A transformer-based GPR image clutter removal method

Abstract

This invention relates to the field of image processing and discloses a transformer-based GPR image clutter removal method, comprising the following steps: constructing a transformer deep learning algorithm model; the model includes a feature extraction layer, a feature fusion layer, and a feature output layer; the feature extraction layer includes a sequentially connected convolutional layer, three consecutive axis-based transformer modules, and a cross-layer attention fusion module; the feature fusion layer uses an encoder-decoder hierarchical structure, with the encoder containing four stages and the decoder containing three stages, and weighted skip connections between the encoder and decoder; the feature output layer includes three consecutively connected axis-based transformer modules, a cross-layer attention fusion module, and a convolutional layer; after training the model, the trained model is used for clutter removal. The method disclosed in this invention can remove clutter while retaining the effective signal, improving processing accuracy.

Description

Technical Field

[0001] This invention relates to image processing methods, and more particularly to a transformer-based GPR image clutter removal method. Background Technology

[0002] Ground penetrating radar (GPR) is a geophysical method that uses antennas to transmit and receive high-frequency electromagnetic waves to detect the internal material properties and distribution patterns of a medium. As a non-invasive and non-destructive detection method, GPR has a wide range of applications. In the civilian sector, GPR can be used to detect road quality and underground pipelines. However, during actual data acquisition, the signals received by GPR often contain a large amount of noise. This is because the electromagnetic properties of underground media vary, such as conductivity and dielectric constant, and are also affected by environmental electromagnetic interference, ground clutter, and the radar acquisition system itself. This noise can severely interfere with the effective signal, reducing the clarity and interpretability of GPR images, affecting the detection accuracy and resolution of underground targets, and may even lead to incorrect interpretations and judgments. Therefore, effective clutter removal techniques are needed to improve the quality of GPR images.

[0003] Currently, GPR image clutter removal methods are mainly divided into two categories: traditional signal processing-based methods and deep learning-based methods. Traditional methods remove clutter using classic signal processing techniques such as filtering, wavelet transform, and principal component analysis. These methods rely on mature signal theory and have a clear operational process in simple clutter scenarios (such as uniform background noise), but their performance is poor in complex scenarios, failing to meet the dual requirements of accurate preservation of effective signal and effective clutter suppression in complex environments. Deep learning methods, on the other hand, learn the characteristic differences between clutter and effective signal from a large amount of GPR image data and construct a clutter removal model. Compared to traditional methods, this approach has a stronger ability to suppress nonlinear clutter and can handle more complex signal distributions. Therefore, deep learning-based GPR image clutter removal technology has become a research hotspot.

[0004] GPR image data not only contains superimposed information of clutter and valid signals, but also contains spatial structural features (such as the geometry of the target) and temporal correlations of signals (such as signal responses at different detection depths). Therefore, effectively utilizing deep learning methods to deeply mine the hidden features and correlation patterns in this data is crucial for improving the clutter removal effect of ground-penetrating radar images in complex scenes. Early deep learning methods, such as fully convolutional networks (FCN) and their variant U-Net, while effectively extracting local details when processing spatial features of images, neglected the integration of global information. These methods were designed to focus more on spatial dimension feature learning. However, for ground-penetrating radar images, which contain both spatial structural complexity and temporal correlations of signals, relying solely on spatial dimension modeling often fails to fully distinguish between dynamic clutter and static valid signals, resulting in the loss of edge details of valid signals or the retention of some dynamic clutter after clutter removal. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a transformer-based GPR image clutter removal method to preserve valid signals while removing clutter.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A transformer-based GPR image clutter removal method includes the following steps:

[0008] Step 1: Construct a deep learning algorithm model for the transformer;

[0009] The model includes a feature extraction layer, a feature fusion layer, and a feature output layer. The feature extraction layer includes a convolutional layer connected in sequence, three consecutive axis basis transformer modules, and a cross-layer attention fusion module.

[0010] The feature fusion layer uses an encoder-decoder hierarchical structure. The encoder contains four stages, each consisting of a downsampling layer and multiple axis-based transformer modules. The decoder contains three stages, each consisting of an upsampling layer and multiple axis-based transformer modules, and a weighted skip connection is made between the encoder and the decoder.

[0011] The feature output layer includes three consecutive axis basis transformer modules, a cross-layer attention fusion module, and a convolutional layer connected in sequence.

[0012] Step 2, train the model;

[0013] Real data was collected in sand with different relative permittivity using the GPR system. The data was preprocessed to obtain the GPR real image dataset. The open-source hybrid GPR image dataset CLT-GPR was obtained and used together with the GPR real image dataset to construct the dataset required for training, which was divided into training set, validation set and test set.

[0014] The training set images are input into the model for training, the validation set images are used to evaluate the model's accuracy and adjust the parameters, and the test set is used to evaluate the model's generalization ability and prediction accuracy.

[0015] Step 3: Use the trained model to remove clutter;

[0016] After preprocessing the GPR image containing clutter, it is input into a qualified model for clutter removal.

[0017] In the above scheme, the axis-based transformer module includes a normalization layer, an axis-based multi-head self-attention module, a hybrid expert module, a gating network, and a dynamic weighted fusion mechanism;

[0018] The axis-based multi-head self-attention module includes a height-axis multi-head attention module and a width-axis multi-head attention module; the input features of the axis-based transformer module and the output features of the axis-based multi-head self-attention module are respectively input into the hybrid expert module and the gating network after element-wise addition.

[0019] The hybrid expert module includes four expert modules, each consisting of a normalization layer and a dual-gated feedforward network or a frequency-domain enhanced feedforward network, wherein there are two dual-gated feedforward networks and two frequency-domain enhanced feedforward networks; each expert module independently receives the features output by the axis-based multi-head self-attention module and outputs its own feature map;

[0020] The gated network consists of 3×3 convolutional layers and a softmax activation function. The gated network first extracts spatial features from the input features, and then normalizes them using the softmax activation function to generate dynamic weights for each expert.

