GPR Data Reconstruction Method and Device Based on RA-U-Net Network

Abstract

The present invention discloses a data processing method, specifically relating to a GPR data reconstruction method and device based on the RA-U-Net network. The method includes: acquiring target B-scan data and background B-scan data; replacing some of the A-scan data included in the target B-scan data with zero values to obtain training input B-scan data; subtracting the target B-scan data from the background B-scan data to obtain corresponding labeled B-scan data; training the RA-U-Net network using the training input B-scan data and the corresponding labeled B-scan data; inputting the B-scan data to be reconstructed into the trained RA-U-Net network for data reconstruction processing to obtain reconstructed B-scan data. This method can reconstruct GPR B-scan data and perform direct wave removal processing.

Description

Technical Field

[0001] The present invention belongs to a data processing method, and specifically relates to a GPR data reconstruction method and device based on a RA-U-Net network. Background Art

[0002] Ground Penetrating Radar (GPR) is a non-destructive testing technology that emits high-frequency electromagnetic waves for shallow subsurface detection, and obtains information about the subsurface structure by collecting scattered signals in the underground area. The GPR transmitting antenna emits electromagnetic waves underground at each scan point on the scan line. When the electromagnetic wave signal encounters the interface between different media or an anomaly with electromagnetic parameters different from the background, reflection and scattering phenomena will occur, and part of the signal will return to the surface and be received by the GPR receiving antenna. These received signals can generate one-dimensional (A-scan) signals, two-dimensional (B-scan) profiles or three-dimensional (C-scan) images of the subsurface structure, which are used to detect targets or evaluate the spatial position, shape, size and dielectric properties of the subsurface structure, etc.

[0003] Specifically, an A-scan echo data can be obtained at each position on the scan line, and multiple A-scan echo data obtained at each position on the scan line constitute GPR B-scan data. Further, multiple GPR B-scan data corresponding to multiple one-dimensional scan lines can constitute a GPR C-scan data.

[0004] When GPR is collecting data, it is extremely vulnerable to various factors, resulting in incomplete data collection, such as environmental factors like uneven ground surface and complex terrain, external factors like construction conditions and technical failures, and internal factors of the instrument like mismatches between sampling intervals and sampling speeds. The above situations will all lead to random or regular data loss, resulting in the scattering echoes of underground targets also showing spatial sampling missing, and further leading to a decline in GPR imaging quality, affecting subsequent data interpretation and analysis.

[0005] Current methods for missing data recovery are mainly interpolation methods and deep learning methods. Researchers use simple linear interpolation methods or directly ignore missing traces, resulting in low quality of the reconstructed GPR data, which has a negative impact on the interpretation and analysis of GPR data and the recognition of target signals. Summary of the Invention

[0006] The technical problem to be solved by the present invention is the problem of low quality of the reconstructed GPR data by existing methods. In order to achieve higher-quality missing data reconstruction, the present invention provides a GPR data reconstruction method and device based on a RA-U-Net network.

[0007] The content of the present invention includes:

[0008] In a first aspect, an embodiment of the present invention provides a GPR data reconstruction method based on an RA-U-Net network, including:

[0009] Obtaining target B-scan data in a first medium scenario and background B-scan data in a second medium scenario, where the first medium scenario includes pipeline targets, and the second medium scenario is the medium scenario obtained by removing the pipeline targets from the first medium scenario;

[0010] Replacing some A-scan data included in the target B-scan data with zero values to obtain training input B-scan data;

[0011] Subtracting the target B-scan data from the background B-scan data to obtain label B-scan data corresponding to the training input B-scan data;

[0012] Iteratively training the RA-U-Net network using the training input B-scan data and the corresponding label B-scan data to obtain a trained RA-U-Net network, where the RA-U-Net network is constructed based on the U-Net network;

[0013] Inputting the B-scan data to be reconstructed into the trained RA-U-Net network for data reconstruction processing to obtain reconstructed B-scan data with the direct wave removed.

[0014] Optionally, the obtaining target B-scan data in the first medium scenario and background B-scan data in the second medium scenario includes:

[0015] Constructing the first medium scenario including the pipeline targets;

[0016] In the first medium scenario, scanning along a one-dimensional survey line to obtain the target B-scan data, where the size of the target B-scan data is M×N, N is the number of scanning points on the one-dimensional survey line, M is the number of time sampling points, and M and N are positive integers;

[0017] Removing the pipeline targets from the first medium scenario to obtain the second medium scenario;

[0018] In the second medium scenario, scanning along the one-dimensional survey line to obtain the background B-scan data, where the size of the background B-scan data is M×N.

[0019] Optionally, before iteratively training the RA-U-Net network using the training input B-scan data and the corresponding labeled B-scan data to obtain a trained RA-U-Net network, the method further includes:

[0020] Construct the RA-U-Net network based on the U-Net network. The U-Net network is an encoder-decoder network architecture, including an encoder, a decoder, and a skip connection module. The encoder is used to gradually downsample the input into feature maps, the decoder is used to gradually restore the image resolution, and the skip connection module is used to connect the feature maps in the encoder to the corresponding levels in the decoder. The encoder includes a two-dimensional convolutional module;

[0021] Construct a nested residual module to replace the two-dimensional convolutional module in the encoder. The nested residual module includes a shallow residual block;

[0022] Construct an attention gating module and introduce the attention gating module into the skip connection module. The attention gating module is used to perform attention weighting on the high-level features output by the nested residual module and the feature maps passed after upsampling by the decoder.

[0023] Optionally, the shallow residual block includes an input path and a residual path. The input path sequentially includes a first convolutional layer and a batch normalization layer. The residual path includes a second convolutional layer to match the size and number of channels of the output of the input path and the output of the residual path. The residual path is used to implement the identity mapping from the input to the output;

[0024] The output of the shallow residual block satisfies:

[0025] L(x) = F(x) + H(x);

[0026] where x represents the feature input to the shallow residual block, F(x) is the output of the input path, and H(x) is the output of the residual path.

