A missing data-oriented closed-loop ground penetrating radar intelligent inversion method

Abstract

The application discloses a missing data-oriented closed-loop ground penetrating radar intelligent inversion method, and steps include: S1 generating sample data for training and testing; S2 designing a closed-loop inversion network; S3 calculating inversion loss and forward loss; S4 synchronously optimizing trainable parameters of the inversion and forward subnetworks through back propagation, so that the inversion subnetwork predicts a dielectric constant model conforming to physical reality when input data is incomplete. The technical problem of how to accurately and robustly invert underground medium structure when channel loss or noise interference exists in ground penetrating radar data is solved. Under normal interference-free conditions, high-precision ground penetrating radar inversion can be realized, and under the condition that data loss or noise interference exists, high inversion accuracy and robustness can still be maintained.

Description

Technical Field

[0001] This invention belongs to the field of ground penetrating radar data processing and imaging technology, and in particular relates to a closed-loop intelligent inversion method for ground penetrating radar with missing data. Background Technology

[0002] Ground penetrating radar (GPR), a high-resolution near-surface detection technology, has been widely used in fields such as underground structure detection, engineering health monitoring, and environmental assessment, playing a crucial role in geophysical exploration due to its non-destructive testing advantages. High-quality GPR data is the foundation for subsequent imaging and inversion, directly determining the reliability of imaging accuracy, anomaly identification, and underground target location. However, in complex geological and engineering environments, GPR data is often affected by noise, signal attenuation, and interference, easily leading to local missing or incomplete data, resulting in decreased data quality and consequently affecting inversion accuracy and stability.

[0003] However, GPR data processing and inversion still have certain limitations in dealing with missing data, especially in complex geological environments. Traditional interpolation, filtering, and data imputation methods, while simple to implement, struggle to accurately recover the true signal, often leading to distortion or overfitting and causing deviations between the inversion results and the actual geological structure. Furthermore, missing data in complex environments can cause anomaly identification errors, target location errors, and even difficulties in convergence during the inversion process, thus reducing the reliability and applicability of the method. Therefore, achieving stable and high-precision GPR inversion under missing data conditions has become a critical problem urgently needing to be solved in current research and engineering applications.

[0004] In recent years, deep learning methods have provided new opportunities for GPR data inversion. Compared with traditional methods, deep learning can automatically learn complex nonlinear mapping relationships from large-scale samples through an end-to-end training process, effectively transforming raw radar signals into information on underground electrical structures. Models such as Convolutional Neural Networks (CNNs) have outstanding advantages in feature extraction and spatial pattern recognition, and can suppress noise interference while maintaining high resolution, thereby significantly improving imaging accuracy and computational efficiency. This allows deep learning to maintain good adaptability and robustness in complex environments, laying the foundation for real-time or near-real-time underground structure inversion. However, most existing methods still adopt an open-loop structure, that is, unidirectionally mapping input data to output results, lacking feedback and correction mechanisms for prediction results. When faced with missing data or uncertainties, this open-loop mode is prone to error accumulation, exhibiting insufficient generalization ability and unstable results. Therefore, how to introduce feedback regulation, adaptive optimization, and physical constraints into the deep learning framework has become a key issue to promote the further development of intelligent GPR inversion methods.

[0005] To achieve high-precision and stable GPR inversion in situations with missing data and complex environments, a method is needed that can establish a connection between predictions and observations and possess self-correction and adaptive capabilities. An ideal inversion framework should be able to identify biases by comparing the generated subsurface model with the original data, and continuously optimize the prediction results during the iterative process. Such mechanisms can effectively suppress error propagation, reduce dependence on the initial model and complete data, thereby improving the accuracy, stability, and robustness of the inversion while ensuring physical plausibility. Summary of the Invention

[0006] The purpose of this invention is to provide a closed-loop intelligent inversion method for missing data, in order to solve the technical problem of how to accurately and robustly invert the underground medium structure when there are missing channels or noise interference in the ground penetrating radar (GPR) data.

[0007] The technical solution adopted in this invention is a closed-loop ground-penetrating radar intelligent inversion method for missing data, characterized by the following steps:

[0008] Step S1: Generate sample data for training and testing;

[0009] Step S2: Design a closed-loop inversion network;

[0010] Step S3: Calculate the inversion loss and the forward loss;

[0011] Step S4: Through backpropagation, the trainable parameters of the inversion and forward sub-networks are optimized simultaneously, so that the inversion sub-network can predict a dielectric constant model that conforms to physical reality when the input data is incomplete.