[0021] The dynamic weighted fusion mechanism dynamically assigns weights and performs element-wise multiplication with the outputs of the corresponding expert modules. Then, it sums the elements of all weighted expert output features to obtain the final output features.

[0022] In the above scheme, the height-axis multi-head attention module receives three branches simultaneously from the input feature map. Each branch operates identically: it enhances the input feature representation through a 1×1 convolution, then captures local contextual information through a 3×3 depthwise convolution. The three branches then generate the query Q, key K, and value V, respectively. The outputs Q, K, and V of the three branches are then reshaped to obtain... , , ,Will , , It is split into k attention heads along the channel dimension. and Attention weights are calculated using matrix multiplication to obtain the height axis attention matrix. The height axis attention matrix is ​​then normalized using softmax and weighted with V to obtain the output of a single attention head. Finally, the outputs of all attention heads are concatenated and integrated using a 1×1 convolution to obtain the height axis attention result.

[0023] The structure of the width-axis multi-head attention module is the same as that of the height-axis multi-head attention module; the input of the width-axis multi-head attention module is the output of the height-axis multi-head attention module, and the final output is the attention-enhanced feature after dimensional reshaping.

[0024] In the above scheme, the dual-gated feedforward network first processes the input feature map through two parallel paths. Each path first adjusts the channel dimension through a 1×1 convolution to optimize the feature representation, and then captures local contextual information through a 3×3 depthwise convolution to enhance the local detail representation of the features. In the dual-gated filtering stage, the first path performs a GELU activation function on the convolution-processed features to non-linearly transform the features, and then performs element-wise multiplication with the original convolution-processed features in the second path. The second path performs a GELU activation function on the convolution-processed features to non-linearly transform the features, and then performs element-wise multiplication with the original convolution-processed features in the first path. Subsequently, the output features of the two paths are summed element-wise, and then summed element-wise with the input features after a 1×1 convolution to obtain the dual-gated filtered features.

[0025] In the frequency domain enhancement feedforward network, the input features are first processed through two parallel paths. Each path first adjusts the channel dimension through a 1×1 convolution to optimize feature representation, and then captures local contextual information through a 3×3 depthwise convolution to enhance the local detail representation of the features. The two paths are activated by ReLU, and the output features of the first and second paths are multiplied element-wise to obtain the output features. In the frequency domain enhancement stage, the features output by the parallel feature processing paths are first passed through a 1×1 convolutional layer and padded, and then the features are divided into 4×4 patch blocks. Next, the features are transformed into the frequency domain by a fast Fourier transform, and element-wise multiplication is performed in the frequency domain with the learnable FFT parameters. Then, the features are transformed back into the time domain by an inverse fast Fourier transform, and the output features are obtained by block merging and size clipping.

[0026] In the above scheme, in the cross-layer attention fusion module, multiple input features are first reshaped to unify the feature dimensions for subsequent attention calculations. The reshaped features simultaneously enter three parallel branches, and the three branches operate identically, each passing through two convolutional layers of 1×1 and 3×3. The three branches generate query Q, key K, and value V, respectively. After dimension reshaping, Q and K generate an attention matrix through matrix multiplication. After dimension reshaping, V is multiplied by the attention matrix, then reshaped again, and finally summed element-wise with the input features. Finally, it is integrated through a 1×1 convolution to generate an output feature map that fuses the effective information of multiple input features.

[0027] In the above scheme, the encoder input is the fusion feature output by the cross-layer attention fusion module, denoted as... The encoder consists of four stages. Each stage first performs downsampling through pixel rearrangement, reducing the feature map space size to ( The number of channels doubled. Let i be the encoder stage number. After downsampling, each stage extracts deep features through an increasing number of axis-based transformer modules. The number of axis-based transformer modules in the encoder from the first to the fourth stage is 2, 4, 8, and 16 respectively. Furthermore, the number of attention heads in the axis-based multi-head self-attention modules within each stage's axis-based transformer module is 1, 2, 4, and 8 respectively, gradually strengthening the ability to capture long-distance dependencies and complex features. The final output feature is denoted as... ;

[0028] The decoder consists of three stages to produce features from the encoder output. For input, each stage first performs upsampling through pixel rearrangement: restoring the feature map space size to twice its original size while adjusting the number of channels to the appropriate dimension. After upsampling, each stage optimizes feature details through an increasing number of axis-based transformer modules. The number of axis-based transformer modules in the decoder from the first to the third stage is 2, 4, and 8 respectively; and the number of attention heads in the axis-based multi-head self-attention modules in each stage's axis-based transformer module is 1, 2, and 4 respectively. Simultaneously, a weighted skip connection with a 1×1 convolution is introduced between the axis-based transformer module in the third stage of the encoder and the upsampling result in the first stage of the decoder; a weighted skip connection with a 1×1 convolution is introduced between the axis-based transformer module in the second stage of the encoder and the upsampling result in the second stage of the decoder; and a weighted skip connection with a 1×1 convolution is introduced between the axis-based transformer module in the first stage of the encoder and the upsampling result in the third stage of the decoder. These connections are used to adjust the contribution weights of the encoder and decoder features, reducing information loss. The encoder input features... After passing through the axis-based transformer block, the upsampled results of the output features from the third stage of the decoder are weighted and connected to finally output the reconstructed features.

