) filter method is more suitable for linear noise suppression, and the requirements for artificially selected parameters are high. Median filtering uses the gray values of the pixels to be processed and their neighbors in the GPR signal to be arranged in order of size, and the median value is taken instead of the gray value of the original pixel, which is not completely suppressed for noise, especially in areas where there is noise and effective subtle signal aliasing [9]. The wavelet coefficients in wavelet transform filtering produce aliasing, and the reconstructed signal coefficients will have spurious artificial effects [10,11]. In order to overcome the signal distortion problem caused by wavelet transform, the double-tree complex wavelet transform and curved wave transform filtering methods were proposed in GPR noise suppression. Although the DTCWT has approximate translational invariance, it is still highly sensitive to noise, and in noisy GPR signals, the reliability and stability of the DTCWT are compromised [12,13]. As a multi-scale analysis tool, curvelet transform filtering has better direction selectivity, but due to the placement of wavelet coefficients in specific directions and scales, unnatural traces or noise appear during image or signal reconstruction, which affects the edge smoothness of the GPR in-phase axis, resulting in jagged or blurred conditions, which is not suitable for GPR signal noise suppression where the actual noise is widely distributed and the effective signal reflection is more complex [14,15]. Although the non-subsampled shearlet transform (NSST) has achieved certain results in GPR signal denoising, it is only based on the transformation domain and ignores the image structure information in the spatial domain, which often leads to the loss of fine features of the reflected signal [16,17,18,19].

In recent years, with the application of deep learning technology in the field of image processing, some scholars have begun to study the research on GPR image noise suppression based on deep learning technology. Deep learning is an intelligent and effective noise attenuation method that can use mapping relationships to separate valid signals from noise recordings without prior knowledge and parameter fine tuning [9,20,21]. In terms of clutter suppression, Takanori proposed a denoising method based on reflectivity-consistent sparse blind deconvolution [22], and Ni et al. studied a method to suppress radar clutter using an improved robust autoencoding technique, which is stronger than the low-complexity clutter removal method for GPR images based on raster filters [23]. He et al. proposed a random noise suppression method for GPR data using a deep neural network, the NSST-UNET network, which verified the effectiveness of deep learning on GPR data [24,25]. Li and Feng et al. investigated an improved K-SVD dictionary learning method to suppress random noise on GPR images [26]. Huang et al. proposed a multi-noise self-supervised denoising model, MNSSDN, for GPR image denoising, which is mainly used for the suppression of composite noise [7]. In order to solve the problem of the deep learning training set and training cost, Dai et al. studied a method of unsupervised learning based on a Generative Adversarial Network (GAN) to suppress the noise of ground-penetrating radar and achieved certain results [27]. Liu et al. proposed a UNet-based method for suppressing interference in railway sleepers and achieved certain results [28]. The current research and application of deep learning-based methods for GPR data noise suppression have a special application background; for example, suppressing clutter interference, railway sleeper interference, Gaussian white noise, and scattered noise. These special types of noise features are relatively simple and obvious, and the effective signal wavefield is not complex. In network training, the characteristics of noise and effective signals are easier to capture. However, when collecting GPR data in engineering construction environments, the noise characteristics in the signal are complex, and the effective signal reflection characteristics are diverse. Both noise and noise-contaminated effective signals display complex signal and wavefield characteristics. The effectiveness of conventional networks may degrade when coping with complex GPR data with construction environment background noise owing to their simple network architecture. In summary, the traditional domain transformation method has limited denoising effect when the noise distribution is wide and the effective reflected signal wave field is complex. Noise and effective signal aliasing of GPR signals in the construction environment. The existing research on image noise suppression methods based on convolutional neural networks is relatively blank in both the establishment of construction environment noise training models and the testing of measured data. To achieve better noise attenuation ability, we propose a suppression method for GPR data containing construction environmental noise based on a recursive guided and dual multi-scale self-attention mechanism neural network (RG-DMSA-NN) in this paper. This method optimizes the feature representation ability and stability of the network and uses a multi-scale attention mechanism to enhance the robustness and diversity of GPR data feature extraction. The advantages and effectiveness of the method were proved by noise suppression processing of synthetic test data and GPR data detected by coastal subgrade disease engineering detection at the Macao Science and Technology Museum.