[0027] Optionally, the loss value for iteratively training the RA-U-Net network is determined based on the Huber loss, the MS-SSIM loss, and the perceptual loss;

[0028] The Huber loss satisfies:

[0029]

[0030] where y is the true value, f(x) is the predicted value, and δ is the hyperparameter of the Huber loss function, used to control the threshold;

[0031] The MS - SSIM loss satisfies:

[0032]

[0033] The original image is the first scale. Applying low - pass filtering and downsampling by a factor of two iteratively once gives the second scale, and after M - 1 iterations, it is the Mth scale. In the above formula, M is the total number of scales included in calculating the multi - scale structural similarity loss, μ f(x) is the mean of the predicted values, μ y is the mean of the true values, σ f(x) is the standard deviation of the predicted values, σ y is the standard deviation of the true values, σ f(x)y is the covariance, c1 and c2 are preset constants, β m and γ m are used to define the relative importance of the two components in each scale;

[0034] The perceptual loss satisfies:

[0035]

[0036] Among them, N represents the number of feature maps, i = 1, 2, 3, …, N represents the ith feature map, ||·||2 represents the L2 norm, represents the square of the L2 norm, F(y) is the feature representation of y in the target layer of the pre - trained convolutional neural network, G(f(x)) is the feature representation of f(x) in the target layer, and the target layer is located in the convolutional layer or fully - connected layer of the pre - trained convolutional neural network.

[0037] In a second aspect, an embodiment of the present invention provides a GPR data reconstruction device based on the RA - U - Net network, including:

[0038] An acquisition module, configured to acquire target B - scan data in a first medium scenario and background B - scan data in a second medium scenario. The first medium scenario includes pipeline targets, and the second medium scenario is the medium scenario obtained by removing the pipeline targets from the first medium scenario;

[0039] A first training data construction module, configured to replace some of the A - scan data included in the target B - scan data with zero values to obtain training input B - scan data;

[0040] A second training data construction module, configured to subtract the background B - scan data from the target B - scan data to obtain label B - scan data corresponding to the training input B - scan data;

[0041] A network training module, configured to iteratively train a RA-U-Net network by using the training input B-scan data and the corresponding labeled B-scan data, so as to obtain a trained RA-U-Net network, where the RA-U-Net network is constructed based on the U-Net network;

[0042] A data reconstruction module, configured to input the B-scan data to be reconstructed into the trained RA-U-Net network for data reconstruction processing, so as to obtain the reconstructed B-scan data with the direct wave removed.

[0043] In a third aspect, an embodiment of the present invention provides an electronic device, including: a memory, a processor, and a program stored in the memory and executable on the processor; the processor is configured to read the program in the memory to implement the steps in the GPR data reconstruction method based on the RA-U-Net network as described in the first aspect.

[0044] In a fourth aspect, an embodiment of the present invention provides a readable storage medium for storing a program, where the program, when executed by a processor, implements the steps in the GPR data reconstruction method based on the RA-U-Net network as described in the first aspect.

[0045] The beneficial effects of the present invention are as follows: In the embodiments of the present application, target B-scan data is acquired in a first medium scenario including pipeline targets, and background B-scan data is acquired in a corresponding second medium scenario after removing the pipeline targets. By replacing some of the A-scan data included in the target B-scan data with zero values, training input B-scan data is obtained; by subtracting the background B-scan data from the target B-scan data, the labeled B-scan data corresponding to the training input B-scan data is obtained; finally, the RA-U-Net network is iteratively trained by using the training input B-scan data and the corresponding labeled B-scan data to obtain a trained RA-U-Net network, where the RA-U-Net network is constructed based on the U-Net network. The beneficial effects of the present invention are: Inputting GPR data with missing spatial sampling into the RA-U-Net network to obtain reconstructed GPR data with the direct wave removed. Through the above method, not only can the data reconstruction problem in the case of missing spatial sampling in GPR B-scan be solved, but also the direct wave can be removed from the reconstructed data, improving the data recovery ability and direct wave suppression ability of GPR in the scenario of missing spatial sampling. Description of the Drawings

[0046] Att Figure 1 is one of the flowcharts of the GPR data reconstruction method based on the RA-U-Net network provided by the embodiment of the present invention;

[0047] AttFigure 2 Schematic diagram of the construction process of the data set provided by the embodiment of the present invention;

[0048] Appendix Figure 3 Schematic diagram of the structure of the nested residual module provided by the embodiment of the present invention;

[0049] Appendix Figure 4 Schematic diagram of the structure of the shallow residual block provided by the embodiment of the present invention;

[0050] Appendix Figure 5 Schematic diagram of the structure of the attention gating module provided by the embodiment of the present invention;

[0051] Appendix Figure 6 Schematic diagram of the RA-U-Net network training and data reconstruction process provided by the embodiment of the present invention;

[0052] Appendix Figure 7 Schematic diagram of the structure of the RA-U-Net network provided by the embodiment of the present invention;

[0053] Appendix Figure 8a Schematic diagram of the original GPR data of the processing results of four GPR B-scan data provided by the embodiment of the present invention;

[0054] Appendix Figure 8b Schematic diagram of the result of removing the direct wave by the mean method of the processing results of four GPR B-scan data provided by the embodiment of the present invention;

[0055] Appendix Figure 8c Schematic diagram of the missing data generated by spatial random sampling of the processing results of four GPR B-scan data provided by the embodiment of the present invention;

[0056] Appendix Figure 8d Schematic diagram of the test output result of the RA-U-Net network of the processing results of four GPR B-scan data provided by the embodiment of the present invention;

[0057] Appendix Figure 8e Schematic diagram of the true label data of the processing results of four GPR B-scan data provided by the embodiment of the present invention;

[0058] Appendix Figure 9 Schematic diagram of the GPR data reconstruction device based on the RA-U-Net network provided by the embodiment of the present invention;

[0059] Appendix Figure 10 Schematic diagram of the structure of the electronic device provided by the embodiment of the present invention. Detailed implementation manners

[0060] In the embodiments of the present application, the term "and / or" describes the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. The character " / " generally indicates that the associated objects before and after are in an "or" relationship. In the embodiments of the present application, the term "plural" refers to two or more, and other quantifiers are similar. The terms "first", "second", etc. in the specification and claims of the present application are used to distinguish similar objects, rather than to describe a specific order or sequence. It should be understood that such terms can be interchanged under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first" and "second" are usually of the same type, and do not limit the number of objects. For example, the first object can be one or multiple.