[0012] Furthermore, the specific steps of S1 are as follows:

[0013] S11, the original B-scan data is generated using the two-dimensional random medium method;

[0014] S12, introduce missing regions into the original B-scan data, and apply the loss function through a masking function. Define and apply a mask to the original B-scan data to obtain a B-scan image containing missing data.

[0015] Furthermore, the specific steps of S2 are as follows:

[0016] S21, Design the inverse subnetwork architecture and the forward subnetwork architecture;

[0017] S22, the B-scan image of the missing data obtained in S12 The input is fed into the inversion subnetwork architecture, and the output is the predicted dielectric constant distribution. ;

[0018] S23, the predicted dielectric constant distribution obtained in S22 Input the forward subnetwork and output the complete synthetic B-scan image. ;

[0019] S24, to synthesize the complete B-scan image Images with missing data By comparing the results, the generated error signals guide the optimization direction of the trainable parameters of the inversion subnetwork in real time through a closed-loop feedback path, and iteratively update the trainable parameters of the inversion and forward subnetworks.

[0020] Furthermore, in S21, the inversion sub-network architecture adopts a four-layer encoder-decoder structure. Each layer of the encoder contains two convolutional blocks and a max pooling layer. The convolutional block is composed of a convolutional kernel, a batch normalization layer, and a ReLU activation function in sequence. Each layer of the decoder includes a transposed convolution and a skip connection. The forward sub-network architecture is symmetrical to the inversion sub-network structure, but the weights are independent.

[0021] Furthermore, the specific steps of S3 are as follows:

[0022] S31, the inversion loss is calculated using the mean squared error and multi-scale structural similarity, as shown in the following formula:

[0023]

[0024]

[0025]

[0026] in, For mean square error loss, For the sample size, For the first The actual label of each sample For the first Predicted label for each sample, For multi-scale structural similarity loss, For the first Structural similarity index at different scales It is the coarsest scale. Weights for each scale, For inversion loss;

[0027] S32, a masking mechanism is introduced to calculate the forward modeling loss function, as shown in the following formula:

[0028]

[0029] in, Indicates the first The masked missing region of each sample Indicates the first The emphasized missing regions of each sample, This represents the adjustment coefficient. This represents the multi-scale structural similarity loss between forward modeling predictions and the actual B-scan. For the loss of orthogonal modeling, For actual B-scan images, The predicted B-scan image;

[0030] S33, Calculate the total loss function, the formula is as follows:

[0031]

[0032] in, For the total loss, The weights for the inversion loss, The weights for the inversion loss.

[0033] Furthermore, in step S4, the backpropagation algorithm is used to automatically calculate the total loss. relative to the trainable parameters of the inverted subnetwork Trainable parameters of the subnetwork The gradients are calculated, and the trainable parameters of the inverse and forward subnetworks are updated in real time based on the two gradients, iterating until the model converges.

[0034] The beneficial effects of this invention are:

[0035] This invention achieves high-precision ground-penetrating radar inversion under normal, interference-free conditions, and maintains high inversion accuracy and robustness even with missing data or noise interference. Compared with traditional interpolation methods, this invention utilizes a closed-loop feedback mechanism to dynamically correct the prediction results and combines a multi-scale loss function to balance overall accuracy and local structural features, thereby effectively avoiding overfitting and imaging blurring, and improving applicability and reliability under complex operating conditions. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a schematic diagram of the CL-UNet network architecture based on a closed-loop structure, as presented in this invention.

[0038] Figure 2 This is a schematic diagram of the sub-network architecture in the CL-UNet network based on the closed-loop structure of this invention.

[0039] Figure 3 This is a schematic diagram of the B-scan data and inversion results of the first type of B-scan image during the verification experiment of this invention. (a) is the B-scan image with missing data, (b) is the complete synthesized B-scan image, (c) is the predicted B-scan image of the forward sub-network, (d) is the actual dielectric constant model, (e) is the B-scan image obtained by CL-UNet, and (f) is the B-scan image obtained by OL-UNet.