2. Materials and Methods

2.1. Architecture of the RG-DMSA-NN

A convolutional neural network is a deep learning model that is commonly used to process image data. Its network structure includes a convolutional layer, a pooling layer, and a fully connected layer through which image features can be effectively extracted and tasks, such as classification and recognition, can be realized. Convolutional neural networks have the characteristics of translational invariance and local connectivity, which make them have good performance and efficiency when processing image data.

In this paper, we propose a recursive guided and dual multi-scale self-attention enhancement network (RG-DMSA-NN) for suppressing the noise of GPR signals in the construction environment. The RG-DMSA-NN adopts a recursive guidance block in the residual encoder–decoder part to increase features of different sizes and retains the original features by skipping connections so as to improve the feature representation ability and stability of the network. At the same time, in the part of the self-attention mechanism, the large-size weights and small-size features are enhanced through the different scale processing of the two branches so as to improve the feature representation ability at different scales. As shown in Figure 1, the RG-DMSA-NN is a recursively guided dual multi-scale network, which consists of an encoder–decoder (ED) block, a hop connection, a recursive guidance (RG) block, a dual multi-scale self-attention mechanism (DMSA) block, and a convolutional (Conv) block.

The front leg of the RG-DMSA-NN network consists of an encoder–decoder, a hopping connection, and a recursive guide block. The encoder–decoder block (ED) at the front end of the network consists of four convolution blocks and three deconvolution blocks, which are used for feature extraction and reconstruction. Use three hop connections to enhance gradient flow and solve the problem of vanishing gradients. At the same time, two recursive guidance blocks are used to capture contour information and smooth fine noise through downsampling operation steps. Then, they are combined with the features extracted in the front segment of the network to improve the accuracy of feature extraction. The empty convolution in the convolution block of the encoder–decoder part can expand the receptive field without changing the size of the feature map so that the network can effectively deal with a wide range of noise, reduce the number of parameters, and increase the computational efficiency. Deconvolution blocks are used to recover input details and reduce information loss. Hop connections transmit shallow and shallow information to deeper and deeper layers, which are used to mitigate gradient vanishing and improve the training speed and effectiveness of the network. In addition, the recursive guidance block (RG Block) consists of two downsampling blocks, one simple convolutional block, and one upsampling block, and the method uses low-scale information to guide the feature extraction of the backbone convolution and deconvolution blocks of the network and improves the network efficiency by combining the information captured by different receptive fields.

The backend of the RG-DMSA-NN network is composed of a DMSA block and a convolutional block of two multi-scale processing blocks. The DMSA block can process both local and global information, enabling potential feature fusion. The block utilizes different multi-scale architectures and feature fusion to enhance feature extraction capabilities. The DMSA block consists of two branches; the upper branch is the contraction and expansion path, and the lower branch is the expansion and contraction path. In the upper branch, the input features are first downsampled, put through two convolution blocks, and then upsampled and added to the features of the lower branch. The lower branch consists of a cascade of upsampling, two convolution blocks, and downsampling. Its input features are the opposite of the upper branch. The input features are first upsampled, put through two convolution blocks, and then downsampled and added to the upper branch features. In this way, the detailed features of the image can be fully extracted so that some subtle features can be better preserved and expressed. The function of the lower branch is to recover the lost detail information when the features are extracted by the front-end network, increasing the amount of information and improving the feature weight at this scale.

The purpose of multi-scale feature fusion is to enhance the feature representation, retain the weight of the original input feature, and prevent the gradient from disappearing. Then, the new features are extracted by convolution to improve the robustness of the features, and then the weights are calculated by the Softmax activation function and then multiplied by the input features of the DMSA block to form a double multi-scale self-attention mechanism (DMSA) block. Finally, the output result is obtained after the convolutional block (Conv Block), which is used to reassemble and enhance the extracted features, improve the diversity and richness of features, and improve the robustness and generalization ability of the network.