[0061] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.

[0062] Please refer to Figure 1 , Figure 1 which is a schematic flowchart of the GPR data reconstruction method based on the RA-U-Net network provided by the embodiments of the present invention. The method specifically includes the following steps:

[0063] Step 101, obtain target B-scan data in the first medium scenario and background B-scan data in the second medium scenario. The first medium scenario includes pipeline targets, and the second medium scenario is the medium scenario obtained by removing the pipeline targets from the first medium scenario.

[0064] Step 102, replace some of the A-scan data included in the target B-scan data with zero values to obtain training input B-scan data.

[0065] Step 103, subtract the background B-scan data from the target B-scan data to obtain the label B-scan data corresponding to the training input B-scan data.

[0066] Step 104, use the training input B-scan data and the corresponding label B-scan data to iteratively train the RA-U-Net network to obtain a trained RA-U-Net network. The RA-U-Net network is constructed based on the U-Net network.

[0067] Step 105: Input the B-scan data to be reconstructed into the trained RA-U-Net network for data reconstruction processing to obtain the reconstructed B-scan data with direct waves removed.

[0068] Please refer to Figure 2 , pre-construct a homogeneous or random medium scenario with a horizontal or undulating interface, in which pipeline targets are buried. The obtained medium scenario is the first medium scenario (also referred to as the target medium scenario), and the medium scenario obtained by removing the pipeline targets from the first medium scenario is the second medium scenario (also referred to as the background medium scenario).

[0069] Optionally, in some embodiments, step 101 includes:

[0070] Construct the first medium scenario including the pipeline targets;

[0071] Under the first medium scenario, scan along a one-dimensional survey line to obtain the target B-scan data. The size of the target B-scan data is M×N, where N is the number of scan points on the one-dimensional survey line, and M is the number of time sampling points. M and N are positive integers;

[0072] Remove the pipeline targets from the first medium scenario to obtain the second medium scenario;

[0073] Under the second medium scenario, scan along the one-dimensional survey line to obtain the background B-scan data. The size of the background B-scan data is M×N.

[0074] Specifically, use simulation software (such as gprMax) to scan the first medium scenario along a one-dimensional survey line. The survey line is perpendicular to the axial direction of the underground pipeline, and there are N scan points on the survey line. At each scan point, the transmitting antenna emits electromagnetic waves into the ground, and the receiving antenna receives the scattered echoes to obtain an A-scan echo data. The number of time sampling points is M. A total of N A-scan echo data are obtained from N scan points. Each A-scan echo data has M time sampling points, forming the target B-scan data with a size of M×N. Repeat the above steps in the second medium scenario to obtain the background B-scan data with a size of M×N.

[0075] Randomly extract A-scan data from the target B-scan data according to a preset percentage (denoted as P). During the extraction process, keep the spatial order and size of the target B-scan data unchanged. After extraction, the A-scan data of these measurement points are replaced with zero values to obtain the B-scan data with a spatial sampling missing rate of P, which can be used as the input data for the training of the RA-U-Net network in the future. Among them, P can be set and adjusted according to actual needs, and specific details are not limited here.

[0076] The ground penetrating radar (GPR) emits electromagnetic wave signals to the surface. The direct coupling wave between the transmitting and receiving antennas and the reflected wave from the surface form a direct wave. The target B-scan data and the background B-scan data have the same background information. By subtracting the two, the B-scan data with the direct wave removed can be obtained, which can be used as the true label data for the training of the RA-U-Net network in the future.

[0077] When the electromagnetic wave signal emitted by the GPR passes through the surface, a part of it is reflected by the surface. The reflected wave from the surface and the direct coupling wave between the transmitting and receiving antennas form a strong direct wave signal, which will interfere with the detection of the target scattering signal. The suppression of the direct wave interference signal is of great significance for improving the detection accuracy of underground target signals and the imaging resolution of the GPR. Due to the non-uniformity of the surface, the direct wave signal reflected by the surface by the electromagnetic wave has non-uniform characteristics, making it a difficult point to suppress the direct wave. Through the above method, the GPR B-scan data with the direct wave removed can be obtained, realizing the suppression of the direct wave.

[0078] In specific implementation, according to the above method, Y groups of GPR sample data are collected. Each group of GPR sample data includes a training input B-scan data and its corresponding label B-scan data. According to actual requirements, the sizes of all B-scan data in the Y groups of GPR sample data are readjusted to 256×256, and then the sample data set for iterative training of the RA-U-Net network can be obtained.

[0079] It should be noted that multiple GPR B-scan data corresponding to multiple one-dimensional survey lines can form a GPR C-scan data. The processing of the GPR C-scan data is realized by processing each B-scan data one by one and then combining them into a C-scan, which will not be elaborated here specifically.

[0080] Optionally, in some embodiments, before step 104, the method further includes:

[0081] Construct an RA-U-Net network based on the U-Net network. The U-Net network is an encoder-decoder network architecture, including an encoder, a decoder, and a skip connection module. The encoder is used to gradually downsample the input into a feature map, the decoder is used to gradually restore the image resolution, and the skip connection module is used to connect the feature map in the encoder to the corresponding layer in the decoder. The encoder includes a two-dimensional convolution module;

[0082] Construct a nested residual module to replace the two-dimensional convolution module in the encoder. The nested residual module includes a shallow residual block;

[0083] Construct an attention gating module and introduce the attention gating module into the skip connection module. The attention gating module is used to perform attention weighting on the high-level features output by the nested residual module and the feature map passed after upsampling by the decoder.

[0084] Construct the RA-U-Net network based on the U-Net network. The U-Net network consists of a symmetric encoder and decoder. The encoder gradually downsamples the input into feature maps, and the decoder is used to gradually restore the image resolution. The skip connection connects the feature maps in the encoder with the corresponding levels in the decoder. Design a nested residual module to replace the traditional two-dimensional convolution module in the encoder. The nested residual module is mainly composed of shallow residual blocks. Add an attention mechanism to the network, construct an attention gating module, and introduce it into the skip connection of the network to perform attention weighting on the high-level features output by the encoder residual module and the feature map passed after upsampling by the decoder, and then perform feature fusion.