[0040] Figure 4 This is a schematic diagram of the B-scan data and inversion results of the first type of B-scan image during the verification experiment of this invention. (a) is the B-scan image with missing data, (b) is the complete synthesized B-scan image, (c) is the predicted B-scan image of the forward sub-network, (d) is the actual dielectric constant model, (e) is the B-scan image obtained by CL-UNet, and (f) is the B-scan image obtained by OL-UNet.

[0041] Figure 5 This is a schematic diagram of the loss curves in the network training and validation process of this invention, where Train Loss is the training loss and Valid Loss is the validation loss.

[0042] Figure 6 These are schematic diagrams of the inversion results of the measured data under different missing proportions, where (a) is the B-scan image of the original measured data, (b) is the measured B-scan image of the data with 20% random missing, (c) is the measured B-scan image of the data with 40% random missing, and (d) is the measured B-scan image of the data with 60% random missing.

[0043] Figure 7 These are schematic diagrams illustrating the inversion results of data with different missing proportions after applying the CL-UNet of the present invention. (a) is the B-scan image of the original data, (b) is the B-scan image of data with 20% random missing, (c) is the B-scan image of data with 40% random missing, and (d) is the B-scan image of data with 60% random missing.

[0044] Figure 8These are schematic diagrams of the inversion results of data with different missing proportions after applying OL-UNet. (a) is the B-scan image of the original data, (b) is the B-scan image of data with 20% random missing, (c) is the B-scan image of data with 40% random missing, and (d) is the B-scan image of data with 60% random missing.

[0045] Figure 1 In the diagram, loss_a is the loss for predicting the non-missing part between the B-scan and the original B-scan, and loss_b is the loss for predicting the missing part between the B-scan and the original B-scan. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] Example

[0048] In practical ground-penetrating radar (GPR) detection, the underground medium often exhibits complex and non-uniform characteristics. Furthermore, due to environmental interference, equipment malfunctions, or limitations in detection conditions, the acquired B-scan data frequently suffers from missing channels or noise contamination, directly affecting the accuracy of the inversion results. To address this practical need, this invention proposes a closed-loop intelligent GPR inversion method for missing data, as illustrated in the following diagram. Figure 1 As shown, the specific steps are as follows:

[0049] Step S1, Sample Data Construction: By establishing a typical subsurface medium model and using the GPR forward modeling method, sample data for training and testing is generated. This sample includes both complete signals and introduces varying degrees of data gaps to simulate different scenarios that may be encountered in actual detection, thereby enhancing the robustness and adaptability of the model. The specific steps are as follows:

[0050] S11. Construct training sample data. A two-dimensional random medium method is used to generate training sample data that closely approximates actual observation conditions, i.e., the original B-scan data. The modeling process fully considers stratigraphic undulations and non-uniformity, and sets the dielectric constant according to the actual environment. The value range of is [2, 15], to simulate typical media such as dry soil, wet soil, concrete, and air cavities. The random medium generation function can be expressed as:

[0051]

[0052] in, As the reference dielectric constant, The disturbance intensity factor, , They represent the horizontal and vertical directions, respectively. , They are respectively , The autocorrelation length in the direction, For random medium generation function, It is a random perturbation function.

[0053] S12, Construct missing sample data by introducing missing regions into the original B-scan data. Based on the potential amount of missing data in the actual data, set the missing data ratio according to low, medium, and high missing levels. Preferably, in this embodiment, the missing ratios are set to 20%, 40%, and 60%, respectively. The loss is masked using a mask function. The definition is as follows:

[0054]

[0055] A mask is applied to the synthesized B-scan data to obtain a B-scan image containing missing data, as shown below:

[0056]

[0057] in, For a complete B-scan image, B-scan image representing missing data.

[0058] This step ensures that the network is exposed to and learns different missing scenarios during the training phase, thereby gaining the ability to recover and reconstruct missing data.