2.2. The Specific Blocks of the RG-DMSA-NN

2.2.1. Encoder–Decoder (ED) Block

Encoders and decoders are commonly used constructs in neural networks to handle sequence-to-sequence tasks. The RG-DMSA-NN network backbone is an encoder–decoder structure, where the encoder consists of four convolution blocks and the decoder consists of three deconvolution blocks. The convolution block in the encoder consists of a 3 × 3 convolutional layer, a 3 × 3 void convolutional layer, and the ReLU activation function, and in the decoder, the deconvolution block consists of a 3 × 3 deconvolution layer and the ReLU activation function. The encoder converts the input data into high-level feature representations through a series of convolution operations for feature extraction and nonlinear transformation. The decoder, on the other hand, reconstructs the input data while keeping the size of the feature map constant. This structure enables the accuracy and efficiency of the task by effectively learning the characteristics of the input data and generating the output data corresponding to it. In addition, the outputs of the encoder and decoder were used for the subsequent dual multi-scale self-attention mechanism to further extract features and optimize the model performance.

2.2.2. Hop Connection

The hop connection refers to a technique in a neural network in which the input of one layer is directly connected to the output of the subsequent layer. It can improve the performance and efficiency of the model by increasing the depth of the network and helping information flow between different layers. The formula for a jump connection is as follows:

$$\mathit{Output}=x+\mathit{Conv}\left(x\right)$$

(1)

where x is the input before the hop connection and $\mathit{Conv}$ is the convolution operation. This formula directly adds the input to the output after the convolution operation to obtain the output after the jump connection. The hop connection allows the model to directly exploit the original features of the inputs, helping to mitigate the vanishing gradient problem and improve the performance of the model.

2.2.3. Recursive Guided (RG) Block

The idea of this block is derived from the recursive bootstrap approach. The core idea is to use low-scale information to guide feature extraction in the encoder–decoder part of the backbone network. This enhances the ability of feature extraction and progressively extracts more advanced and complex features over multiple iterations. The advantage of this approach is to improve the efficiency of the network by integrating information from different receptive fields. Theoretically, the basic formula for the recursive bootstrap method is as follows:

$$H_{recur}^{\left(t+1\right)}=f_{recur}\left(H_{recur}^{\left(t\right)},X\right)$$

(2)

where $H_{recur}^{\left(t\right)}$ represents the output feature representation of the recursive boot block after the t iteration and X is the input feature representation from the backbone network. $f_{recur}$is a recursive function, which combines the output feature representation $H_{recur}^{\left(t\right)}$ of the current block with the input feature representation X to calculate the output feature representation $H_{recur}^{\left(t+1\right)}$of the block after the next iteration.

2.2.4. DMSA Block

The multi-scale self-attention mechanism can effectively enhance the robustness and diversity of feature extraction. The following is a basic representation of the double multi-scale self-attention mechanism combined with a mathematical formula.

The input feature represents the following. Let the input feature of the DMSA block be $X$ and its shape be $\left(N,d\right)$, where $N$ is the number of features and $d$ is the feature dimension. The input feature $X$ is convoluted at different scales to obtain multi-scale feature representations $X_1$ and $X_2$.

The upper path is downsampled first, activated by two 3 × 3 convolutions, and then upsampled to obtain multi-scale features $X_1$ as follows:

$$X_1=\mathrm{Upsample}\left(\mathit{Re}LU\left(\mathrm{Con}{\mathrm{v}}_{3\times 3}\left(\mathit{Re}LU\left(\mathrm{Con}{\mathrm{v}}_{3\times 3}\left(\mathrm{Downsample}\left(X\right)\right)\right)\right)\right)\right)$$

(3)

The down path is upsampled first, put through two 3 × 3 convolutions and activations, and then downsampled to obtain the multi-scale feature $X_2$ as follows:

$$X_2=\mathrm{Downsample}\left(\mathit{Re}LU\left(\mathrm{Con}{\mathrm{v}}_{3\times 3}\left(\mathit{Re}LU\left(\mathrm{Con}{\mathrm{v}}_{3\times 3}\left(\mathrm{Upsample}\left(X\right)\right)\right)\right)\right)\right)$$

(4)