[0085] The nested residual module is mainly composed of shallow residual blocks. A skip connection is added to each convolutional layer of the nested residual module, which is a nested combination of multiple shallow residual blocks. Please refer to Figure 3 and Figure 4 , Figure 4 is the structural schematic diagram of the shallow residual block (ResidualBlock, ResB), that is, Figure 3 the ResB module shown in Figure 4 which contains two branches. The left branch is the skip connection, which contains a 1×1 convolution to match the size and number of channels of the output of the right branch; the right branch contains a two-dimensional convolution.

[0086] As Figure 3 shown, the nested residual module processes the input features in two paths. Path one contains a shallow residual block; Path two sequentially includes a shallow residual block, a convolutional layer, and a batch normalization layer (Batch Normalization, BN). The convolutional kernel size of the convolutional layer is 3×3, the stride is 1, and the padding is 1. The results of the two paths are added and processed through the ReLU activation function and then output. Through the above settings, the neural network can learn the residual information of each layer instead of completely re-learning the original function, making it easier to train deep networks.

[0087] Optionally, in some embodiments, the shallow residual block includes an input path and a residual path. The input path sequentially includes a first convolutional layer and a batch normalization layer. The residual path includes a second convolutional layer to match the size and number of channels of the output of the input path and the output of the residual path. The residual path is used to implement the identity mapping from the input to the output.

[0088] The output of the shallow residual block satisfies:

[0089] L(x) = F(x) + H(x);

[0090] Wherein, x represents the feature input to the shallow residual block, F(x) is the output of the input path, and H(x) is the output of the residual path.

[0091] Specifically, as Figure 4 shown, the shallow residual block includes two main parts: an input path and a residual path. The input path is a traditional neural network structure, which sequentially includes a convolutional layer (i.e., the first convolutional layer) and a batch normalization layer. The convolutional kernel size of the first convolutional layer is 3×3, the stride is 1, and the padding is 1. The residual path is an identity mapping from the input to the output, i.e., a skip connection, and includes a convolutional layer with a size of 1×1 (i.e., the second convolutional layer) to match the dimensions and number of channels of the output of the input path and the output of the residual path. The results of the input path and the residual path are summed, and then passed through the ReLU activation function to obtain the output of the shallow residual block.

[0092] In this embodiment, a nested residual module is designed to replace the traditional two-dimensional convolutional module in the U-Net network encoder, which can make full use of the residual information of each layer, alleviate the problem of gradient disappearance in the training of deep networks, enhance the feature extraction ability, and accelerate the efficiency of network convergence.

[0093] Construct an Attention Gates (AG) module, as Figure 5 shown, the Attention Gates inputs a feature signal and a gating signal, which are the high-level feature x l output from the l-th layer residual block of the encoder and the feature map g passed after upsampling in the decoder, respectively. After attention weighting, feature fusion is performed. The attention coefficient α l is calculated, and the process can be described as:

[0094]

[0095]

[0096] Wherein, the attention coefficient α i ∈[0,1], g i correspond to the feature vectors of each pixel value i of the two feature maps respectively; W x and W g represent the transformation coefficients of the features x l and g respectively, and ψ is the transformation coefficient of the combination of the two features; W g 、W x 、ψ all include convolutional and batch normalization operations, the convolutional kernel size is 1×1, the stride is 1, the padding is 0, b g and b ψ are the bias terms corresponding to the convolution; Θatt represent ψ, W x , W g , b g , b ψ The above series of parameters; i represents the spatial dimension, c represents the channel dimension, σ1 is the ReLU activation function, and σ2 is the Sigmoid function.

[0097] The output of the attention gating module is the element-wise multiplication of the attention coefficient and the input high-level feature x l :

[0098]

[0099] By constructing the attention gating module and introducing it into the skip connection of the network, the interaction between the data missing area and other related parts can be strengthened, more detailed information can be reconstructed during the signal recovery process, and the continuity and accuracy of signal recovery can be enhanced.

[0100] In this embodiment, the design of the nested residual module can alleviate the problem of gradient disappearance in the training of deep networks, enhance the feature extraction ability and accelerate the efficiency of network convergence; the design of the attention module can strengthen the interaction between the data missing area and other related parts, and enhance the continuity and accuracy of signal recovery.

[0101] Finally, initialize the network parameters of the RA-U-Net network, and use the training input B-scan data and the corresponding label B-scan data to iteratively train the RA-U-Net network to obtain a trained RA-U-Net network.

[0102] The specific steps of training the RA-U-Net network using the dataset obtained above in step 104 are as follows:

[0103] S1: Initialize the training parameters of the RA-U-Net network and train using the dataset obtained in the above manner.

[0104] S2: Perform batch training on the RA-U-Net network. The batch size is set to p, that is, each batch trains p GPR sample data with a spatial sampling missing rate of P. Then, each training round performs k batch trainings, is the ceiling function, and Y, k, and p are all positive integers. At the beginning of each training round, the order of the training set samples is shuffled so that the batch-processed GPR sample data is randomly selected to improve the effect of network training.

[0105] S3: Use the B-scan data with a spatial sampling missing rate of P in one of the k groups of training data that has not been trained in S2 above as the input for training the RA-U-Net network, and use the B-scan data with the direct wave removed as the true label data to train the RA-U-Net network.

[0106] S4: Repeat the steps of S2 to S3 until one training epoch is completed.

[0107] S5: Repeat the steps of S2 to S4 until the loss error of the RA-U-Net network tends to be stable, then the training of the RA-U-Net network is completed. Specifically, during network training, let L n be the loss error of the nth training epoch, L n-1 be the loss error of the (n - 1)th training epoch, L n-2 be the loss error of the (n - 2)th training epoch, L n-3 be the loss error of the (n - 3)th training epoch, where n ≥ 4. When for all i (i = 1, 2, 3) it satisfies |L n - L n-i | ≤ ε, where ε is a constant with a very small relative loss magnitude value, indicating that the model has reached stability after the nth training.

