A ground penetrating radar data super-resolution reconstruction method based on wavelet domain physical prior

Abstract

This application discloses a super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors, comprising: S1, acquiring a low-resolution input image and preprocessing it; S2, mapping the single-channel information of the input image to a 64-dimensional feature space; S3, gradually reducing the spatial size of the feature map and increasing the channel dimension to 1024 through downsampling operations, and embedding an enhancement mechanism in the first two stages; S4, embedding the wavelet transform as a physical prior into a network, performing multi-scale decomposition through fixed basis functions, and constructing a joint spatial-frequency domain feature representation; S5, further expanding the receptive field by using a residual structure and a multi-scale dilated convolution method; S6, gradually restoring the spatial resolution of the image through upsampling operations symmetrical to the downsampling operations in S3, and setting a multi-scale skip connection mechanism between the corresponding levels of the downsampling and upsampling operations; S7, mapping the feature map through a 1×1 convolutional layer combined with a Tanh activation function to output the final super-resolution image.

Description

Technical Field

[0001] This application relates to the field of ground-penetrating radar signal processing technology, specifically to a super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors. Background Technology

[0002] Ground penetrating radar (GPR) is a highly efficient and non-destructive detection technology widely used in geological exploration, underground pipeline inspection, and archaeological research. Its working principle involves emitting high-frequency electromagnetic waves and receiving reflected signals to obtain information about the distribution and structure of underground targets. However, in practical applications, due to the faster attenuation of electromagnetic waves at higher frequencies, and the combined effects of GPR's transmission power and dynamic range limitations, it is difficult to acquire high-resolution high-frequency electromagnetic wave signals from the mid-to-deep underground (5-20m) depths, thus affecting detection accuracy. To address this issue, current methods mainly employ frequency domain topology and subspace methods based on signal processing, as well as inverse Q-compensation techniques. Due to the nonlinearity of GPR signals and the anisotropic nature of underground media, frequency domain topology and subspace methods cannot recover the true underground signal, often leading to signal distortion and spurious frequencies. Inverse Q-compensation techniques cannot accurately calculate the Q-values ​​of all signals at different locations, and relying on manual and single-point Q-compensation techniques rarely yields successful applications in practical GPR signal processing. Therefore, further research is needed. Summary of the Invention

[0003] The purpose of this application is to provide a super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors. The specific technical solution is as follows:

[0004] A super-resolution reconstruction method for ground-penetrating radar (GPR) data based on wavelet domain physical priors includes: S1, acquiring a low-resolution input image and preprocessing it; S2, mapping the single-channel information of the preprocessed input image in S1 to a 64-dimensional feature space; S3, gradually reducing the spatial size of the feature map obtained in S2 and increasing the channel dimension to 1024 through downsampling operations, and embedding an enhancement mechanism for sensing the geometric structure and spatial distribution in the GPR echo signal in the first two stages of the downsampling operation; S4, using wavelet transform to compensate for the lack of spatial features in the enhanced high-dimensional feature map in S3, and achieving dual-dimensional feature enhancement in both the spatial and frequency domains through feature mining in the frequency domain. Wavelet transform is embedded into the network as a physical prior. By leveraging the time-frequency localization properties of fixed basis functions, it compensates for the insufficient ability of simple spatial features to express the physical laws of electromagnetic wave propagation. S5: Based on S4, residual structure and multi-scale dilated convolution are used to further expand the receptive field without increasing additional computational overhead or losing resolution, thereby improving the efficiency of capturing deep global contextual information. S6: Based on S5, upsampling operations symmetrical to the downsampling operation in S3 are used to gradually restore the spatial resolution of the image, and a multi-scale skip connection mechanism is set between the corresponding layers of the downsampling and upsampling operations. S7: The feature map after upsampling and feature fusion in S6 is mapped and output as the final super-resolution image through a 1×1 convolutional layer combined with the Tanh activation function.

[0005] S8. Establish training sets for low-resolution and high-resolution ground-penetrating radar (GPR), specifically: S8.1. Obtain continuous single-point GPR profile data at the actual acquisition location using two different center frequency antennas: A (high frequency) and B (low frequency); S8.2. Obtain continuous time-series GPR profile data at the actual acquisition location using two different center frequency antennas: C (high frequency) and D (low frequency); S8.3. Analyze the A and B data to obtain stratigraphic information H for the detection area. S8.4 Analyze the C and D data to obtain the noise signal N from the actual acquisition; S8.5 Randomly vary the layer thickness and other parameters of the acquired layer H information to obtain random undulating layers H1, H2, H3, H4 and H5. Based on the random undulating layer information of H1, H2, H3, H4 and H5, establish models M1, M2, M3, M4 and M5; where the horizontal axis length of the model is 10m, the vertical axis depth is 8m, and the grid accuracy is 0.01m; randomly add target media of different sizes such as cavities, steel bars and pipes to M1, M2, M3, M4 and M5. After assigning relative permittivity values ​​to the strata and target media in the model, new MO1, MO2, MO3, MO4 and MO5 are formed; S8.6 Simulate the method network constructed in S1-S7 using finite difference, respectively simulating low-frequency and high-frequency ground penetrating radar images, and establish training set samples for low-resolution and high-resolution ground penetrating radar.

[0006] Preprocessing in S1 includes noise removal, brightness and contrast adjustment, and image cropping and / or scaling to improve image quality, reduce interference factors, and lay a good foundation for the subsequent core reconstruction process.

[0007] In S2, when mapping the single-channel information of the input image to the 64-dimensional feature space, an initial convolution block is used. The initial convolution block includes two consecutive 3×3 convolutional layers, a batch normalization layer, and a ReLU activation function. The convolution stride is 1 and the padding is 1, which is used to ensure that the spatial size of the feature map after convolution is consistent with that of the input image.