[0059] Step S2: Design a closed-loop inversion network to adapt to uncertainties in actual radar detection. The closed-loop inversion network consists of an inversion subnetwork and a forward subnetwork. The inversion subnetwork receives the original B-scan image (including missing data) and outputs a predicted dielectric constant distribution model. The forward subnetwork generates a synthetic B-scan image based on the prediction model and compares it with the original input image to form a closed-loop feedback. The architecture diagrams of the forward and inversion subnetworks are shown below. Figure 2 As shown. The specific steps are as follows:

[0060] S21, Design the inverse sub-network architecture and the forward sub-network architecture, as follows:

[0061] The inversion sub-network architecture employs a four-layer encoder-decoder structure. In the encoder path, each layer contains two convolutional blocks, each consisting of a 3x3 convolutional kernel, a batch normalization layer, and a ReLU activation function, followed by a 2x2 max-pooling layer with a stride of 2 for downsampling and multi-level feature extraction. In the decoder path, each layer first uses a 2x2 transposed convolution for upsampling to restore spatial resolution. Then, it performs skip connections with the feature maps of the corresponding layers in the encoder path to fuse high-resolution details with high-level semantic information, ensuring the complete detail of the output dielectric constant model.

[0062] Forward subnetwork architecture: Symmetrical to the inverse subnetwork structure, but does not share weights, it is specifically used to simulate the propagation process of radar waves in actual underground media, mapping the dielectric constant model to a B-scan image.

[0063] S22, the B-scan image of the missing data obtained in S12 The input is fed into the inversion subnetwork architecture, and the output is the predicted dielectric constant distribution. The specific formula is as follows:

[0064]

[0065] in, To invert the subnetwork architecture, These are the trainable parameters of the inverted subnetwork.

[0066] S23, the predicted dielectric constant distribution obtained in S22 Input the forward subnetwork and output the complete synthetic B-scan image. The specific formula is as follows:

[0067]

[0068] in, For a forward sub-network architecture, These are the trainable parameters of the orthogonal subnetwork.

[0069] S24, to synthesize the complete B-scan image Images with missing data By comparing the results, a "self-check" is achieved. The generated error signal guides the optimization direction of the trainable parameters of the inversion subnetwork in real time through the closed-loop feedback path, and iteratively updates the trainable parameters of the inversion and forward subnetworks to complete the "self-correction". This dynamic correction mechanism enables the model to directly predict the dielectric constant model that conforms to physical laws from the missing data, significantly reducing prediction bias and enhancing the model's adaptability to uncertain conditions in actual detection.

[0070] In this invention, the trainable parameters of both the inverse and forward subnetworks are obtained through automatic learning and optimization via an end-to-end supervised learning training process. The purpose of this process is to find an optimal set of parameters. and This minimizes the total loss function of the entire closed-loop network.

[0071] Step S3: Calculate the inversion loss and forward loss to optimize both the inversion and forward processes during model training, thereby improving performance under conditions of actual missing data. The specific steps are as follows:

[0072] S31, the inversion loss is calculated using mean squared error (MSE) and multi-scale structural similarity (MS-SSIM) to constrain the difference between the predicted and true values ​​of the dielectric constant distribution. The formula is as follows:

[0073]

[0074] in, For mean square error loss, For the sample size, For the first The actual label of each sample For the first Predicted labels for each sample.

[0075]

[0076] in, For multi-scale structural similarity loss, For the first Structural similarity index at different scales It is the coarsest scale. Weights for each scale, For the first The actual label of each sample For the first Predicted labels for each sample.

[0077]

[0078] in, This is the loss from the inversion.

[0079] S32 introduces a masking mechanism to calculate the forward modeling loss function, distinguishing between missing and complete regions and constraining the consistency between the synthesized B-scan data and the real data. The formula is as follows:

[0080]

[0081] in, Indicates the first The masked missing regions of each sample are removed, and only complete data is retained. Indicates the first Emphasizing missing regions in individual samples to guide network repair; Indicates the adjustment coefficient, preferably. Set to 0.6; This represents the multi-scale structural similarity loss between the forward modeling prediction and the actual B-scan (and) (The calculation method is the same) For the loss of orthogonal modeling, For actual B-scan images, The image is the predicted B-scan image.

[0082] S33, Calculate the total loss function, the formula is as follows:

[0083]

[0084] in, Total loss; The preferred weights for the inversion loss are: Set to 0.6; The preferred weights for the inversion loss are: Set it to 0.4.

[0085] Step S4: Use the backpropagation algorithm to automatically calculate the total loss. relative to the trainable parameters of the inverted subnetwork Trainable parameters of the subnetwork The gradient is calculated, and the trainable parameters of the inversion and forward sub-networks are updated in real time based on the two gradients. The iteration continues until the model converges, enabling the inversion sub-network to learn to predict a dielectric constant model that is more in line with physical reality when the input data is incomplete. This effectively suppresses error accumulation and overfitting, and improves the inversion stability in practical applications.