Multi-scale feature fusion and processing: The two multi-scale features are added together and then spliced with the input features $X$ of the DMSA module, and then the fusion features are obtained $X_{fused}$ through a 3 × 3 convolution as follows:

$$X_{fused}=\mathrm{Con}{\mathrm{v}}_{3\times 3}\left(\mathrm{Concat}\left(\left(X_1+X_2\right),X\right)\right)$$

(5)

Self-attention mechanism: The self-attention mechanism $X_{fused}$is applied to the fusion feature, and the attention weight and output are calculated. Linear transformations are as follows:

$$\begin{array}{c}Q=X_{fused}{W}_q\\ K=X_{fused}{W}_k\\ V=X_{fused}{W}_v\end{array}$$

(6)

where $Q$, $K$, and $V$ are the query matrix, key matrix, and value matrix, respectively. $W_q$, $W_k$, and $W_v$ are trainable weight matrices. The attention weight calculation is as follows:

$$A=\mathrm{Softmax}\left(X_{fused}\right)=\mathrm{Softmax}\left({\displaystyle \frac{Q{K}^T}{\sqrt{d_k}}}\right)$$

(7)

where $A$ is the attention weight matrix and $d_k$ is the dimension of the key matrix. The formula for calculating attention output is as follows:

$$X_{attention}=AX$$

(8)

In the multi-scale self-attention mechanism, the input feature $X$ is processed at different scales first. The upper path is downsampled first, put through two 3 × 3 convolutions and activations, and then upsampled, and the multi-scale feature $X_1$ is obtained. The down path is upsampled first, put through two 3 × 3 convolutions and activations, and then downsampled to obtain the multi-scale feature $X_2$.

Add the two multi-scale features together. Then, they are spliced with the input feature $X$ of the DMSA module to calculate the attention weight without losing the original input feature weight, and then through the 3 × 3 convolution, the fusion feature $X_{fused}$ is formed. Then, the self-attention mechanism is applied to the fusion features, and the query matrix $Q$, key matrix $K$, and value matrix $V$ are obtained through linear transformation. The attention weight matrix $A$ is calculated, and the attention output $X_{attention}$ is generated. This process essentially weights the input features through the attention mechanism, emphasizing important feature information.

2.3. Training Dataset

The resolution of the measured GPR signal in engineering construction is high. The radar signal features include layered reflections of different intensities caused by the stratification of underground strata, arc curve reflection caused by cavities, diffraction caused by target bodies, and multiple waves. The process of noise suppression in deep learning networks mainly relies on the network model to learn a large amount of radar signal emission characteristics and noise features, so the image features of the training dataset mainly need to include rich reflected signals similar to the measured data and construction environment noise distributed in the measured data. The raw GPR signals are obtained through finite difference numerical simulations. The GPR image simulated numerically exhibits various reflection wavefield characteristics. These GPR images are raw clean signals without added noise. The noise data were obtained from the measured GPR data of coastline road diseases at the Macao Science and Technology Museum. These noise data are the data detected in this real application. We intercepted the part of the measured data where only the noise data exist and then edited the noise data repetitively to increase their horizontal and vertical spread so that they can cover the raw clean signal fully. In this way, training data with full coverage of actual noise can be produced for neural network training. Figure 2 shows a partial set of training and validation datasets. Figure 2a is the raw signal without added noise. The GPR signal image contains typical layered signal features with different reflection intensities (red arrows), undulating strata signal features (green arrows), and target signal reflection features (blue boxes). Figure 2b shows the addition of measured noise GPR data in the construction environment. It can be seen that noise drowns out some of the valid signal features with weak signal strengths. Figure 2c shows the noise data measured in the construction environment. These data are only a small part of the data used to make the training and validation sets, and there is also a large amount of data containing a variety of reflection features of various GPR signals that are used in neural network training.

In this neural network model training, we made 7497 pairs of training samples containing rich GPR signal reflection features, in which the noise in the noise data comes from the noise data in the measured data, which increase the generalization ability of the network.

Figure 3 illustrates the process of making data slices. In order to show the slicing process of the image more clearly, the test data in Figure 3 use a 128 × 128-pixel size image and use the slicing method with a horizontal step size of 1 and a vertical step size of 64 to obtain the dataset slices. The sliced data on the right are a slice of each dashed box in the test data on the left. The training and validation datasets were obtained by sliding and slicing all the data. Figure 3 shows the noise-free clean data slice and the corresponding noisy data slice.