[0008] When performing downsampling operations in S3, four consecutive downsampling coding blocks are used. Each downsampling coding block includes a 2×2 max pooling layer and two 3×3 convolutional units. The max pooling layer has a stride of 2 and is used to halve the spatial size of the feature map. The two 3×3 convolutional units have a stride of 1 and padding of 1 and are used to perform depth extraction and double the number of channels on the downsampled features without changing the size of the feature map.

[0009] In S3, when embedding the enhancement mechanism, a hybrid enhancement module consisting of channel attention and collaborative attention is embedded at the output of the first two downsampling coding blocks. This module is designed for the feature extraction and super-resolution reconstruction of GPR images. The computational flow and parameters of the channel attention module are adapted to the channel dimension differences at the deployment location. It retains the core logic of squeezing, excitation, and recalibration to achieve accurate selection and response enhancement of effective feature channels of GPR images. It is deployed at the output of the first and second downsampling coding blocks of the encoder, with corresponding feature channel numbers of 128 and 256, respectively. Both channel attention modules adjust the number of neurons in the fully connected layer according to the channel dimension to control the computational load while ensuring feature calibration accuracy. The collaborative attention module receives the feature map after recalibration by the channel attention module as input, continues the channel dimension at the deployment location, and fixes the pooling kernel size and convolution kernel parameters for the input resolution features of the GPR image to avoid overcomputation. The collaborative attention module achieves spatial attention enhancement through bidirectional spatial pooling, feature fusion encoding, weight generation, and spatial recalibration.

[0010] The channel attention module enhancement steps in S3 include:

[0011] S3.1. The input feature map is compressed into spatial information through global average pooling, transforming the two-dimensional spatial features into a one-dimensional channel descriptor, expressed as:

[0012] ,

[0013] in, The two-dimensional matrix is ​​the input to the feature map. To represent the squeeze mapping function of global average pooling, the spatial dimension ( ) Dimensionality reduced to (1 1), This is a value representing the global distribution characteristics of the channel after the compression operation;

[0014] S3.2. A two-stage fully connected layer is used to construct the non-linear dependency relationship between channels. The first-stage fully connected layer reduces the channel dimensionality and introduces the ReLU activation function to complete the non-linear mapping. The second-stage fully connected layer restores the original number of channels and generates the channel attention weight vector through the Sigmoid activation function, expressed as:

[0015] ,

[0016] in, For the Sigmoid activation function, For ReLU, It acts on the original feature map;

[0017] S3.3 Multiply the weight vector element-wise with the original feature map along the channel dimension to complete the adaptive recalibration of the feature channels.

[0018] The steps to enhance the collaborative attention module in S3 include:

[0019] S3.4. Perform one-dimensional global average pooling on the feature map after calibration in S3.3 along the horizontal and vertical directions, respectively, as follows:

[0020] ,

[0021] ,

[0022] in, The feature vectors in the vertical direction, The feature vector in the horizontal direction;

[0023] S3.5, will and The feature vectors from these two directions are concatenated in space, and expressed as:

[0024] ,

[0025] in, It serves as an intermediate variable, containing fused information encoded in both spatial directions;

[0026] S3.5, after fusion Restored to horizontal direction and vertical direction Two feature vectors are used, and a horizontal spatial attention weight map is generated by the Sigmoid activation function, which is expressed as:

[0027] ,

[0028] ;

[0029] S3.6 Multiply the two weight maps generated in S3.5 element-wise with the calibrated feature map in S3.3 to complete the spatial dimension recalibration of the features.

[0030] S4 includes:

[0031] S4.1. Using the discrete wavelet transform based on the Haar wavelet basis to apply input features in the frequency domain. Decompose to generate low-frequency approximate components. And high-frequency detail components in the horizontal, vertical, and diagonal directions. , , The decomposition process is represented as follows:

[0032] ,

[0033] Each subband has a dimension of 1. ;

[0034] S4.2. Perform targeted lightweight convolution processing on different frequency components, expressed as:

[0035] ;

[0036] S4.3. Inverse wavelet transform is used to reconstruct the spatial domain, thereby effectively capturing subtle reflection interface information in ground-penetrating radar images, expressed as:

[0037] .

[0038] In S5, residual structures and multi-scale dilated convolution methods are implemented through residual multi-scale dilation blocks, specifically including:

[0039] S5.1. Using an input convolutional layer built from standard convolutional operations, preliminary local extraction of input features is performed, reducing the dimension to [missing information]. Input feature map Mapped to a number of channels intermediate feature map ;

[0040] S5.2, Through the U-Net encoding and decoding symmetrical structure built from an internal symmetrical structure containing multiple layers of encoding and decoding, in order to For input, through The process of learning and encoding multi-scale contextual features, in which... The encoding / decoding unit, representing a U-Net-like architecture, expands the receptive field in the encoding path by increasing the dilation rate of convolutional layers or performing stepwise downsampling, without significantly increasing the number of parameters. The internal computational flow is expressed as follows:

[0041] ,

[0042] in, This is the initial feature mapping;

[0043] S5.3, through element-wise summation operation The multi-scale depth features are residually concatenated with the original input, and the final output is:

[0044] .

[0045] Also includes:

[0046] S9. Mean squared error loss is used as the training optimization criterion. Gradients are propagated to each layer of the network through backpropagation to drive iterative parameter optimization, ensuring pixel-level feature reconstruction accuracy. During training, batch mean squared error loss is used to update parameters. During testing, RMSE and PSNR metrics are combined to further evaluate the reconstruction effect, expressed as follows:

[0047] ,

[0048] in, These are the height and width of the image, respectively. For super-resolution image reconstruction in The pixel value of the location, For true high-resolution label images in The pixel value of the location.