[0108] Optionally, in some embodiments, the loss value for iterative training of the RA-U-Net network is determined based on the Huber loss, multi-scale structural similarity (MS-SSIM) loss, and perceptual loss;

[0109] The Huber loss satisfies:

[0110]

[0111] where y is the true value, f(x) is the predicted value, and δ is the hyperparameter of the Huber loss function for controlling the threshold; within this threshold, the mean squared error is used, and outside it, the absolute error is used, specifically as follows:

[0112]

[0113] The MS-SSIM loss satisfies:

[0114]

[0115] In the above formula, M is the total number of scales included in calculating the multi-scale structural similarity loss, μ f(x) is the mean of the predicted value, μ y is the mean of the true value, σf(x) is the standard deviation of the predicted value, σ y is the standard deviation of the true value, σ f(x)y is the covariance, c1 and c2 are preset constants, β m and γ m are used to define the relative importance of two components in each scale. In specific implementation, to avoid unstable situations of division by zero, two constants c1 = 0.01 2 and c2 = 0.03 2 are given.

[0116] It should be understood that the MS-SSIM loss calculates the weighted sum of the structural similarity losses at multiple scales, and these scales can be achieved by blurring or sampling the image. The original image is the first scale, applying low-pass filtering and downsampling by a factor of two iteratively once is the second scale, and after M - 1 iterations is the Mth scale.

[0117] The perceptual loss satisfies:

[0118]

[0119] where N represents the number of feature maps, i = 1, 2, 3, …, N represents the ith feature map, ·2 represents the L2 norm, represents the square of the L2 norm, F(y) is the feature representation of y at the target layer in the pre-trained convolutional neural network, G(f(x)) is the feature representation of f(x) at the target layer, and the target layer is located in the convolutional layer or fully connected layer of the pre-trained convolutional neural network.

[0120] In this embodiment, the loss value for iterative training of the RA-U-Net network can be expressed as:

[0121] L total = f(L Huber , L MS-SSIM , L perceptual )

[0122] L Huber is the Huber loss, which is more suitable for handling outliers than the mean square error. The Huber loss function combines the mean square error and the absolute error, using the mean square error when the error is small and the absolute error when the error is large, thus balancing the sensitivity to outliers.

[0123] L MS-SSIM represents the MS-SSIM loss, which calculates the weighted sum of the structural similarity losses at multiple scales, and these scales can be achieved by blurring or sampling the image.

[0124] L perceptualIt represents perceptual loss, which measures the difference between images based on perceptual similarity. It captures the texture, structure, and semantic information of images by extracting feature representations in a neural network, rather than just the difference in pixel values. Typically, perceptual loss uses a pre-trained convolutional neural network (such as VGG) to extract features and takes the difference between the generated matrix and the real matrix on these features as the loss. Such a design enables perceptual loss to better guide the deep model to generate more realistic data.

[0125] In this embodiment, a comprehensive loss function is designed, including Huber loss, multi-scale structural similarity loss, and perceptual loss. Combining these three as the loss value function for the iterative training of the RA-U-Net network can guide the network to converge to an effective solution more efficiently and accurately.

[0126] In the embodiment of this application, target B-scan data is obtained in the first medium scenario containing pipeline targets, and background B-scan data is obtained in the corresponding second medium scenario after removing pipeline targets. By replacing some A-scan data included in the target B-scan data with zero values, training input B-scan data is obtained; by subtracting the target B-scan data from the background B-scan data, the labeled B-scan data corresponding to the training input B-scan data is obtained; finally, the RA-U-Net network is iteratively trained using the training input B-scan data and the corresponding labeled B-scan data to obtain a trained RA-U-Net network. The RA-U-Net network is constructed based on the U-Net network. The beneficial effects of the present invention are: inputting GPR data with missing spatial sampling parts into the RA-U-Net network to obtain reconstructed GPR data with direct wave suppression. Through the above method, not only can the recovery of GPR signals with missing spatial sampling parts be achieved efficiently and with high precision, but also the suppression of direct waves can be realized, improving the recognition accuracy of underground target signals and the imaging resolution of ground penetrating radar.

[0127] Inputting GPR data with missing spatial sampling parts into the trained RA-U-Net network can obtain GPR reconstructed data with direct wave suppression. After processing each of the multiple B-scan data that make up the GPR C-scan data in the above manner and then combining them, the processing of the GPR C-scan data can be realized.

[0128] See Figure 6 , and the following takes a specific embodiment as an example for illustration.

[0129] In this embodiment, 570 sets of GPR B-scan simulation data are obtained using the gprMax simulation software. The C-scan profile is a spatial combination of multiple B-scans, so the present invention is not limited to the processing of GPR B-scan data, but is also applicable to the processing of GPRC-scan data. The processing of GPR C-scan data is achieved by processing the multiple B-scan data that make up the C-scan data one by one and then combining them, and the details are not repeated here. The GPR B-scan simulation data set is divided into a training set, a validation set, and a test set according to 7:1:2, that is, 399 sets of data are used to train the RA-U-Net network, and 57 and 114 sets of data are used for network verification and testing.

[0130] First, a random medium scene with an undulating interface is constructed, in which a horizontal cylindrical pipeline target is buried (the first medium scene can be obtained at this time). The gprMax simulation software is used to scan the detection scene along a one-dimensional survey line, and the survey line direction is perpendicular to the axis direction of the underground pipeline. At each position of the survey line, an A-scan echo data is obtained. The multiple A-scan echo data obtained at each position on the survey line constitute a GPR B-scan data containing the pipeline target, that is, the target B-scan data. In the simulation scene, the pipeline target is removed and the background medium scene is kept unchanged. At this time, the second medium scene can be obtained. Repeat the above process in the second medium scene to obtain GPR B-scan data without pipeline targets, that is, background B-scan data. The target B-scan data is randomly extracted by A-scan at 70%. During the extraction process, the spatial order and size of each channel of the target B-scan data are kept unchanged. After extraction, the A-scan data of these measurement points are replaced with zero values ​​to obtain GPR data with a spatial sampling missing rate of 70%, which is the training input B-scan data. The target B-scan data is subtracted from the background B-scan data (the former minus the latter) to obtain the GPR B-scan data with suppressed direct waves, which is the corresponding label B-scan data.

[0131] According to the above method, 570 sets of GPR B-scan data were collected, and all data sizes were resized to 256 × 256 to obtain the data set for network training. Among them, 399 sets of GPR data with a spatial sampling missing rate of 70% and GPR B-scan data with suppressed direct waves were used as network input and real label data sets to train the RA-U-Net network, and 57 sets of simulation data and 114 sets of simulation data were used for network verification and testing.