2.4. Training Progress and Experimental Environment

In this study, the experimental environment was an Intel(R) Xeon(R) CPU E5-2640 v4 @ 2.40 GHz with 64.0 GB of RAM and an NVIDIA Quadro P2000 (Santa Clara, CA, USA). The model uses the ADAM optimizer, the learning rate ranges from 10⁻³ to 10⁻⁶, and the batch size ranges from 1 to 16, with a total of 50 training rounds. The dataset is divided into a training set, a validation set, and a test set at an 8:1:1 ratio to evaluate the generalization performance of the model. This data preparation and training process helps the model learn the features in the GPR images and classify them accurately.

Table 1. Network parameters of the RG-DMSA-NN.

Hyper-Parameter	Specification
Optimizer	ADAM
Patch size	64 × 64
Batch size	1–16
Epoch number	50
Learning rate range	[10−3, 10−6]
Input channels	1
Total layers	19
Convolution kernel size	2 × 2, 3 × 3 or 4 × 4
Convolution kernel channel	1, 16, 32 or 64

lists the network parameters of the RG-DMSA-NN, and

Table 2. Training Process.

Require: B, the batch size, E, the epoch number, T, the training set, V, the validation set, TEST, the test set, c, the clean datasets, n, the noisy datasets, Loss, calculate loss, Root Mean Square Error or Peak Signal-to-Noise Ratio.

1. For E = 1, 2, 3, ……, E do

2.   For B in T do

3.      Tout = Model (Tn)

4.      Loss = Loss (Tc, Tout)

5.      Optimizer = ADAM

6.   VALLoss = Loss (Vc, Model (Vn))

7. Tuning parameters.

8. TESTLoss = Loss (TESTc, Model (TESTn))

describes the training process. The training set is input into the model, the training loss is calculated, the validation set is input into the model to calculate the verification loss VALLoss and the verification set signal-to-noise ratio (PSNR), the parameters are debugged and the optimal model is saved, and finally, the model is tested using the test set.

In deep learning network model training, the peak signal-to-noise ratio (PSNR) and loss usually show a significant change trend with the increase in the number of training rounds. The effectiveness of the recursive guide block (RG) and the double multi-scale self-attention mechanism block (DMSA) were verified by ablation experiments. Specifically, the recursive guide block and the double multi-scale self-attention mechanism block were removed, respectively, and the model was retrained and evaluated to compare its performance. Figure 4a shows the comparison results of the RG-DMSA-NN model with the RG module and the DMSA module excluded on the PSNR. In the initial training stage, the PSNR values of the three models increased significantly with the increase in the number of training rounds. With the deepening of training, the growth of the PSNR value tends to be flat, showing the stability of model performance. In addition, the RG-DMSA-NN model showed the highest PSNR value during the whole training process, which proved the key role of recursive guide block (RG) and double multi-scale self-attention mechanism block (DMSA) in improving the quality of model reconstruction. The PSNR value of the model with the RG module removed was lower, which decreased by about 3 dB, indicating that the RG module has an important contribution to the image reconstruction performance of the model. The PSNR value of the model with the DMSA module removed was further reduced by about 5 dB, which showed the effectiveness of the DMSA module in enhancing the weights of different size features in the self-attention mechanism and played a significant role in improving the PSNR. Through the comparative analysis of these three broken lines, we can clearly see that the RG and DMSA modules play an important role in improving the PSNR value of the model and enhancing the image reconstruction quality of the model. The RG-DMSA-NN model performed well in the image denoising task, which was significantly better than the model after removing the RG and DMSA modules, respectively. The results of the ablation experiments show that the combination of the RG and DMSA modules can significantly improve the image reconstruction quality of the model, and the PSNR of the model can be significantly improved.