[0029] In the above scheme, the hybrid loss function used in model training is as follows:

[0030] ;

[0031] in, =2, =0.005, used to balance the contributions of the two loss functions; It is a smoothing loss function. It is an adversarial loss function. It is a wavelet loss function;

[0032] The smoothing loss function is defined as:

[0033] ;

[0034] in, For the i-th image as input, This is the predicted value for the i-th image output by the model. Let be the true value of the i-th image; x is the image input, and n is the number of images;

[0035] The adversarial loss function is defined as:

[0036] ;

[0037] ;

[0038] ;

[0039] in, Let be the generator loss function. Let G(·) be the discriminator loss function, D(·) be the generator output, E(·) be the discriminator output, and z be the generator input latent variable, and x be the image input. These are fake samples generated by the generator. It is the prior distribution of z. This represents the probability distribution of generated samples learned by the generator. It is the probability distribution of the real sample. The objective of the adversarial loss function is to minimize the adversarial loss in the generator G and maximize the adversarial loss in the discriminator D, with the two being optimized iteratively and alternately.

[0040] The wavelet loss function is defined as:

[0041] ;

[0042] ;

[0043] Where x is the image input and y is the actual value of the image. It is the attenuation factor of the i-th level wavelet decomposition. It is the wavelet decomposition result of the image input at the i-th level and wavelet subband w. It is the wavelet decomposition result of the true value of the image at the i-th level and wavelet subband w; The four types of wavelet decomposition are: LL for low-frequency-low-frequency subband, HL for high-frequency-low-frequency subband, LH for low-frequency-high-frequency subband, and HH for high-frequency-high-frequency subband. It is a structural similarity loss function. It is the mean of x within the local window. It is the mean of y within the local window. It is the variance of x within the local window. It's a method where y is within a local window. It is the covariance of x and y within the local window. and To avoid a stability constant with a denominator of 0, we take... It is 6.50, take It is 58.52.

[0044] In the above scheme, the formula of the shaft-based transformer module is as follows:

[0045] ;

[0046] ;

[0047] In the formula, For the input features of the axis-based transformer module, The output characteristics of the axis-based multi-head self-attention module. The output features of the hybrid expert module are represented by LN, which represents layer normalization. Represents the computational axis-basis attention mechanism. This represents the hybrid expert module.

[0048] In the above scheme, the axis-based multi-head self-attention module generates query Q, key K, and value V after 3×3 convolution, and its expression is:

[0049] ;

[0050] ;

[0051] ;

[0052] In the formula, This represents the 1×1 convolution weights used to generate query Q. This represents the weights of the 3×3 depthwise convolution that generates query Q. This represents the 1×1 convolution weights that generate key K. The weights represent the weights of the 3×3 depthwise convolution that generates key K. This represents the 1×1 convolution weights that generate the value V. The weights represent the weights of the 3×3 depthwise convolution that generate the value V; This represents the input feature map of the axis-based multi-head self-attention module;

[0053] Channel dimension per attention head for:

[0054] ;

[0055] In the formula, C is the original number of feature channels. For the number of heads;

[0056] Dimensionally reshape Q, K, and V respectively, denoted as: , , ;

[0057] To achieve multi-head self-attention, the reshaped , , The feature channel is segmented into k attention heads, i.e.: ;

[0058] ;

[0059] ;

[0060] in, , , They represent , , The kth attention head;

[0061] The multi-head self-attention of the j-th attention head is represented as:

[0062] ;

[0063] In the formula, SA represents the self-attention operation; , , They represent , , The j-th attention head; This is a scaling factor used to alleviate the gradient vanishing problem of the softmax function caused by excessively large values ​​after the dot product operation;

[0064] The output feature formula is:

[0065] ;

[0066] In the formula, Concat represents the concatenation operation; This represents the 1×1 convolution weight in the axis-based multi-head self-attention module, used to adjust the channel dimension of the concatenated features;

[0067] Finally, for Dimensional reshaping is performed to obtain the output features of the axis-basis multi-head self-attention module. .

[0068] In the above scheme, the formula for the dual-gated feedforward network is as follows:

[0069] ;

[0070] ;

[0071] In the formula, The output characteristics of the axis-based multi-head self-attention module The normalized features are used as input features for the dual-gated feedforward network. The weights of the 1×1 convolution in the first branch of the dual-gated feedforward network are... These are the weights of the 3×3 depthwise convolution in the first branch of the dual-gated feedforward network. The weights of the 1×1 convolution in the second branch of the dual-gated feedforward network are... Here, represents the weights of the 3×3 depthwise convolution in the second branch of the dual-gated feedforward network, and DG represents the dual-gated output of the dual-gated feedforward network. This is an element-wise multiplication operation. For GELU activation function, For 1×1 convolution weights in a dual-gated feedforward network, The output characteristics of a dual-gated feedforward network;

[0072] The formula for the frequency domain enhancement feedforward network is as follows:

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] In the formula, The output characteristics of the axis-based multi-head self-attention module The normalized features are used as input features for the frequency domain enhanced feedforward network. To enhance the dual-gated output in the frequency domain feedforward network, The features after block division These are the features after FFT enhancement. To enhance the weights of the 1×1 convolution in the first branch of the feedforward network in the frequency domain, To enhance the weights of the 3×3 depthwise convolution in the first branch of the feedforward network in the frequency domain, To enhance the weights of the 1×1 convolution in the second branch of the feedforward network in the frequency domain, To enhance the weights of the 3×3 depthwise convolution in the second branch of the feedforward network in the frequency domain, This is an element-wise multiplication operation. The activation function is ReLU, and the split operation is a 4×4 block division. It is a two-dimensional real Fourier transform. This is the two-dimensional real inverse Fourier transform. For learnable frequency domain enhancement parameters, For restructuring operations, To enhance the output characteristics of the feedforward network in the frequency domain.