[0086] This invention introduces a forward modeling subnetwork, incorporating the physical process of radar wave propagation (learned by the forward modeling subnetwork) as a strong constraint into the optimization objective. This forces the inversion subnetwork to output a dielectric constant model that can withstand the test of physical laws; that is, the inversion subnetwork must output a prediction result that matches the true dielectric constant distribution and can be consistent with measured B-scan data through forward modeling. Essentially, the forward modeling subnetwork provides an inherent physical regularization for the inversion subnetwork, enabling the model not only to learn data mappings but also to infer a physically consistent overall structure from partial information. This mechanism greatly improves the model's generalization ability and robustness to data gaps and noise interference, effectively suppresses overfitting, and achieves a unity between data-driven approaches and physical mechanisms, providing a more interpretable and reliable solution for ground-penetrating radar data inversion.

[0087] Experimental verification

[0088] The Adam optimizer is used, with an initial learning rate set to The accuracy decreases with each iteration. During training, the input is a B-scan image containing missing data, and the output is the predicted dielectric constant model and the repaired B-scan. In the prediction phase, the network first outputs the dielectric constant model, and then generates the repaired B-scan through a forward sub-network. The final prediction result is compared with the true model.

[0089] To comprehensively evaluate the performance of the proposed closed-loop intelligent inversion method (CL-UNet), two sets of experiments were designed: 1) comparing it with the open-loop deep learning method on synthetic data; 2) verifying its effectiveness and robustness in practical applications on measured GPR data.

[0090] Figure 3 , Figure 4 The inversion results of two different B-scan methods, CL-UNet and the open-loop deep learning method (OL-UNet), are presented. Figure 3 (a) and Figure 4 (a) is the B-scan image of the missing data. Figure 3 (b) and Figure 4 (b) is the complete synthetic B-scan image. Figure 3 (c) and Figure 4 (c) is the predicted B-scan image of the forward subnetwork. Figure 3 (d) and Figure 4 (d) is the actual dielectric constant model. Figure 3 (e) and Figure 4 (e) is the B-scan image obtained by CL-UNet. Figure 3 (f) and Figure 4 (f) is the B-scan image obtained by OL-UNet.

[0091] from Figure 3 The position of the first bounding box in the inversion results shows that CL-UNet has higher inversion accuracy and provides a clearer inversion of hierarchical interfaces. Observation Figure 4 At box 1, CL-UNet demonstrates more accurate inversion of the layered interface. At box 2, the anomalous body shape inverted by CL-UNet is closer to the real model; while OL-UNet suffers from missing information, resulting in incomplete anomalous body shapes. Therefore, CL-UNet exhibits superior inversion performance and higher inversion accuracy.

[0092] Figure 5 The loss curves during network training and validation are shown. The total loss value of CL-UNet decreases steadily and converges with the number of iterations, proving the stability and effectiveness of the closed-loop optimization process.

[0093] Figures 6-8 The inversion results of the measured data under different missing proportions are shown. The original B-scan images of the measured data and the B-scan images of the measured data with random missing proportions of 20%, 40%, and 60% are displayed. Figure 6 As shown in (a)~(d), after applying CL-UNet, the original and randomly missing 20%, 40%, and 60% of the data are represented as follows: Figure 7 As shown in (a)~(d), after applying OL-UNet, the original and randomly missing 20%, 40%, and 60% of the data are represented as follows. Figure 8 As shown in (a)~(d).

[0094] observe Figure 6 In the B-scan analysis, the hyperbolic signals in red boxes 1 and 2 are misaligned, while the hyperbolic signals in yellow boxes 3 and 4 are layered. When there is no data loss, observation... Figure 7 and Figure 8 In (a), the inversion results of CL-UNet and OL-UNet are basically similar, but CL-UNet is superior in terms of detail restoration. For example, in the yellow box (No. 3), CL-UNet provides clearer layering and well-defined boundaries, while OL-UNet shows blurred boundaries. In the red box (No. 2), CL-UNet depicts the thrust fault boundaries more clearly, while OL-UNet depicts them more blurred. This indicates that both methods can effectively invert subsurface structures, but CL-UNet excels in detail restoration.