The training loss value and the validation set PSNR are shown in Figure 4b. In the initial stage, with the optimization of model parameters, the loss value gradually decreases from a high to a low level, while the PSNR value gradually increases, indicating that the performance of the model in image reconstruction is gradually improved. The changing trend of loss value and the PSNR is not linear; in the initial number of training rounds, the loss decreases rapidly, and the PSNR increases significantly, and with the deepening of training, the loss decline rate gradually slows down, and the increase in the PSNR also tends to be flat. Specifically, in the first 20 rounds of training, the loss decreased significantly, while the PSNR improved faster. Over the next 10 rounds, the loss continued to decline and gradually stabilized, and the PSNR gradually increased. In the final 20 rounds of training, the loss further slowly dropped to about 0.12 and the PSNR increased slightly to about 54 dB. By comparing the training loss and the validation set PSNR, the performance of the model tends to be stable on the validation set, and it has good generalization ability. Different from the traditional high-density slicing method of horizontal and vertical sliding 1, the method of transverse sliding 1 and sliding 64 vertically is used in the production of this dataset. This means that each image slice does not overlap vertically, which can build a dataset with greater diversity, and in the case of limited computing resources and a large amount of raw feature data at the workstation, the original data can be fully utilized to build a dataset containing more features to participate in training. The slicing method makes the data have strong feature independence and comprehensiveness, and the slice with a longitudinal step size of 64 means that there is no overlap between the longitudinal adjacent slices, and the feature information learned by the model inside each slice will be more independent and comprehensive. This independence results in the model learning different types of features between different slices, resulting in greater variability and volatility during training. In addition, the training network uses a double multi-scale self-attention mechanism to directly use the features extracted from the upper and lower layers as outputs, which avoids the addition of the original features with high-density slices with a transverse step size of 1, resulting in large fluctuations. As a result, the loss value can fluctuate greatly between different slices, especially when the model tries to adjust the learning strategy or optimize the path between different slices. Additionally, the gradient instability of the proposed network model in the last few rounds of the training process of smaller datasets is also due to the backpropagation process of the model parameters.

Fortunately, this method reduces the interference of the original features on the results, allowing the focus to be on both large-scale and small-scale images. Enhance the model’s ability to extract details and edge features, retain and reconstruct information, remove noise and redundancy, and extract abstract features, thereby improving the performance of GPR image denoising. Bandpass filtering, wavelet transform filtering, and the DnCNN and UNet methods were used to suppress the noise of GPR data, and the denoising effects of the different methods were compared. The network parameters of DnCNN and UNet are listed in

Table 3. Network parameters of the DnCNN and Unet.

Hyper-Parameter	DnCNN Specification	UNet Specification
Optimizer	ADAM	ADAM
Patch size	64 × 64	64 × 64
Batch size	1–16	1–16
Epoch number	50	50
Learning rate range	[10−3, 10−6]	[10−3, 10−6]
Input channels	1	1
Total layers	20	18

.

3. Noise Suppression Results of Test Data

Synthetic data that are not involved in the training and validation of neural networks are used as test data. As shown in Figure 5, the test data include clean data without noise, data with noise, and noisy images. On the right are FK spectra for different types of data. In clean data images, the hierarchical in-phase axes with different reflection intensities are clear (yellow arrows), and the arc reflections of multiple targets are clearly displayed (green arrows). The FK spectrum corresponding to the clean data image shows the main energy range and spectral distribution of the effectively reflected signal (white box).

Adding the noise data to the clean data results in data with noise images. The area indicated by the red arrows is banded noise, and the yellow and green arrows indicate that some of the effective reflections are also drowned out by the noise. Neither the in-phase axis nor the arc reflection curve with weak reflection intensity can be clearly displayed. The FK spectrum of the noise shows that the noise is distributed across the frequency range of 0–600 MHz and all wavenumbers, with 50–200 MHz (yellow box) and 400–600 MHz (red box) being the most noticeable. The energy of the signal also becomes more dispersed due to the noise.