[0049] The beneficial effects of this application are that by constructing a fusion-efficient and robust ground-penetrating radar super-resolution reconstruction model, the sharpness and structural fidelity of the reconstructed images are significantly improved, and the reconstruction results show a high degree of similarity to high-resolution reference images. Specifically, by introducing wavelet domain physical priors and coordinate attention mechanisms, non-physical artifacts are effectively suppressed, reducing the number of artifacts in the low signal-to-noise ratio region (<10 dB) by 68% compared to existing methods. This invention employs an end-to-end deep learning framework, optimizing computational efficiency while ensuring reconstruction performance, making it suitable for real-time processing of large-scale ground-penetrating radar data. Furthermore, by adjusting the wavelet basis functions and attention parameters, the technical solution of this invention can be further extended to signal super-resolution reconstruction tasks in other fields such as seismic exploration and medical imaging. Attached Figure Description

[0050] Figure 1This is a flowchart illustrating the application process.

[0051] Figure 2 This is a diagram of the SCAWT-U-Net network structure in this application;

[0052] Figure 3 This is a comparison image of the super-resolution reconstruction of the thin-stratum model in this application;

[0053] Figure 4 This is a comparison of the reconstructed spectral data of the thin-stratum model in this application;

[0054] Figure 5 This is a comparison chart of the data processing effects of a single channel with 400 sampling channels in this application;

[0055] Figure 6 This is a comparison image of the super-resolution reconstruction of the complex stratigraphic model in this application;

[0056] Figure 7 This is a comparison of the reconstructed spectral data of the complex stratigraphic model in this application;

[0057] Figure 8 This is a comparison chart of the data processing effects of sampling channel 100 in this application;

[0058] Figure 9 This is a comparison image of the super-resolution reconstruction of permafrost exploration data in this application;

[0059] Figure 10 This is a comparison chart of the reconstructed spectrum of permafrost detection data in this application;

[0060] Figure 11 This is a comparison chart of the single-channel data processing effect of sampling channel 2210 in this application;

[0061] Figure 12 This is a schematic diagram of the model in S8 of this application;

[0062] Figure 13 This is a schematic diagram of low-resolution ground-penetrating radar data and high-resolution ground-penetrating radar simulation data in this application. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to specific embodiments and accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this application. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0064] like Figure 1 and Figure 2 As shown, a super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors includes:

[0065] S1. Acquire a low-resolution input image and perform preprocessing. Specifically, preprocessing includes noise removal, brightness and contrast adjustment, and image cropping and / or scaling to improve image quality, reduce interference factors, and lay a good foundation for the subsequent core reconstruction process.

[0066] S2. Map the preprocessed single-channel information of the input image from S1 to a 64-dimensional feature space. Specifically, an initial convolutional block is used, which includes two consecutive 3×3 convolutional layers, a batch normalization layer, and a ReLU activation function. The convolution stride is 1 and the padding is 1 to ensure that the spatial size of the feature map after convolution is consistent with that of the input image.

[0067] S3. The feature map obtained in S2 is gradually reduced in spatial size and the channel dimension is increased to 1024 through downsampling. An enhancement mechanism for sensing the geometric structure and spatial distribution in the ground-penetrating radar echo signal is embedded in the first two stages of the downsampling operation. Specifically, the downsampling operation is performed using four consecutive downsampling coding blocks. Each downsampling coding block includes a 2×2 max-pooling layer and two 3×3 convolutional units. The max-pooling layer has a stride of 2 to halve the spatial size of the feature map. The two 3×3 convolutional units have a stride of 1 and padding of 1, used to perform depth extraction and double the number of channels on the downsampled features without changing the feature map size. When embedding the enhancement mechanism, a hybrid enhancement module consisting of channel attention and collaborative attention is embedded at the output of the first two downsampling coding blocks. This module is designed for the feature extraction and super-resolution reconstruction of GPR images. The operation process and parameters of the channel attention module are adapted according to the channel dimension differences at the deployment location. The core logic of squeezing, excitation, and recalibration is retained to achieve accurate selection and response enhancement of effective feature channels of GPR images. The module is deployed at the output of the first and second downsampling coding blocks of the encoder, with corresponding feature channel numbers of 128 and 256, respectively. The number of neurons in the fully connected layer is adjusted according to the channel dimension of both channel attention modules to control the amount of computation while ensuring the accuracy of feature calibration. The collaborative attention module receives the feature map after recalibration by the channel attention module as input, continues the channel dimension at the deployment location, and fixes the pooling kernel size and convolution kernel parameters for the input resolution features of the GPR image to avoid overcomputation. The collaborative attention module achieves spatial attention enhancement through bidirectional spatial pooling, feature fusion encoding, weight generation, and spatial recalibration.

[0068] The channel attention module enhancement steps include:

[0069] S3.1. The input feature map is compressed into spatial information through global average pooling, transforming the two-dimensional spatial features into a one-dimensional channel descriptor, expressed as:

[0070] ,

[0071] in, The two-dimensional matrix is ​​the input to the feature map. To represent the squeeze mapping function of global average pooling, the spatial dimension ( ) Dimensionality reduced to (1 1), This is a value representing the global distribution characteristics of the channel after the compression operation.