[0132] Construct the RA-U-Net network. Based on the U-Net encoder-decoder network architecture, design a nested residual module to replace the traditional two-dimensional convolutional module in the encoder. The structure of the nested residual module is as follows:Figure 3 and Figure 4 as shown. An attention gating module is constructed and introduced into the skip connections of the network. Attention weighting is performed on the high-level features output by the encoder residual block and the feature map passed after upsampling by the decoder, and then feature fusion is performed. The structure of the attention gating is shown in Figure 5 as shown. A combined loss function is designed, including the Huber loss, multi-scale structural similarity loss, and perceptual loss, and their linear combination is used as the network training loss function. In this embodiment, a linear combination of the three is adopted, but it is not limited to the linear combination, and a non-linear combination method can also be used. The RA-U-Net network structure is as shown in Figure 7 as shown.

[0133] The RA-U-Net network is trained using 399 sets of simulation data. The number of training epochs is set to 30, the initial learning rate is set to 0.01, the batch training size is 4, and 4 samples are trained in one batch training. The network training loss function is a linear combination of the Huber loss, MS-SSIM loss, and perceptual loss:

[0134]

[0135] The weights of the three loss functions are 0.5, 0.3, and 0.2 respectively. The perceptual loss extracts features from 4 levels of the pre-trained VGG19 network, namely "conv1_1", "conv2_1", "conv3_1", and "conv4_1".

[0136] During the training process of the RA-U-Net network, in each batch training, 4 sets of GPR data with a spatial sampling missing rate of 70% and the corresponding true label data are input into the network for training, and the reconstructed GPR data suppressing the direct wave is output. The loss function value is calculated by comparing the output data with the true label data and accumulated to the previous batch training loss value. In one training epoch, all samples are trained according to the batch size, the network parameters are updated and optimized according to the loss function value, and then the network training of the next training epoch is carried out. After 30 training epochs, the loss function value tends to be stable, the network training is completed, and the model and parameter values of the network training are saved.

[0137] 114 sets of GPR data with a spatial sampling missing rate of 70% are input into the trained RA-U-Net network to test the training effect of the network. And the network trained with the single cylindrical pipeline target GPR simulation data is used to test the double cylindrical pipeline target GPR simulation data. Figures 8a - 8e contains the processing results of four GPR B-scan data. Among them, the figures in the first column and the second column are the results of the single cylindrical pipeline target simulation data, and the figures in the third column and the fourth column are the results of testing the double cylindrical pipeline target simulation data.Figure 8a shows the original GPR data. In the image, the direct wave signal has a large and uneven intensity, while the target signal is relatively weak, which will seriously affect the detection and recognition of the target signal; Figure 8b is the effect of suppressing the direct wave using the traditional mean method. Due to the uneven direct wave signal caused by the undulating ground surface, the direct wave signal cannot be effectively suppressed; Figure 8c is the GPR data with a 70% spatial sampling missing rate; Figure 8d is the test output result of the RA-U-Net network. It not only restores the target signal but also suppresses the direct wave interference signal. Comparing Figure 8e with the true label data, the network test result has achieved a good restoration effect visually. As can be seen from the test results of the double-target data in the third column of Figures 8a - 8e , the network has a good restoration effect on the target hyperbolic signal, but in other details, such as the mutual interference wave signal between targets, it is not restored.

[0138] Table 1 gives Figures 8a - 8e the accuracy results of the 4 groups of data shown in

[0139] and the average value of the accuracy results of the 114 groups of data in the test set. The three index values of Mean Square Error (MSE), Peak signal-to-noise ratio (PSNR), and Structural Similarity (SSIM) are all calculated based on the comparison of the model test results with the true label data. From the results in the table, it can be seen that even when the spatial sampling missing rate of the GPR data is relatively large (70%), the single-target GPR data (Sample 1 and Sample 2) in the test set still achieve high accuracy in all three indexes; there is no double-target GPR data sample in the training set, but the double-target GPR data (Sample 3 and Sample 4) tested also obtain high accuracy values, indicating that the reconstruction effect of the network is very good; the three average index values of the 114 groups of test data also achieve high accuracy.

[0140]

[0141] The GPR missing data reconstruction and direct wave suppression method based on the RA-U-Net network implemented by the present invention can not only reconstruct the GPR data with partially missing spatial sampling with high accuracy but also suppress the direct wave signal on the horizontal ground or undulating ground during network training, completing the dual-target tasks of GPR missing signal restoration and direct wave suppression, which is helpful for the extraction of underground target echo characteristics. The present invention effectively realizes the dual-target tasks of missing signal restoration and direct wave signal suppression, and well solves the problem that the direct wave cannot be effectively suppressed under the condition of uneven ground surface.

[0142] AsFigure 9 As shown in Figure 9 , an embodiment of the present invention further provides a GPR data reconstruction device 900 based on an RA-U-Net network, including:

[0143] An acquisition module 901, configured to acquire target B-scan data in a first medium scenario and background B-scan data in a second medium scenario, where the first medium scenario includes pipeline targets, and the second medium scenario is the medium scenario obtained by removing the pipeline targets from the first medium scenario;

[0144] A first training data construction module 902, configured to replace some A-scan data included in the target B-scan data with zero values to obtain training input B-scan data;

[0145] A second training data construction module 903, configured to subtract the background B-scan data from the target B-scan data to obtain label B-scan data corresponding to the training input B-scan data;

[0146] A network training module 904, configured to iteratively train an RA-U-Net network using the training input B-scan data and the corresponding label B-scan data to obtain a trained RA-U-Net network, where the RA-U-Net network is constructed based on a U-Net network;

[0147] A data reconstruction module 905, configured to input the B-scan data to be reconstructed into the trained RA-U-Net network for data reconstruction processing to obtain a reconstructed B-scan data with the direct wave removed.