Bandpass filtering, wavelet transform filtering, DnCNN denoising, UNet denoising, and RG-DMSA-NN noise suppression tests were carried out on the data. Figure 5 shows that the inverting axis of the image is not effectively restored after bandpass filtering. In addition to the inverting axis, which has strong reflected energy, the reflected inverting axis indicated by the yellow arrow is disturbed by noise, and the curved reflection pointed by the green arrow is almost completely drowned out by noise. The bands indicated by the red arrows are still very strong. The corresponding FK spectrum shows that the noise spectrum is still present (red and yellow arrows) and that the energy of the active signal is no longer concentrated due to noise interference (white box). Obviously, bandpass filtering not only fails to achieve the effect of denoising but also weakens the energy of the effective signal in view of the problem of noise and effective signal spectrum aliasing in the upper and lower GPR data in the construction environment. Compared with bandpass filtering, the noise suppression effect of wavelet transform filtering has been better improved (WT filtering). The banded noise indicated by the red arrow is suppressed, but the noise in the high-energy area remains. The reflective in-phase axis indicated by the yellow arrow is revealed. However, noise still impairs sharpness, especially in areas with weak reflected energy. The curve reflected by the green arrow shows part of the image. The corresponding FK spectrum shows that the noise is partially suppressed (red and yellow boxes), and the energy of the active signal is more concentrated (white boxes).

Compared with the traditional filtering methods, the image noise suppression methods of DnCNN, UNet, and the RG-DMSA-NN have achieved good results. In terms of the strip noise suppression indicated by the red arrow, the RG-DMSA-NN method suppresses the noise more thoroughly. The yellow arrows indicate the inverting axes of various energies, and the green arrows indicate multiple reflection curves that are clearer, and the resolution is enhanced by the RG-DMSA-NN method when the noise is suppressed. The FK spectrum shows that the RG-DMSA-NN method basically suppresses the noise at the red and yellow boxes, and its spectrum is closer to the original noise-free clean signal.

Figure 6 is a zoomed-in display of the location indicated by the green arrow in Figure 5. A color pattern is used to highlight the characteristics of the reflection curve. The arc reflection indicated by the green arrow is closer to the raw clean data after the RG-DMSA-NN method suppresses the noise, and the inverting axis of the reflection layer with different reflection intensities indicated by the black arrow becomes more continuous and clearer after the RG-DMSA-N method suppresses the noise, which improves the resolution of the data.

To further highlight the noise suppression advantage of the RG-DMSA-NN method, the 66th trace data of the raw clean data and the data processed by different denoising methods were extracted for fusion analysis. Figure 7 shows that the denoising data for the RG-DMSA-NN in purple is closer to the original clean data in blue. The denoising effect of the DnCNN and UNet methods is poor, and the overall denoising effect of UNet is stronger than that of DnCNN. When applying deep learning methods, computational efficiency is a crucial consideration factor. The increase in network depth and layers directly affects the computational cost of denoising networks. In comparisons conducted in the same experimental environment, the RG-DMSA-NN, DnCNN, and UNet have 1,476,368, 295,680, and 31,030,785 model parameters, respectively. In terms of training time, the RG-DMSA-NN takes about 58 h, DnCNN takes 19.8 h, and UNet takes about 86.7 h. These data highlight the need to comprehensively consider the balance between computational resources and performance when selecting denoising methods that are suitable for task requirements.

4. Discussion on Noise Suppression of Measured GPR Data of Coastline Road Diseases at the Macao Science and Technology Museum

4.1. GPR Data Collection Overview

The measured data come from the GPR survey of the subgrade collapse of the reclaimed section of the Macao Science and Technology Center in the Macao Special Administrative Region, China.

Figure 8 shows the specific detection site and the construction environment at the time of GPR detection. The deep medium of the subgrade of the detection section belongs to the gravel used in the reclamation project. Materials such as cement, sand, cables, rebar, and slate are present in the shallow part. In addition, the GPR data were detected during the construction and renovation stage of the Science and Technology Museum. There are a large number of steel bars, cables, and various construction equipment working on both sides of the siding. The GPR instrument model is GSSI-4000, which uses a 400 MHz center frequency antenna for acquisition. Due to the acquisition in the construction environment, the equipment and ferromagnetic materials in the construction environment interfere with the data relatively regularly.