[0078] Through the above technical solution, the transformer-based GPR image clutter removal method provided by the present invention has the following beneficial effects:

[0079] 1. This invention uses measured step-frequency GPR data to draw GPR images, and combines this with open-source GPR image data to form a hybrid dataset for training the model. Based on the LLFormer model, this invention proposes a frequency-domain enhanced feedforward network. On top of a standard FFN (feedforward network), a frequency-domain enhancement mechanism is introduced. Through Fourier transform, features are processed in the frequency domain, enabling the model to enhance its ability to capture high and low frequency features, thus adapting it to electromagnetic wave-based data such as GPR images.

[0080] 2. This invention introduces a hybrid expert model (MoE) mechanism in the transformer module. Through expert networks and gated scheduling, combined with dual-gated feedforward networks and frequency-domain enhanced feedforward networks, it achieves the learning of spatial and frequency-domain features, while improving the model's expressive power and balancing computational efficiency.

[0081] 3. This invention introduces a newly designed hybrid loss function during the model training stage. This loss function combines a smoothing loss function, an adversarial loss function, and a wavelet loss function. This loss function combines pixel-level differences, adversarial learning mechanisms, and multi-scale structural similarity. It can optimize the image structure at different frequency scales while ensuring that the texture and details of the image are closer to the real image. It can also stabilize the training process and improve the generalization ability and robustness of the model. Attached Figure Description

[0082] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0083] Figure 1 This is a schematic diagram of a deep learning algorithm model of transformer disclosed in an embodiment of the present invention.

[0084] Figure 2 This is a schematic diagram of the shaft-based transformer module;

[0085] Figure 3 Here are schematic diagrams of axis-based multi-head self-attention modules; (a) is the height axis multi-head attention module, and (b) is the width axis multi-head attention module.

[0086] Figure 4 This is a schematic diagram of a dual-gated feedforward network;

[0087] Figure 5 Schematic diagram of frequency domain enhancement feedforward network;

[0088] Figure 6 This is a schematic diagram of the cross-layer attention fusion module;

[0089] Figure 7 The clutter removal effect of the model of this invention and other models on a target is compared. (a) is the original image, (b) is SVD, (c) is RPCA, (d) is LLFormer, and (e) is the model of this invention.

[0090] Figure 8 The clutter removal effect of the model of this invention on two targets is compared with other models. (a) is the original image, (b) is SVD, (c) is RPCA, (d) is LLFormer, and (e) is the model of this invention.

[0091] Figure 9 The clutter removal performance of the model of this invention and other models for three targets is compared. (a) is the original image, (b) is SVD, (c) is RPCA, (d) is LLFormer, and (e) is the model of this invention. Detailed Implementation

[0092] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0093] This invention provides a transformer-based method for decluttering GPR images, specifically including the following steps:

[0094] Step 1: Construct a deep learning algorithm model for the transformer;

[0095] like Figure 1 As shown, the GPR image first undergoes shallow feature extraction through a 3×3 convolutional layer, outputting shallow feature F0. This shallow feature F0 is then passed through three consecutive axis basis transformer modules to output intermediate features F1, F2, and F3, respectively. These intermediate features F1, F2, and F3 are input to a cross-layer attention fusion module to learn inter-layer attention weights and adaptively fuse features from different layers, resulting in the fused feature F. in The fused feature F in The input is fed into an encoder containing four stages to further extract deep features. These deep features are then fed into a decoder containing three stages to optimize feature details. Simultaneously, the output features from each stage of the encoder are fused with the corresponding stage features of the decoder through weighted skip connections to output the reconstructed feature F. The reconstructed feature F is then passed through three axis-based transformer modules to further optimize details. The features output from each of the three axis-based transformer modules are then fed into another cross-layer attention fusion module to fuse multi-scale features, ultimately generating the enhanced feature. The enhanced feature is then fed into a 3×3 convolutional layer to output a clutter-free GPR image.

[0096] Specifically, the deep learning algorithm model of transformer includes a feature extraction layer, a feature fusion layer, and a feature output layer. Each layer will be described separately below.

[0097] I. Feature Extraction Layer

[0098] The feature extraction layer consists of sequentially connected convolutional layers, three consecutive axis basis transformer modules, and a cross-layer attention fusion module.

[0099] 1. Shaft-based transformer module

[0100] like Figure 2As shown, the axis-based transformer module includes a normalization layer, an axis-based multi-head self-attention module, a hybrid expert module (MOE), a gating network, and a dynamic weighted fusion mechanism. The input features are first processed through the normalization layer and the axis-based multi-head self-attention module to obtain enhanced features. The result of element-wise summation of the enhanced features and the input features serves as the input to the hybrid expert module. This input is then processed through an expert network composed of DGFN and EDFN, and after alternating updates, the serialized features are obtained.

[0101] The formula for the shaft-based transformer module is as follows:

[0102] ;

[0103] ;

[0104] In the formula, For the input features of the axis-based transformer module, The output characteristics of the axis-based multi-head self-attention module. The output features of the hybrid expert module are represented by LN, which represents layer normalization. Represents the computational axis-basis attention mechanism. This represents the hybrid expert module.

[0105] (1) Axis-based multi-head self-attention module

[0106] like Figure 3 As shown, the axis-based multi-head self-attention module includes a height-axis multi-head attention module and a width-axis multi-head attention module.

[0107] like Figure 3 As shown in (a), in the height-axis multi-head attention module, the input feature map is simultaneously input into three branches. Each branch operates identically, using a 1×1 convolution to enhance the input feature representation, followed by a 3×3 depthwise convolution to capture local contextual information. The three branches then generate the query Q, key K, and value V, respectively. The outputs Q, K, and V of the three branches are then reshaped to obtain... , , ,Will , , It is split into k attention heads along the channel dimension. and Attention weights are calculated using matrix multiplication to obtain the height axis attention matrix. The height axis attention matrix is ​​then normalized using softmax and weighted with V to obtain the output of a single attention head. Finally, the outputs of all attention heads are concatenated and integrated using a 1×1 convolution to obtain the height axis attention result.