[0095] When 20% of the data is lost, OL-UNet's performance degrades, particularly with the appearance of some spurious stripes in the red boxes 1 and 2. CL-UNet remains stable, exhibiting less data loss and a clear hierarchical structure, indicating that moderate data loss has a greater impact on OL-UNet than CL-UNet, which maintains higher inversion accuracy and stability. When 40% of the data is missing, OL-UNet shows obvious spurious stripes and loses crucial subsurface information, especially in the yellow box 4. While also affected, CL-UNet retains more complete subsurface details, such as complete layered information below 2.5m and visible layer boundaries in the yellow box 3, demonstrating that despite a higher proportion of lost data, CL-UNet still performs well. When 60% of the data is missing, OL-UNet's results lose almost all identifiable subsurface structures. Although affected, CL-UNet still retains some inversion capability and provides key information, showing better robustness under extreme data loss conditions, while OL-UNet's inversion results become unusable. Experimental results show that CL-UNet can effectively predict underground structural information and derive an accurate dielectric constant model, verifying the practical value and good performance of CL-UNet.

[0096] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0097] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A closed-loop ground-penetrating radar intelligent inversion method for missing data, characterized by the following steps: include: Step S1: Generate sample data for training and testing; Step S2: Design a closed-loop inversion network; Step S3: Calculate the inversion loss and the forward loss; Step S4: Through backpropagation, the trainable parameters of the inversion and forward sub-networks are optimized simultaneously, so that the inversion sub-network can predict a dielectric constant model that conforms to physical reality when the input data is incomplete. The specific steps of S1 are as follows: S11, the original B-scan data is generated using the two-dimensional random medium method; S12, introduce missing regions into the original B-scan data, and apply the loss function through a masking function. Define and apply a mask to the original B-scan data to obtain a B-scan image containing missing data; The specific steps of S2 are as follows: S21, Design the inverse subnetwork architecture and the forward subnetwork architecture; S22, the B-scan image of the missing data obtained in S12 The input is fed into the inversion subnetwork architecture, and the output is the predicted dielectric constant distribution. ; S23, the predicted dielectric constant distribution obtained in S22 Input the forward subnetwork and output the complete synthetic B-scan image. ; S24, to synthesize the complete B-scan image Images with missing data By comparison, the generated error signal guides the optimization direction of the trainable parameters of the inversion subnetwork in real time through the closed-loop feedback path, and iteratively updates the trainable parameters of the inversion and forward subnetworks. In S21, the inversion subnetwork architecture adopts a four-layer encoder-decoder structure. Each layer of the encoder contains two convolutional blocks and a max pooling layer. The convolutional block is composed of a convolutional kernel, a batch normalization layer, and a ReLU activation function in sequence. Each layer of the decoder includes a transposed convolution and a skip connection. The forward subnetwork architecture is symmetrical to the inversion subnetwork structure, but the weights are independent. The specific steps of S3 are as follows: S31, the inversion loss is calculated using the mean squared error and multi-scale structural similarity, as shown in the following formula: ； ； ； in, For mean square error loss, For the sample size, For the first The actual label of each sample For the first Predicted label for each sample, For multi-scale structural similarity loss, For the first Structural similarity index at different scales It is the coarsest scale. Weights for each scale, For inversion loss; S32, a masking mechanism is introduced to calculate the forward modeling loss function, as shown in the following formula: ； in, Indicates the first The masked missing region of each sample Indicates the first The emphasized missing regions of each sample, This represents the adjustment coefficient. This represents the multi-scale structural similarity loss between forward modeling predictions and the actual B-scan. For the loss of orthogonal modeling, For actual B-scan images, The predicted B-scan image; S33, Calculate the total loss function, the formula is as follows: ； in, For the total loss, The weights for the inversion loss, The weights for the inversion loss.

2. The intelligent inversion method for closed-loop ground-penetrating radar retrieval based on missing data according to claim 1, characterized in that, In step S4, the backpropagation algorithm is used to automatically calculate the total loss. relative to the trainable parameters of the inverted subnetwork Trainable parameters of the subnetwork The gradients are calculated, and the trainable parameters of the inverse and forward subnetworks are updated in real time based on the two gradients, iterating until the model converges.

Images