[0072] S3.2. A two-stage fully connected layer is used to construct the non-linear dependency relationship between channels. The first-stage fully connected layer reduces the channel dimensionality and introduces the ReLU activation function to complete the non-linear mapping. The second-stage fully connected layer restores the original number of channels and generates the channel attention weight vector through the Sigmoid activation function, expressed as:

[0073] ,

[0074] in, For the Sigmoid activation function, For ReLU, It acts on the original feature map.

[0075] S3.3 Multiply the weight vector element-wise with the original feature map along the channel dimension to complete the adaptive recalibration of the feature channels.

[0076] The steps to enhance the collaborative attention module include:

[0077] S3.4. Perform one-dimensional global average pooling on the feature map after calibration in S3.3 along the horizontal and vertical directions, respectively, as follows:

[0078] ,

[0079] ,

[0080] in, The feature vectors in the vertical direction, This is the feature vector in the horizontal direction.

[0081] S3.5, will and The feature vectors from these two directions are concatenated in space, and expressed as:

[0082] ,

[0083] in, It is an intermediate variable that contains fused information encoded in both spatial directions.

[0084] S3.5, after fusion Restored to horizontal direction and vertical direction Two feature vectors are used, and a horizontal spatial attention weight map is generated by the Sigmoid activation function, which is expressed as:

[0085] ,

[0086] .

[0087] S3.6 Multiply the two weight maps generated in S3.5 element-wise with the calibrated feature map in S3.3 to complete the spatial dimension recalibration of the features.

[0088] S4. Wavelet transform is used to compensate for the lack of spatial features in the enhanced high-dimensional feature map of S3. Through feature mining in the frequency domain, dual-dimensional feature enhancement in both the spatial and frequency domains is achieved. Specifically, wavelet transform is embedded into the network as a physical prior. By leveraging the time-frequency localization properties of fixed basis functions, the inadequacy of simple spatial features in expressing the physical laws of electromagnetic wave propagation is compensated for, including:

[0089] S4.1. Using the discrete wavelet transform based on the Haar wavelet basis to apply input features in the frequency domain. Decompose to generate low-frequency approximate components. And high-frequency detail components in the horizontal, vertical, and diagonal directions. , , The decomposition process is represented as follows:

[0090] ,

[0091] Each subband has a dimension of 1. .

[0092] S4.2. Perform targeted lightweight convolution processing on different frequency components, expressed as:

[0093] .

[0094] S4.3. Inverse wavelet transform is used to reconstruct the spatial domain, thereby effectively capturing subtle reflection interface information in ground-penetrating radar images, expressed as:

[0095] .

[0096] S5. Building upon S4, residual structures and multi-scale dilated convolution methods are employed to further expand the receptive field without increasing computational overhead or sacrificing resolution, thereby improving the efficiency of capturing deep global contextual information. Specifically, the residual structure and multi-scale dilated convolution methods are implemented through residual multi-scale dilation blocks, including:

[0097] S5.1. Using an input convolutional layer built from standard convolutional operations, preliminary local extraction of input features is performed, reducing the dimension to [missing information]. Input feature map Mapped to a number of channels intermediate feature map .

[0098] S5.2, Through the U-Net encoding and decoding symmetrical structure built from an internal symmetrical structure containing multiple layers of encoding and decoding, in order to For input, through The process of learning and encoding multi-scale contextual features, in which... The encoding / decoding unit, representing a U-Net-like architecture, expands the receptive field in the encoding path by increasing the dilation rate of convolutional layers or performing stepwise downsampling, without significantly increasing the number of parameters. The internal computational flow is expressed as follows:

[0099] ,

[0100] in, This is the initial feature mapping.

[0101] S5.3, through element-wise summation operation The multi-scale depth features are residually concatenated with the original input, and the final output is:

[0102] .

[0103] S6. Based on S5, the spatial resolution of the image is gradually restored by an upsampling operation that is symmetrical to the downsampling operation in S3, and a multi-scale jump connection mechanism is set between the corresponding levels of the downsampling operation and the upsampling operation.

[0104] S7. The feature map after upsampling and feature fusion in S6 is mapped through a 1×1 convolutional layer combined with the Tanh activation function to output the final super-resolution image.

[0105] like Figure 12 and Figure 13As shown, S8 establishes training sets for low-resolution and high-resolution ground-penetrating radar (GPR), specifically: S8.1, acquiring continuous single-point acquisition of GPR profile data from two different center frequency antennas at the actual acquisition location: A (high frequency) and B (low frequency); S8.2, acquiring continuous time acquisition of GPR profile data from two different center frequency antennas at the actual acquisition location: C (high frequency) and D (low frequency); S8.3, analyzing data A and data B to obtain stratigraphic information H of the detection area. S8.4 Analyze the C and D data to obtain the noise signal N from the actual acquisition; S8.5 Randomly vary the layer thickness and other parameters of the acquired layer H information to obtain random undulating layers H1, H2, H3, H4 and H5. Based on the random undulating layer information of H1, H2, H3, H4 and H5, establish models M1, M2, M3, M4 and M5; where the horizontal axis length of the model is 10m, the vertical axis depth is 8m, and the grid accuracy is 0.01m; randomly add target media of different sizes such as cavities, steel bars and pipes to M1, M2, M3, M4 and M5. After assigning relative permittivity values ​​to the strata and target media in the model, new MO1, MO2, MO3, MO4 and MO5 are formed; S8.6 Simulate the method network constructed in S1-S7 using finite difference, respectively simulating low-frequency and high-frequency ground penetrating radar images, and establish training set samples for low-resolution and high-resolution ground penetrating radar.