[0108] like Figure 3 As shown in (b), the structure of the width axis multi-head attention module is the same as that of the height axis multi-head attention module; the input of the width axis multi-head attention module is the output of the height axis multi-head attention module, and the final output is the attention-enhanced feature after dimensional reshaping.

[0109] The input features of the axis-based transformer module and the output features of the axis-based multi-head self-attention module are element-wise added together and then input into the hybrid expert module and the gating network, respectively.

[0110] In the axis-based multi-head self-attention module, a 3×3 convolution generates a query Q, a key K, and a value V, whose expression is:

[0111] ;

[0112] ;

[0113] ;

[0114] In the formula, This represents the 1×1 convolution weights used to generate query Q. This represents the weights of the 3×3 depthwise convolution that generates query Q. This represents the 1×1 convolution weights that generate key K. The weights represent the weights of the 3×3 depthwise convolution that generates key K. This represents the 1×1 convolution weights that generate the value V. The weights represent the weights of the 3×3 depthwise convolution that generate the value V; This represents the input feature map of the axis-based multi-head self-attention module;

[0115] Channel dimension per attention head for:

[0116] ;

[0117] In the formula, C is the original number of feature channels. For the number of heads;

[0118] Dimensionally reshape Q, K, and V respectively, denoted as: , , ;

[0119] To achieve multi-head self-attention, the reshaped , , The feature channel is segmented into k attention heads, i.e.: ;

[0120] ;

[0121] ;

[0122] in, , , They represent , , The kth attention head;

[0123] The multi-head self-attention of the j-th attention head is represented as:

[0124] ;

[0125] In the formula, SA represents the self-attention operation; , , They represent , , The j-th attention head; This is a scaling factor used to alleviate the gradient vanishing problem of the softmax function caused by excessively large values ​​after the dot product operation;

[0126] The output feature formula is:

[0127] ;

[0128] In the formula, Concat represents the concatenation operation; This represents the 1×1 convolution weight in the axis-based multi-head self-attention module, used to adjust the channel dimension of the concatenated features;

[0129] Finally, for Dimensional reshaping is performed to obtain the output features of the axis-basis multi-head self-attention module. .

[0130] (2) Hybrid Expert Module

[0131] The hybrid expert module consists of four expert modules, each composed of a normalization layer and either a dual-gated feed-forward network (DGFN) or an enhanced frequency domain feed-forward network (EDFN). There are two dual-gated feed-forward networks and two enhanced frequency domain feed-forward networks. Each expert module independently receives features output from the axis-based multi-head self-attention module and outputs its own feature map.

[0132] The formula for the hybrid expert module is as follows:

[0133] ;

[0134] In the formula, This represents the feature output of the k-th expert extracted from the stacked tensor; Expand the tensor to include the dimensions of the gate weights; For element-wise multiplication; K represents the number of experts. This is the final output of the hybrid expert module.

[0135] like Figure 4 As shown, the dual-gated feedforward network includes two parallel feature processing paths and a dual-gated filtering mechanism; both paths consist of 1×1 convolutional layers and 3×3 depth convolutional layers to enrich the local details of the input features and adjust the channel dimensions; the dual-gated filtering mechanism is implemented by executing the GELU activation function and element-wise multiplication in the two paths respectively. Specifically, after the input feature map enters the dual-gated feedforward network, it is first processed through two parallel paths. Each path first uses a 1×1 convolution to adjust the channel dimension to optimize feature representation, and then uses a 3×3 depthwise convolution to capture local contextual information and enhance the local detail representation of the features. In the dual-gated filtering stage, the first path applies the GELU activation function to the convolution-processed features to non-linearly transform the features, and then performs element-wise multiplication with the original convolution-processed features in the second path. The second path applies the GELU activation function to the convolution-processed features to non-linearly transform the features, and then performs element-wise multiplication with the original convolution-processed features in the first path. Subsequently, the output features of the two paths are summed element-wise, and then summed with the input features after a 1×1 convolution to obtain the dual-gated filtered features.

[0136] The formula for a dual-gated feedforward network is as follows:

[0137] ;

[0138] ;

[0139] In the formula, The output characteristics of the axis-based multi-head self-attention module The normalized features are used as input features for the dual-gated feedforward network. The weights of the 1×1 convolution in the first branch of the dual-gated feedforward network are... These are the weights of the 3×3 depthwise convolution in the first branch of the dual-gated feedforward network. The weights of the 1×1 convolution in the second branch of the dual-gated feedforward network are... Here, represents the weights of the 3×3 depthwise convolution in the second branch of the dual-gated feedforward network, and DG represents the dual-gated output of the dual-gated feedforward network. This is an element-wise multiplication operation. For GELU activation function, For 1×1 convolution weights in a dual-gated feedforward network, This represents the output characteristics of a dual-gated feedforward network.