[0148] Optionally, the acquisition module 901 includes:

[0149] A construction unit, configured to construct the first medium scenario including the pipeline targets;

[0150] A first scanning unit, configured to perform scanning along a one-dimensional survey line in the first medium scenario to obtain the target B-scan data, where the size of the target B-scan data is M×N, N is the number of scanning points on the one-dimensional survey line, M is the number of time sampling points, and M and N are positive integers;

[0151] A processing unit, configured to remove the pipeline targets from the first medium scenario to obtain the second medium scenario;

[0152] A second scanning unit, configured to perform scanning along the one-dimensional survey line in the second medium scenario to obtain the background B-scan data, where the size of the background B-scan data is M×N.

[0153] Optionally, the GPR data reconstruction device 900 based on the RA-U-Net network further includes:

[0154] A first construction module, configured to construct the RA-U-Net network based on the U-Net network. The U-Net network is an encoder-decoder network architecture, including an encoder, a decoder, and a skip connection module. The encoder is used to gradually downsample the input into a feature map. The decoder is used to gradually restore the image resolution. The skip connection module is used to connect the feature map in the encoder to the corresponding layer in the decoder. The encoder includes a two-dimensional convolution module;

[0155] A second construction module, configured to construct a nested residual module to replace the two-dimensional convolution module in the encoder. The nested residual module includes a shallow residual block;

[0156] A third construction module, configured to construct an attention gating module and introduce the attention gating module into the skip connection module. The attention gating module is used to perform attention weighting on the high-level features output by the nested residual module and the feature map passed after upsampling by the decoder.

[0157] Optionally, the shallow residual block includes an input path and a residual path. The input path sequentially includes a first convolutional layer and a batch normalization layer. The residual path includes a second convolutional layer to match the size and number of channels of the output of the input path and the output of the residual path. The residual path is used to implement the identity mapping from the input to the output;

[0158] The output of the shallow residual block satisfies:

[0159] L(x) = F(x) + H(x);

[0160] where x represents the feature input to the shallow residual block, F(x) is the output of the input path, and H(x) is the output of the residual path.

[0161] Optionally, the loss value for iterative training of the RA-U-Net network is determined based on the Huber loss, the MS-SSIM loss, and the perceptual loss;

[0162] The Huber loss satisfies:

[0163]

[0164] where y is the true value, f(x) is the predicted value, and δ is the hyperparameter of the Huber loss function, used to control the threshold;

[0165] The MS-SSIM loss satisfies:

[0166]

[0167] The original image is the first scale. Applying low-pass filtering and downsampling by a factor of two iteratively once results in the second scale, and after M - 1 iterations, it is the Mth scale. In the above formula, M is the total number of scales included in calculating the multi-scale structural similarity loss, μ f(x) is the mean of the predicted values, and μ y is the mean of the true values, σ f(x) is the standard deviation of the predicted values, and σ y is the standard deviation of the true values, and σ f(x)y is the covariance, c1 and c2 are preset constants, and β m and γ m are used to define the relative importance of the two components in each scale;

[0168] The perceptual loss satisfies:

[0169]

[0170] where N represents the number of feature maps, i = 1, 2, 3,..., N represents the ith feature map, ·2 represents the L2 norm, represents the square of the L2 norm, F(y) is the feature representation of y in the target layer of the pre-trained convolutional neural network, G(f(x)) is the feature representation of f(x) in the target layer, and the target layer is located in the convolutional layer or fully connected layer of the pre-trained convolutional neural network.

[0171] The GPR data reconstruction device 900 based on the RA-U-Net network provided in the embodiments of the present application can execute the above method embodiments, and its implementation principle and technical effects are similar, so they will not be elaborated here in this embodiment.

[0172] It should be noted that the division of units in the embodiments of the present application is illustrative, only a logical function division, and there may be other division methods in actual implementation. In addition, in each embodiment of the present application, the functional units can be integrated in one processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above integrated units can be implemented in the form of hardware or in the form of software functional units.

[0173] When the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a processor-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) or a processor to execute all or part of the steps of the methods described in various embodiments of this application. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs that can store program codes.

[0174] As Figure 10 As shown, an embodiment of this application provides an electronic device 1000, including: a memory 1002, a processor 1001, and a program stored on the memory 1002 and executable on the processor 1001; the processor 1001 is configured to read the program in the memory 1002 to implement the steps in the GPR data reconstruction method based on the RA-U-Net network as described above.

[0175] The embodiments of the present application further provide a readable storage medium. A program is stored on the readable storage medium. When the program is executed by a processor, it implements each process of the above-mentioned embodiments of the GPR data reconstruction method based on the RA-U-Net network and can achieve the same technical effects. To avoid repetition, it will not be elaborated here. Among them, the readable storage medium can be any available medium or data storage device accessible by the processor, including but not limited to magnetic memories (such as floppy disks, hard disks, magnetic tapes, magneto-optical disks (MO), etc.), optical memories (such as compact disks (CD), digital versatile discs (DVD), Blu-ray discs (BD), high-definition versatile discs (HVD), etc.), and semiconductor memories (such as read-only memories (ROM), erasable programmable read-only memories (EPROM), electrically erasable programmable read-only memories (EEPROM), non-volatile memories (NAND FLASH), solid-state disks (SSD)).

[0176] It should be noted that in this article, the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or further includes elements inherent to such process, method, article or device. Without further limitations, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, article or device including that element.

[0177] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-described example methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, disk, optical disc) and includes several instructions for causing a terminal (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in various embodiments of the present application.

[0178] The embodiments of the present application have been described above in conjunction with the accompanying drawings. However, the present application is not limited to the above specific implementation manners. The above specific implementation manners are merely illustrative and not restrictive. Under the inspiration of the present application, those of ordinary skill in the art can also make many forms without departing from the purpose of the present application and the scope protected by the claims, and all of them fall within the protection scope of the present application.