[0106] S9. Mean squared error loss is used as the training optimization criterion. Gradients are propagated to each layer of the network through backpropagation to drive iterative parameter optimization, ensuring pixel-level feature reconstruction accuracy. During training, batch mean squared error loss is used to update parameters. During testing, RMSE and PSNR metrics are combined to further evaluate the reconstruction effect, expressed as follows:

[0107] ,

[0108] in, These are the height and width of the image, respectively. For super-resolution image reconstruction in The pixel value of the location, For true high-resolution label images in The pixel value of the location.

[0109] To make this application easier to understand, the following examples illustrate this further.

[0110] Network training

[0111] Hardware configuration: Intel(R) Xeon(R) CPU E5-2640 v4 @ 2.40GHz processor, NVIDIA Quadro P2000 (5GB) graphics card, 64GB of RAM; Software environment: Windows 10 operating system.

[0112] The dataset uses paired GPR super-resolution data, covering typical geological scenes such as horizontal strata, inclined strata, and hyperbolic subsurface anomalies. It contains 6400 pairs of low-resolution inputs and high-resolution labels, sourced from actual ground-penetrating radar acquisition and simulation generation. During preprocessing, all image pixel values ​​were normalized to the [0,1] interval to eliminate the influence of dimensions and improve training stability. The dataset was then randomly divided into training, validation, and test sets in an 8:1:1 ratio, and finally converted into a single-channel tensor format to adapt to the network input.

[0113] Training parameters were set based on task requirements and hardware constraints: the Adam optimizer was selected, with an initial learning rate of 1×10⁻⁶. -1 The learning rate is dynamically adjusted using the ReduceLROnPlateau scheduler. When the validation set loss does not decrease for three consecutive rounds, the learning rate is reduced to 0.5 times the original value. The batch size is set to 16 to balance computational efficiency and memory usage. The training rounds are preset to 10 rounds and are paired with an early stopping strategy (patience=3). If the validation set loss does not fall below the current optimal value for three consecutive rounds, the training is automatically terminated. The loss function uses MSE loss, and gradient clipping (max_norm=1.0) is introduced to prevent gradient explosion and ensure the stability of the training process.

[0114] The training process follows a closed loop of data loading, model initialization, iterative training, validation and evaluation, and model saving. DataLoader is used to load the training set in an out-of-order manner and the validation set in an ordered manner. During model initialization, the convolutional layer weights are initialized using a He normal distribution. After each training round, the system switches to eval mode to disable gradient calculation in order to verify model performance. The validation set loss and evaluation metrics such as PSNR, SSIM, and RMSE are calculated. The optimal model with the lowest validation loss is saved, and the loss curve and visualization comparison are monitored in real time to promptly detect overfitting or training anomalies.

[0115] ablation experiment

[0116] To quantitatively verify the necessity and synergistic contribution of the SE-CA hybrid attention module, wavelet transform module, and RSU module in the wavelet domain physical prior-based ground-penetrating radar data super-resolution reconstruction method (SCAWT-U-Net) disclosed in this application, multiple sets of comparative ablation models were constructed by sequentially removing individual core modules or combined modules, using the complete SCAWT-U-Net as the baseline model. All models were trained under the same hardware and software environment, dataset partitioning, and training parameters as the baseline model to ensure experimental fairness and comparability. The experiments used Peak Signal-to-Noise Ratio (PSNR) and Root Mean Square Error (RMSE), commonly used in the field of super-resolution reconstruction, as core objective evaluation indicators. Simultaneously, the model training time was statistically analyzed to evaluate computational efficiency. Higher PSNR and lower RMSE indicate better model reconstruction accuracy and structural fidelity. The quantitative results of the ablation experiments are shown in Table 1.

[0117] Table 1: Comparison of quantitative results from ablation experiments

[0118]

[0119] The following comparative test was conducted using GPR B-scan data from thin-stratum and complex-stratum models.

[0120] Figure 3 A comparison of super-resolution reconstruction results of ground-penetrating radar data for thin-stratum models, including Figure 3 (a) is the original low-resolution data. Figure 3 (b) is the original high-resolution ground truth data. Figure 3 (c) shows the U-Net reconstruction results. Figure 3 (d) shows the reconstruction results of SCAWT-U-Net in this paper. The red arrows in the figure mark three types of core geological features: shallow horizontal reflection interface, middle thin weak reflection feature area, and deep hyperbolic reflection and bottom scattering feature area, which are used to visually compare the recovery capabilities of different algorithms for key structures.

[0121] Figure 3 In (a), the three key features marked by the red arrows are severely degraded: the shallow reflection phase axis is blurred and discontinuous, the weak reflection features of the middle thin layer are masked by noise and aliasing echoes, and the deep hyperbolic reflection contour is blurred and the details of the bottom scattering features are lost, making it impossible to achieve accurate stratification identification and geological interpretation of thin strata. Figure 3 (b) clearly demonstrates the complete structure of the thin strata: the shallow reflective interface, marked by the red arrow, is continuous and smooth; the middle thin layer has clear stratification boundaries; the deep hyperbolic reflective morphology is complete; and the bottom scattering features are rich in detail, serving as the true benchmark for subsequent algorithm performance evaluation in the reconstruction test. Figure 3In (c), although the U-Net reconstruction improved the overall image clarity and restored the general outline of the strata to some extent, there were still shortcomings in the feature areas indicated by the red arrows: the shallow layer reflection phase axis was enhanced but still had local blurring, and the reflection phase axis of the middle thin layer was still overlapping, making it impossible to accurately distinguish adjacent thin layers. The U-Net reconstruction results were generally good, but there were still some visual differences from the original high-resolution ground truth, making it difficult to meet the needs of fine identification of thin strata.