[0140] like Figure 5 As shown, the frequency domain enhancement feedforward network includes two parallel feature processing paths and a frequency domain enhancement mechanism. Both paths consist of 1×1 convolutional layers and 3×3 depthwise convolutional layers. Specifically, after the input features enter the frequency domain enhancement feedforward network, they are first processed through two parallel paths. Each path first adjusts the channel dimension through a 1×1 convolution to optimize feature representation, and then processes the features through a 3×3 depthwise convolution. Deep convolution captures local contextual information, enhancing the representation of local details in features. Two paths pass through the ReLU activation function, and the output features of the first and second paths are multiplied element-wise to obtain the output features. The frequency domain enhancement mechanism dynamically adjusts the weights of different frequency components by using learnable FFT parameters in the frequency domain. In the frequency domain enhancement stage, the features output by the parallel feature processing path first pass through a 1×1 convolutional layer and are padded, then the features are divided into 4×4 patch blocks. Next, a Fast Fourier Transform is performed on the features to transform them to the frequency domain, and element-wise multiplication is performed in the frequency domain with the learnable FFT parameters. Then, an Inverse Fast Fourier Transform is used to transform the features back to the time domain, and the output features are obtained through block merging and size clipping.

[0141] The formula for frequency domain enhancement feedforward network is as follows:

[0142] ;

[0143] ;

[0144] ;

[0145] ;

[0146] In the formula, The output characteristics of the axis-based multi-head self-attention module The normalized features are used as input features for the frequency domain enhanced feedforward network. To enhance the dual-gated output in the frequency domain feedforward network, The features after block division These are the features after FFT enhancement. To enhance the weights of the 1×1 convolution in the first branch of the feedforward network in the frequency domain, To enhance the weights of the 3×3 depthwise convolution in the first branch of the feedforward network in the frequency domain, To enhance the weights of the 1×1 convolution in the second branch of the feedforward network in the frequency domain, To enhance the weights of the 3×3 depthwise convolution in the second branch of the feedforward network in the frequency domain, This is an element-wise multiplication operation. The activation function is ReLU, and the split operation is a 4×4 block division. For two-dimensional real Fourier transform, This is the inverse Fourier transform of two-dimensional real numbers. For learnable frequency domain enhancement parameters, For restructuring operations, To enhance the output characteristics of the feedforward network in the frequency domain.

[0147] The hybrid expert module consists of four experts formed by combining DGFN and EDFN, which are updated alternately to obtain serialized features.

[0148] (3) Gated network

[0149] The gating network consists of 3×3 convolutional layers and a softmax activation function. The gating network first extracts spatial features from the input features, and then normalizes them using the softmax activation function to generate dynamic weights for each expert.

[0150] (4) Dynamic weighted fusion mechanism

[0151] The dynamic weighted fusion mechanism dynamically assigns weights and performs element-wise multiplication with the outputs of the corresponding expert modules. Then, it sums the elements of all weighted expert output features to obtain the final output features.

[0152] 2. Cross-layer attention fusion module

[0153] like Figure 6 As shown, the cross-layer attention fusion module takes N consecutive layers of input features as input (denoted as N). In the experiment, N=3, H is the feature map height, W is the width, and C is the number of channels. First, the input features are reshaped to obtain the reshaped features. This is to facilitate subsequent attention calculations. Reshaped features Simultaneously, the program enters three parallel branches, each performing the same operation: generating query Q, key K, and value V through 1×1 convolution and 3×3 depthwise convolution, respectively. Q and K are then reshaped into 2D matrices. , A scaling factor is introduced through dot product calculation. Adjusting the weight scale yields an N×N dimensional attention matrix; V is then reshaped as follows: After being weighted with the attention matrix and reshaped in dimensions, it is combined with the features The elements are summed, and then integrated through a 1×1 convolution to output the fused features.

[0154] II. Feature Fusion Layer

[0155] The feature fusion layer uses an encoder-decoder hierarchical structure. The encoder consists of four stages, each consisting of a downsampling layer and multiple axis-based transformer modules. The decoder consists of three stages, each consisting of an upsampling layer and multiple axis-based transformer modules, and a weighted skip connection is made between the encoder and decoder.

[0156] The encoder input is the fused feature output from the cross-layer attention fusion module, denoted as... The encoder consists of four stages. Each stage first performs downsampling through pixel rearrangement, reducing the feature map space size to ( The number of channels doubled. Let i be the encoder stage number. After downsampling, each stage extracts deep features through an increasing number of axis-based transformer modules. The number of axis-based transformer modules in the encoder from the first to the fourth stage is 2, 4, 8, and 16 respectively. Furthermore, the number of attention heads in the axis-based multi-head self-attention modules within each stage's axis-based transformer module is 1, 2, 4, and 8 respectively, gradually strengthening the ability to capture long-distance dependencies and complex features. The final output feature is denoted as... .

[0157] The decoder consists of three stages to produce features from the encoder output. For input, each stage first performs upsampling through pixel rearrangement: restoring the feature map space size to twice its original size while adjusting the number of channels to the appropriate dimension. After upsampling, each stage optimizes feature details through an increasing number of axis-based transformer modules. The number of axis-based transformer modules in the decoder from the first to the third stage is 2, 4, and 8 respectively; and the number of attention heads in the axis-based multi-head self-attention modules in each stage's axis-based transformer module is 1, 2, and 4 respectively. Simultaneously, a weighted skip connection with 1×1 convolution is introduced between the axis-based transformer module in the third stage of the encoder and the upsampling result in the first stage of the decoder; a weighted skip connection with 1×1 convolution is introduced between the axis-based transformer module in the second stage of the encoder and the upsampling result in the second stage of the decoder; and a weighted skip connection with 1×1 convolution is introduced between the axis-based transformer module in the first stage of the encoder and the upsampling result in the third stage of the decoder. These connections are used to adjust the contribution weights of the encoder and decoder features, reduce information loss, and improve reconstruction accuracy. The encoder input features... After passing through the axis-based transformer block, the upsampled result of the output feature of the third stage of the decoder is weighted and connected to finally output the reconstructed feature F.

[0158] III. Feature Output Layer

[0159] The feature output layer consists of three consecutive axis basis transformer modules, a cross-layer attention fusion module, and a 3×3 convolutional layer connected in sequence.