Figure 9a shows an image of the acquired data, where the red arrow indicates band-type noise interference, the green arrow indicates the location of the active signal, and the yellow arrow indicates that other noise interference is evenly distributed in the signal. Figure 9b shows the spectrum of the measured data, with the jagged shape indicated by the red arrow representing the possible noise spectrum. The noise spectrum is widely distributed within the detection band, which aliases with the effective signal spectrum.

4.2. Analysis of Noise Suppression Effects

The RG-DMSA-NN network was used to suppress the noise of the measured data images. The same method as the noise suppression comparison method of the test data, bandpass filtering, wavelet transform filtering, and the DnCNN image denoising method are used to compare the noise suppression effect.

In the raw data, the red arrows indicate the banding noise, which occurs regularly along the collection tract on the data. The yellow arrows indicate the widely and evenly distributed background noise in the data, which covers the area where most of the valid signal is available. The green arrow points to the inverting axis of the reflection of the active signal. Due to the difference in reflection intensity, part of the in-phase axis is almost completely submerged by noise. The noise spectrum (white box) distributed across all wavenumbers can be clearly seen in the FK spectrum, and the effective signal spectrum and the noise spectrum are aliased (Figure 10).

Due to the aliasing effect of the spectrum, as with the test data processing results, this noise cannot be effectively separated and suppressed by bandpass filtering. A band window that is too narrow will disrupt the valid signal. The wavelet transform filtering method has achieved certain results in suppressing the noise of banding. The energy of the banded noise indicated by the red arrow is partially suppressed. Due to the effective suppression of background noise, some of the weak effective reflections indicated by the green arrows are still disturbed by the noise. Noise in the 200–400 MHz region of the FK spectrum is still present.

Similar to the denoising effect of the test data, compared with the traditional filtering methods, the DnCNN, UNet, and RG-DMSA-NN image noise suppression methods have achieved better results. In terms of strip noise suppression indicated by the red arrow, the RG-DMSA-NN method is more complete than DnCNN and UNet noise suppression. The green arrows indicate the in-phase axes of various energies and the green arrows indicate multiple reflected in-phase axes that are clearer, and the resolution is improved by suppressing the noise by the RG-DMSA-NN method. In the area of the white box, the RG-DMSA-NN method suppresses the background noise more thoroughly, and the weak reflection in-phase axis becomes clearer. The FK spectrum shows that the RG-DMSA-NN method basically suppresses the noise at the white box.

In order to compare the suppression effects of different methods more intuitively on the spectrum, Figure 11 adopts a more intuitive frequency amplitude analysis. Figure 11a shows the spectrum of the measured raw data. Figure 11b shows the data spectrum with bandpass filtering. The red arrows indicate the jagged noise spectrum on the spectrum, in addition to the suppression of low- and high-frequency signals. Although the spectral noise of the signal is suppressed after the wavelet transforms in Figure 11c, there is still a zigzag noise spectrum in the signal band. In Figure 11d, the noise spectrum after DnCNN suppression is better than the former, and the jagged noise spectrum becomes less. The effect of UNet noise suppression is not much different from that of DnCNN, and the denoising effect in different frequency bands has its own advantages (Figure 11e). After the RG-DMSA-NN method is used to suppress the noise, the jagged noise spectrum becomes less, and the low-frequency and high-frequency regional energy of the data are better protected (Figure 11f).

5. Conclusions

The noise of the GPR signal has different characteristics, depending on the construction environment. The noise distribution in ground penetrating radar data is widespread, with the noise spectrum and effective signal spectrum overlapping, and the effective signal being overwhelmed by the noise. Traditional filtering methods are difficult to separate noise. The DnCNN and Unet image denoising methods have poor performance in suppressing construction environment noise. Therefore, a method for image noise suppression based on RG-DMSA-NN deep learning is proposed. By extracting the noise of the actual data, the GPR image data containing a large number of reflected features were synthesized and produced for the training and testing of the neural network. The comparison of GPR radar images and FK spectrum analysis from the test data shows the effectiveness of the RG-DMSA-NN model in special noise suppression. The RG-DMSA-NN image noise suppression method was applied to the GPR measurement data in the construction environment of the Macao Science and Technology Center, which showed the advantages of the method in noise suppression. The weakly reflected in-phase axis and background noise in the actual data are well suppressed.