[0122] like Figure 3 As shown in (d), the reconstruction results of the SCAWT-U-Net network proposed in this paper are in high agreement with the original high-resolution data. It exhibits excellent recovery performance in the key feature areas marked by red arrows: the shallow reflection interface is highly clear; the aliased echoes of the middle thin layer are effectively separated, and the layer boundaries are smooth and continuous; the deep hyperbolic reflection morphology is accurately restored, and the weak signal details of the bottom scattering features are rich, with no obvious artifacts or oversmoothing phenomena, accurately restoring the real geological structure of the thin strata.

[0123] Figures 4 and 5 demonstrate the joint quantization verification of the super-resolution reconstruction results of the thin-stratum model from two dimensions: frequency domain spectrum and single-channel waveform. This comprehensively evaluates the algorithm's ability to recover high-frequency details of the signal and the fidelity of its time-domain features.

[0124] Figure 4 compares the normalized amplitude spectra of different reconstruction results of ground-penetrating radar data for thin-strata models. The horizontal axis covers the 0-1200 MHz frequency band, and the vertical axis represents the signal amplitude. The center frequency of the original high-resolution data spectrum is approximately 400 MHz, carrying the high-frequency structural information required for fine stratification of thin strata. The center frequency of the original low-resolution data spectrum is approximately 180 MHz, showing a significant shift towards the lower frequency band compared to the true value, and the amplitude decays sharply after 200 MHz, with high-frequency components almost completely truncated, resulting in a significantly narrowed effective bandwidth. Classical U-Net reconstruction has weak recovery capabilities for high-frequency components above 400 MHz, and deviates from the spectral shape of the original high-resolution data. The spectral characteristic curve of the SCAWT-U-Net reconstruction highly coincides with the curve of the original high-resolution data, not only fully recovering the energy distribution in the mid-to-low frequency band, but also restoring the high-frequency components above 400 MHz, achieving center frequency and high-frequency feature recovery consistent with the true value.

[0125] Figure 5 compares the processing results of single-channel data from 400 transverse sampling channels (vertical sampling points 0-250) of ground-penetrating radar data in a thin-stratum model. As shown by the dashed box in the figure, the single-channel waveforms reconstructed by U-Net and SCAWT-U-Net both exhibit richer fluctuations, enhancing data resolution and restoring more details in the smooth areas of the original low-resolution waveform, thus more closely resembling the characteristics of the original high-resolution signal. Further comparison reveals that the waveform reconstructed by U-Net still suffers from the loss of weak reflection details and amplitude and phase distortion; while the waveform reconstructed by SCAWT-U-Net more closely matches the original high-resolution data in finer details, fully preserving weak reflection peaks, exhibiting richer waveform fluctuations, and demonstrating superior time-domain fidelity and frequency extension effect.

[0126] Figure 6 shows a comparison of the super-resolution reconstruction results of ground-penetrating radar data for a complex stratigraphic model. Figure 6(a) shows the original low-resolution data, Figure 6(b) shows the original high-resolution ground truth data, and Figure 6(c) shows the U-Net reconstruction result. Figure 6 (d) shows the reconstruction results of SCAWT-U-Net in this paper.

[0127] Figure 6 In (a), the key features of the original low-resolution data are obviously blurred and the details are attenuated. The reflection phase axis of the undulating strata is locally discontinuous. Moreover, the reflection contour of the underground fault is soft and the boundary is not easily distinguishable. The weak reflection signal of the heterogeneous scattering zone of the medium is partially masked. The overall detail is not rich enough, which affects the refined geological interpretation. Figure 6 (c) The U-Net reconstruction improves the overall image clarity, but key feature recovery is still lacking. The edges of the subsurface faults are slightly blurred, artifacts are not obvious but the contour sharpness is insufficient, and weak reflection signals are still partially obscured, resulting in a visual discrepancy with the ground truth. In Figure 6 (d), the SCAWT-U-Net reconstruction is close to the high-resolution ground truth, with excellent core feature recovery. The undulating strata phase axes in the reconstruction are continuous and smooth, accurately restoring the undulation trend, and the fault reflection edges are clear. Noise in the heterogeneous scattering region of the medium is effectively suppressed, and the details of the weak reflection signals are completely preserved without artifacts or over-smoothing. It accurately replicates the heterogeneous features of complex strata and multiple types of reflection signals.

[0128] Figure 7 compares the normalized amplitude spectra of different reconstruction results of ground-penetrating radar data for complex strata models. The horizontal axis covers the 0-120 Hz frequency band, and the vertical axis represents the signal amplitude. The original high-resolution data spectrum exhibits multi-peak characteristics, with an effective bandwidth covering 0-120 Hz. The energy distribution in the mid-to-high frequency band (30-100 Hz) is continuous, carrying frequency information of multiple types of reflection characteristics in complex strata. The original low-resolution data spectrum shows accelerated energy decay after 20 Hz, and the energy in the mid-to-high frequency band above 30 Hz is significantly lower than the true value, resulting in a loss of detailed frequency information. After U-Net reconstruction, the energy recovery in the mid-to-high frequency band is limited, and the spectrum curve deviates significantly from the shape of the original high-resolution data, still retaining the rapid decay trend of the low-resolution data. The spectrum curve reconstructed by SCAWT-U-Net highly overlaps with the original high-resolution data, accurately restoring the energy characteristics of the mid-to-high frequency band, and showing better consistency with the frequency distribution of the true value.

[0129] Figure 8 compares the processing results of single-channel data from ground-penetrating radar data in complex geological formation model simulation, specifically channel 100 (vertical sampling points 0-250). As shown in the dashed box in the figure, the waveforms reconstructed by U-Net and SCAWT-U-Net are richer in detail than the original low-resolution data, indicating an improvement in resolution. Further comparison reveals that the U-Net reconstructed waveform suffers from local detail loss and slight distortion; the SCAWT-U-Net reconstructed waveform closely matches the high-resolution ground truth, with clear separation of reflection peaks, complete preservation of weak reflection details, and superior temporal fidelity.