[0160] In this invention, all axis-based transformer modules have the same structure, and the two cross-layer attention fusion modules also have the same structure.

[0161] Step 2, train the model;

[0162] 1. Constructing the dataset

[0163] Real-world data was collected using a GPR system in sand with varying relative permittivity. To increase clutter diversity, water was added to different parts of the sand, resulting in soils with relative permittivity ranging from 3 to 7. A linearly polarized Vivaldi antenna operating at frequencies from 0.5 GHz to 3 GHz was used, sealed in a foam box to reduce ambient noise. A stepped-frequency GPR system was employed. Within the 0.5 GHz to 3 GHz frequency range, each axial scan (A-scan) recorded 1024 sampling points. The acquired frequency domain data was converted to the time domain using an inverse Fourier transform. The axial scan along the depth A-scan was then plotted as a B-scan (line scan) image, resized to 256×64, yielding a real-world GPR image dataset. The open-source hybrid GPR image dataset CLT-GPR was acquired and used together with the real-world GPR image dataset to construct the training dataset, which was then divided into training, validation, and test sets.

[0164] 2. Model Training

[0165] The images from the training set are input into the model for training. The model training uses a hybrid loss function as follows:

[0166] ;

[0167] in, =2, =0.005, used to balance the contributions of the two loss functions; It is a smoothing loss function. It is an adversarial loss function. It is a wavelet loss function; in order to combine pixel-level differences, adversarial learning mechanisms and multi-scale structural similarity to generate structure-preserving de-cluttered images.

[0168] The smoothing loss function is defined as:

[0169] ;

[0170] in, For the i-th image as input, This is the predicted value for the i-th image output by the model. Let be the true value of the i-th image; x is the image input, and n is the number of images;

[0171] The adversarial loss function is defined as:

[0172] ;

[0173] ;

[0174] ;

[0175] in, Let be the generator loss function. Let G(·) be the discriminator loss function, D(·) be the generator output, E(·) be the discriminator output, and z be the generator input latent variable, and x be the image input. These are fake samples generated by the generator. It is the prior distribution of z. This represents the probability distribution of generated samples learned by the generator. It is the probability distribution of the real sample. The objective of the adversarial loss function is to minimize the adversarial loss in the generator G and maximize the adversarial loss in the discriminator D, with the two being optimized iteratively and alternately.

[0176] The wavelet loss function is defined as:

[0177] ;

[0178] ;

[0179] Where x is the image input and y is the actual value of the image. It is the attenuation factor of the i-th level wavelet decomposition. It is the wavelet decomposition result of the image input at the i-th level and wavelet subband w. It is the wavelet decomposition result of the true value of the image at the i-th level and wavelet subband w; The four types of wavelet decomposition are: LL for low-frequency-low-frequency subband, HL for high-frequency-low-frequency subband, LH for low-frequency-high-frequency subband, and HH for high-frequency-high-frequency subband. It is a structural similarity loss function. It is the mean of x within the local window. It is the mean of y within the local window. It is the variance of x within the local window. It's a method where y is within a local window. It is the covariance of x and y within the local window. and To avoid a stability constant with a denominator of 0, we take... It is 6.50, take It is 58.52.

[0180] 3. Model Validation and Evaluation

[0181] The model's accuracy is evaluated and parameters are adjusted using images from the validation set, while the model's generalization ability and prediction accuracy are evaluated using the test set.

[0182] Step 3: Use the trained model to remove clutter;

[0183] After preprocessing the GPR image containing clutter, it is input into a qualified model for clutter removal.

[0184] To verify the effectiveness of the model of this invention in GPR image clutter removal scenarios, the visual differences between GPR images processed by different methods and the processed GPR images were evaluated. For example... Figures 7-9 The diagram shows a visual comparison of the model of this invention with other representative methods, including Singular Value Deconposition (SVD), Robust Principal Component Analysis (RPCA), and the LLFormer model.

[0185] Figures 7-9 In the image above, the original image is a GPR image without prior clutter processing. The hyperbola represents the target, and the other waveforms represent clutter that needs to be removed. It can be seen that in the image processed by the SVD method, both the target and clutter are removed in the single-target image; in the two-target and three-target images, only ripples are present, and the target is removed. In the image processed by the RPCA method, regardless of the number of targets, although the direct wave is removed, there is still some attenuation of the target. In the image processed by LLFormer, target details are preserved while clutter is removed. The image processed by the method of this invention not only removes clutter but also better preserves target details. Overall, compared to other methods, the method provided by this invention effectively removes clutter and effectively preserves the target, displaying target details more naturally and showing high consistency with the original image.

[0186] To illustrate the effectiveness of the model, multiple evaluation metrics were used to assess its accuracy, and different clutter removal methods were compared. The mean absolute error (MAE), mean squared error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) were used to evaluate model accuracy. MAE and MSE measure the model's predictive ability by calculating the difference between the true and predicted values; SSIM and PSNR evaluate image quality based on statistical rules of image similarity, comprehensively considering similarity in brightness, contrast, and structure. The evaluation results are shown in Table 1.

[0187] Table 1 Evaluation index data for different models

[0188]

[0189] Note: Downward arrows indicate that smaller parameters produce better results; upward arrows indicate that larger parameters produce better results.

[0190] As shown in Table 1, the model of this invention outperforms traditional methods and LLFormer in all evaluation metrics. Compared to LLFormer, this invention improves PSNR from 52.881 to 53.595 and SSIM from 0.986 to 0.996 by designing a frequency-domain enhanced feedforward network and introducing a hybrid expert mechanism.