Claims

1. A GPR data reconstruction method based on the RA-U-Net network, characterized in that, Including: Obtaining target B-scan data in a first medium scenario and background B-scan data in a second medium scenario, where the first medium scenario includes a pipeline target, and the second medium scenario is the medium scenario obtained by removing the pipeline target from the first medium scenario; Replacing some A-scan data included in the target B-scan data with zero values to obtain training input B-scan data; Subtracting the background B-scan data from the target B-scan data to obtain label B-scan data corresponding to the training input B-scan data; Iteratively training an RA-U-Net network using the training input B-scan data and the corresponding label B-scan data to obtain a trained RA-U-Net network, where the RA-U-Net network is constructed based on the U-Net network; Inputting the B-scan data to be reconstructed into the trained RA-U-Net network for data reconstruction processing to obtain reconstructed B-scan data with direct waves removed; Where, before using the training input B-scan data and the corresponding label B-scan data to iteratively train the RA-U-Net network to obtain a trained RA-U-Net network, the method further includes: Constructing an RA-U-Net network based on the U-Net network. The U-Net network is an encoder-decoder network architecture, including an encoder, a decoder, and a skip connection module. The encoder is used to gradually downsample the input into a feature map, the decoder is used to gradually restore the image resolution, and the skip connection module is used to connect the feature map in the encoder to the corresponding layer in the decoder. The encoder includes a two-dimensional convolution module; Constructing a nested residual module to replace the two-dimensional convolution module in the encoder. The nested residual module includes a shallow residual block; Constructing an attention gating module and introducing the attention gating module into the skip connection module. The attention gating module is used to perform attention weighting on the high-level features output by the nested residual module and the feature map transmitted after upsampling by the decoder; Where, the shallow residual block includes an input path and a residual path. The input path sequentially includes a first convolutional layer and a batch normalization layer. The residual path includes a second convolutional layer to match the size and number of channels of the output of the input path and the output of the residual path. The residual path is used to achieve an identity mapping from the input to the output; The output of the shallow residual block satisfies: L(x) = F(x) + H(x); Where, x represents the feature input to the shallow residual block, F(x) is the output of the input path, and H(x) is the output of the residual path.

2. The method according to claim 1, characterized in that, The obtaining target B-scan data in the first medium scenario and background B-scan data in the second medium scenario includes: Constructing the first medium scenario including the pipeline target; In the first medium scenario, the target B-scan data is obtained by scanning along a one-dimensional survey line. The size of the target B-scan data is M×N, where N is the number of scanning points on the one-dimensional survey line, M is the number of time sampling points, and M and N are positive integers. The pipeline target in the first medium scenario is removed to obtain the second medium scenario. In the second medium scenario, the background B-scan data is obtained by scanning along the one-dimensional survey line. The size of the background B-scan data is M×N.

3. The method according to claim 1 or 2, characterized in that The loss value for the iterative training of the RA-U-Net network is determined based on the Huber loss, MS-SSIM loss, and perceptual loss. The Huber loss satisfies: where y is the true value, f(x) is the predicted value, and δ is the hyperparameter of the Huber loss function, which is used to control the threshold. The MS-SSIM loss satisfies: The original image is the first scale. Applying low-pass filtering and downsampling by a factor of two iteratively once results in the second scale, and after M-1 iterations, it is the Mth scale. In the above formula, M is the total number of scales included in calculating the multi-scale structural similarity loss, μ f(x) is the mean of the predicted values, μ y is the mean of the true values, σ f(x) is the standard deviation of the predicted values, σ y is the standard deviation of the true values, σ f(x)y is the covariance, c1 and c2 are preset constants, β m and γ m are used to define the relative importance of the two components in each scale; The perceptual loss satisfies: Where N represents the number of feature maps, i = 1, 2, 3, …, N represents the i-th feature map, ||·||2 represents the L2 norm, represents the square of the L2 norm, F(y) is the feature representation of y at the target layer in the pre-trained convolutional neural network, G(f(x)) is the feature representation of f(x) at the target layer, and the target layer is located in the convolutional layer or the fully connected layer in the pre-trained convolutional neural network.

4. A GPR data reconstruction device based on the RA-U-Net network, characterized in that, It includes: An acquisition module, which is used to acquire the target B-scan data in the first medium scenario and the background B-scan data in the second medium scenario. The first medium scenario contains a pipeline target, and the second medium scenario is the medium scenario obtained by removing the pipeline target from the first medium scenario. A first training data construction module, which is used to replace some of the A-scan data included in the target B-scan data with zero values to obtain the training input B-scan data. A second training data construction module, which is used to subtract the background B-scan data from the target B-scan data to obtain the label B-scan data corresponding to the training input B-scan data. A network training module, which is used to iteratively train the RA-U-Net network using the training input B-scan data and the corresponding label B-scan data to obtain a trained RA-U-Net network. The RA-U-Net network is constructed based on the U-Net network. A data reconstruction module, which is used to input the B-scan data to be reconstructed into the trained RA-U-Net network for data reconstruction processing to obtain the reconstructed B-scan data with the direct wave removed. Among them, the GPR data reconstruction device based on the RA-U-Net network further includes: A first construction module, which is used to construct the RA-U-Net network based on the U-Net network. The U-Net network is an encoder-decoder network architecture, including an encoder, a decoder, and a skip connection module. The encoder is used to gradually downsample the input into a feature map, the decoder is used to gradually restore the image resolution, and the skip connection module is used to connect the feature map in the encoder to the corresponding layer in the decoder. The encoder includes a two-dimensional convolution module. A second construction module, which is used to construct a nested residual module to replace the two-dimensional convolution module in the encoder. The nested residual module includes a shallow residual block. A third building block for constructing an attention gating module and introducing the attention gating module into the skip connection module, where the attention gating module is used to perform attention weighting on the high-level features output by the nested residual module and the feature map passed after upsampling by the decoder; Among them, the shallow residual block includes an input path and a residual path. The input path sequentially includes a first convolutional layer and a batch normalization layer. The residual path includes a second convolutional layer to match the dimensions and number of channels of the output of the input path and the output of the residual path. The residual path is used to achieve an identity mapping from the input to the output; The output of the shallow residual block satisfies: L(x) = F(x) + H(x); where x represents the feature input to the shallow residual block, F(x) is the output of the input path, and H(x) is the output of the residual path.

5. An electronic device, comprising: A memory, a processor, and a program stored on the memory and executable on the processor; characterized in that the processor is configured to read the program in the memory to implement the steps in the GPR data reconstruction method based on the RA-U-Net network according to any one of claims 1 to 3.

6. A readable storage medium for storing a program, characterized in that, When the program is executed by the processor, it implements the steps in the GPR data reconstruction method based on the RA-U-Net network according to any one of claims 1 to 3.

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