[0130] Figure 9 For comparison of the reconstruction results of ground-penetrating radar measured data of permafrost, among which Figure 9 (a) is the original low-resolution data. Figure 9 (b) shows the U-Net reconstruction results. Figure 9 (c) shows the reconstruction results of SCAWT-U-Net.

[0131] In the original low-resolution data, the reflection phase axes in the areas marked by arrows are blurry and discontinuous, the outlines of the freeze-thaw interface and the fine internal stratigraphic structure are poorly discernible, and weak reflection signals are partially masked by noise, failing to clearly present the vertical stratification of permafrost. The U-Net reconstruction results restored the overall image contrast and some reflection phase axes to a certain extent, but the phase axes of the stratigraphic interfaces remained blurry, failing to fully restore the fine geological structure reflections of the permafrost. The SCAWT-U-Net reconstruction results show continuous and clear shallow reflection phase axes, and the phase axes of the fine interfaces in the middle stratigraphic layers are more clearly distinguishable, accurately preserving the fine details of permafrost stratification. This provides reliable high-resolution data support for engineering applications such as permafrost active layer thickness estimation and underground ice distribution identification.

[0132] Figure 10 shows a comparison of the normalized amplitude spectrum of the permafrost data, with the horizontal axis covering the 0-700 MHz frequency band. The original low-resolution data shows a sharp attenuation of high-frequency components after 250 MHz. After U-Net reconstruction, the high-frequency components are only restored to about 300 MHz, and there is still a significant truncation. In contrast, the spectrum of the SCAWT-U-Net reconstruction is effectively extended to 700 MHz, and the high-frequency components are completely preserved. The overall reconstruction effect is significantly better than that of U-Net.

[0133] Figure 11 shows a comparison of the single-channel data processing results for sampling channel 2210, with the key reflection areas marked by dashed boxes. The original low-resolution waveform is flat with missing weak reflection details. After U-Net reconstruction, the waveform details are improved, but there are still minor reflection gaps in some areas. After SCAWT-U-Net reconstruction, the waveform has richer fluctuations, and the weak reflection peaks are completely preserved, resulting in better measured performance.

Claims

1. A super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors, characterized in that, include: S1. Acquire a low-resolution input image and perform preprocessing; S2. Map the preprocessed single-channel information of the input image in S1 to a 64-dimensional feature space; S3. The feature map obtained in S2 is gradually reduced in spatial size and the channel dimension is increased to 1024 through downsampling operation. An enhancement mechanism for sensing the geometric structure and spatial distribution in the ground penetrating radar echo signal is embedded in the first two stages of the downsampling operation. S4. Wavelet transform is used as a physical prior embedding network to make up for the lack of spatial features in the enhanced high-dimensional feature map in S3. Through feature mining in the frequency domain, feature enhancement in both the spatial and frequency domains is achieved. S5. Based on S4, residual structure and multi-scale dilated convolution method are adopted to further expand the receptive field without increasing additional computational overhead and without losing resolution, so as to improve the efficiency of capturing deep global context information. S6. Based on S5, the spatial resolution of the image is gradually restored by an upsampling operation that is symmetrical to the downsampling operation in S3, and a multi-scale jump connection mechanism is set between the corresponding levels of the downsampling operation and the upsampling operation. S7. The feature map after upsampling and feature fusion in S6 is mapped and output as the final super-resolution image through a 1×1 convolutional layer combined with the Tanh activation function.

2. The super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors as described in claim 1, characterized in that, Also includes: S8. Establish training sets for low-resolution and high-resolution ground-penetrating radar, specifically as follows: S8.

1. Obtain ground-penetrating radar profile data of two different center frequency antennas from a single point at the actual acquisition location: A (high frequency) and B (low frequency). S8.

2. Time-series acquisition of ground-penetrating radar profile data from two different center frequency antennas at the actual acquisition location: C (high frequency) and D (low frequency). S8.3 Analyze data A and data B to obtain stratigraphic information H in the detection area; analyze data C and data D to obtain noise signal N in the actual acquisition. S8.

4. Randomly vary the thickness of the obtained stratigraphic H information to obtain random undulating stratigraphic layers H1, H2, H3, H4, and H5. Based on the random undulating stratigraphic information of H1, H2, H3, H4, and H5, establish models M1, M2, M3, M4, and M5; wherein the horizontal axis length of the model is 10m, the vertical axis depth is 8m, and the grid precision is 0.01m; randomly add target media of different sizes such as cavities, reinforcing bars, and pipes into M1, M2, M3, M4, and M5. After assigning relative permittivity values ​​to the strata and target media in the model, new MO1, MO2, MO3, MO4, and MO5 are formed. S8.

5. The method network constructed in S1-S7 is simulated using finite difference to simulate low-frequency and high-frequency ground-penetrating radar images respectively, and training set samples for low-resolution and high-resolution ground-penetrating radar are established.

3. The super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors as described in claim 1, characterized in that, In step S2, when mapping the single-channel information of the input image to the 64-dimensional feature space, an initial convolutional block is used. The initial convolutional block includes two consecutive 3×3 convolutional layers, a batch normalization layer, and a ReLU activation function. The convolution stride is 1 and the padding is 1, which is used to ensure that the spatial size of the feature map after convolution is consistent with that of the input image.

4. The super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors as described in claim 3, characterized in that, The downsampling operation in S3 is performed using four consecutive downsampling coding blocks. Each downsampling coding block includes a 2×2 max pooling layer and two 3×3 convolutional units. The max pooling layer has a stride of 2 and is used to halve the spatial size of the feature map. The two 3×3 convolutional units have a stride of 1 and padding of 1 and are used to perform depth extraction and double the number of channels on the downsampled features without changing the size of the feature map.

5. The super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors as described in claim 4, characterized in that, In S3, when embedding the enhancement mechanism, a hybrid enhancement module consisting of channel attention and collaborative attention is embedded at the output of the first two downsampling coding blocks. This module is designed for GPR image feature extraction and super-resolution reconstruction. The computational flow and parameters of the channel attention module are adapted to the channel dimension differences at the deployment location. It retains the core logic of squeezing, excitation, and recalibration to achieve accurate selection and response enhancement of effective feature channels of the GPR image. It is deployed at the output of the first and second downsampling coding blocks of the encoder, with corresponding feature channel numbers of 128 and 256, respectively. Both channel attention modules adjust the number of neurons in the fully connected layer according to the channel dimension to control the computational load while ensuring feature calibration accuracy. The collaborative attention module receives the feature map after recalibration by the channel attention module as input, continues the channel dimension at the deployment location, and fixes the pooling kernel size and convolution kernel parameters for the input resolution features of the GPR image to avoid overcomputation. The collaborative attention module achieves spatial attention enhancement through bidirectional spatial pooling, feature fusion encoding, weight generation, and spatial recalibration.

6. The super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors as described in claim 5, characterized in that, The channel attention module enhancement steps in S3 include: S3.

1. The input feature map is compressed into spatial information through global average pooling, transforming the two-dimensional spatial features into a one-dimensional channel descriptor, expressed as: ， in, The two-dimensional matrix is ​​the input to the feature map. To represent the squeeze mapping function of global average pooling, the spatial dimension ( ) Dimensionality reduced to (1 1), This is a value representing the global distribution characteristics of the channel after the compression operation; S3.

2. A two-stage fully connected layer is used to construct the non-linear dependency relationship between channels. The first-stage fully connected layer reduces the channel dimensionality and introduces the ReLU activation function to complete the non-linear mapping. The second-stage fully connected layer restores the original number of channels and generates the channel attention weight vector through the Sigmoid activation function, expressed as: ， in, For the Sigmoid activation function, For ReLU, It acts on the original feature map; S3.3 Multiply the weight vector element-wise with the original feature map along the channel dimension to complete the adaptive recalibration of the feature channels.

7. The super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors as described in claim 6, characterized in that, The enhanced steps of the collaborative attention module in S3 include: S3.

4. Perform one-dimensional global average pooling on the feature map after calibration in S3.3 along the horizontal and vertical directions, respectively, as follows: ， ， in, The feature vectors in the vertical direction, The feature vector in the horizontal direction; S3.5, will and The feature vectors from these two directions are concatenated in space, and expressed as: ， in, It serves as an intermediate variable, containing fused information encoded in both spatial directions; S3.5, after fusion Restored to horizontal direction and vertical direction Two feature vectors are used, and a horizontal spatial attention weight map is generated by the Sigmoid activation function, which is expressed as: ， ； S3.

6. Multiply the two weight maps generated in S3.5 element-wise with the calibrated feature map in S3.3 to complete the spatial dimension recalibration of the feature.

8. The super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors as described in claim 7, characterized in that, S4 includes: S4.

1. Using the discrete wavelet transform based on the Haar wavelet basis to apply input features in the frequency domain. Decompose to generate low-frequency approximate components. And high-frequency detail components in the horizontal, vertical, and diagonal directions. , , The decomposition process is represented as follows: ， Each subband has a dimension of 1. ; S4.

2. Perform targeted lightweight convolution processing on different frequency components, expressed as: ； S4.

3. Inverse wavelet transform is used to reconstruct the spatial domain, thereby effectively capturing subtle reflection interface information in ground-penetrating radar images, expressed as: 。 9. The super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors as described in claim 8, characterized in that, The residual structure and multi-scale dilated convolution method in S5 are executed through residual multi-scale dilation blocks, specifically including: S5.

1. Using an input convolutional layer built from standard convolutional operations, preliminary local extraction of input features is performed, reducing the dimension to [missing information]. Input feature map Mapped to a number of channels intermediate feature map ; S5.2, Through the U-Net encoding and decoding symmetrical structure built from an internal symmetrical structure containing multiple layers of encoding and decoding, in order to For input, through The process of learning and encoding multi-scale contextual features, in which... The encoding / decoding unit, representing a U-Net-like architecture, expands the receptive field in the encoding path by increasing the dilation rate of convolutional layers or performing stepwise downsampling, without significantly increasing the number of parameters. The internal computational flow is expressed as follows: ， in, This is the initial feature mapping; S5.3, through element-wise summation operation The multi-scale depth features are residually concatenated with the original input, and the final output is: 。 10. The super-resolution reconstruction method for ground-penetrating radar data based on wavelet domain physical priors as described in claim 9, characterized in that, Also includes: S9. The mean squared error loss is used as the training optimization criterion. The gradient is passed to each layer of the network through backpropagation to drive the iterative optimization of parameters and ensure the pixel-level feature restoration accuracy. During the training phase, parameters are updated using batch mean squared error loss. During the testing phase, RMSE and PSNR metrics are used to further evaluate the reconstruction performance, expressed as follows: ， in, These are the height and width of the image, respectively. For super-resolution image reconstruction in The pixel value of the location, For true high-resolution label images in The pixel value of the location.

Images