[0191] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A transformer-based GPR image despeckling method, characterized in that, The method comprises the following steps: Step 1, constructing a deep learning algorithm model of transformer; The model comprises a feature extraction layer, a feature fusion layer and a feature output layer, the feature extraction layer comprises a convolution layer, three consecutive axis-based transformer modules connected in sequence and a cross-layer attention fusion module; The feature fusion layer uses an encoder-decoder hierarchical structure, the encoder comprises four stages, each stage comprises one down-sampling layer and multiple axis-based transformer modules; the decoder comprises three stages, each stage comprises one up-sampling layer and multiple axis-based transformer modules, and weighted skip connection is performed between the encoder and the decoder; The feature output layer comprises three consecutive axis-based transformer modules connected in sequence, a cross-layer attention fusion module and a convolution layer; Step 2, training the model; Real data is collected in sand with different relative dielectric constants by using a GPR system, and the data is preprocessed to obtain a GPR real image data set, an open-source mixed GPR image data set CLT-GPR is acquired, and the GPR real image data set is used to construct a required data set for training together with the CLT-GPR, and the data set is divided into a training set, a validation set and a test set; The images of the training set are input into the model for training, the images of the validation set are used to evaluate the precision of the model and adjust the parameters, and the test set is used to evaluate the generalization ability and prediction precision of the model; Step 3, using the trained model to remove clutter; After preprocessing, the GPR image with clutter is input into the qualified model for clutter removal; The axis-based transformer module comprises a normalization layer, an axis-based multi-head self-attention module, a hybrid expert module, a gating network and a dynamic weighted fusion mechanism; The axis-based multi-head self-attention module comprises a height-axis multi-head attention module and a width-axis multi-head attention module; the input features of the axis-based transformer module and the output features of the axis-based multi-head self-attention module are input into the hybrid expert module and the gating network respectively after element addition; The hybrid expert module comprises four expert modules, each expert module comprises a normalization layer and a double-gating feedforward network or a frequency domain enhancement feedforward network, wherein there are two double-gating feedforward networks and two frequency domain enhancement feedforward networks; each expert module independently receives the features output by the axis-based multi-head self-attention module and outputs a respective feature map; The gating network comprises a 3x3 convolution layer and a softmax activation function; the gating network first extracts features in the spatial dimension of the input features, and then generates dynamic allocation weights of each expert through the softmax activation function normalization; The dynamic weighted fusion mechanism performs element multiplication on the output of the corresponding expert module through the dynamic allocation weights, and then performs element summation on all weighted expert output features to obtain the final output features.

2. The transformer-based GPR image despeckling method of claim 1, wherein, In the height-axis multi-head attention module, the input feature map is simultaneously input into three branches. Each branch operates identically: it enhances the input feature representation through a 1×1 convolution, then captures local contextual information through a 3×3 depthwise convolution. The three branches then generate the query Q, key K, and value V, respectively. The outputs Q, K, and V of the three branches are then reshaped to obtain... , , ,Will , , It is split into k attention heads along the channel dimension. and Attention weights are calculated using matrix multiplication to obtain the height axis attention matrix. The height axis attention matrix is ​​then normalized using softmax and weighted with V to obtain the output of a single attention head. Finally, the outputs of all attention heads are concatenated and integrated using a 1×1 convolution to obtain the height axis attention result. The width-axis multi-head attention module structure is the same as the height-axis multi-head attention module; the input of the width-axis multi-head attention module is the output of the height-axis multi-head attention module, and finally, the output is output after dimension reshaping after the self-attention enhancement feature.

3. The transformer-based GPR image despeckling method of claim 1, wherein, In the double-gated feedforward network, the input feature map is first processed through two parallel paths. Each path first adjusts the channel dimension through 1x1 convolution to optimize feature expression, and then captures local context information through 3x3 deep convolution to enhance the local detail representation of the feature. In the double-gated screening stage, the first path performs a GELU activation function on the convolution-processed feature to nonlinearly transform the feature, and then performs element multiplication with the original feature processed by the convolution in the second path. The second path performs a GELU activation function on the convolution-processed feature to nonlinearly transform the feature, and then performs element multiplication with the original feature processed by the convolution in the first path. Then, the output features of the two paths are summed element-wise, and then summed element-wise with the input feature after 1x1 convolution, to obtain the feature after double-gated screening. In the frequency domain enhancement feedforward network, the input feature is first processed through two parallel paths. Each path first adjusts the channel dimension through 1x1 convolution to optimize feature expression, and then captures local context information through 3x3 deep convolution to enhance the local detail representation of the feature. The output features of the first path and the second path are multiplied element-wise after ReLU activation function to obtain the output feature. In the frequency domain enhancement stage, the features output by the parallel feature processing paths are first passed through a 1x1 convolution layer and padded, and then the features are divided into 4x4 patch blocks. Then, the features are subjected to a fast Fourier transform to convert them to the frequency domain, and the features are multiplied element-wise with the learnable fft parameters. Then, the features are converted back to the time domain through inverse fast Fourier transform, and the output features are obtained through block merging and size cropping.

4. The transformer-based GPR image despeckling method of claim 1, wherein, In the cross-layer attention fusion module, multiple input features are first reshaped to unify the feature dimension for subsequent attention calculation. The reshaped features enter three parallel branches simultaneously, and the three branches operate identically, passing through 1x1 and 3x3 convolution layers. The three branches generate query Q, key K, and value V respectively. Q and K are dimensionally reshaped and multiplied by matrix multiplication to generate an attention matrix. V is dimensionally reshaped, multiplied by the attention matrix, and then dimensionally reshaped again. Finally, the output feature map that integrates the effective information of multiple input features is generated by element-wise summing and then passing through a 1x1 convolution.

5. The transformer-based GPR image despeckling method of claim 1, wherein, The encoder input is the fused feature output by the cross-layer attention fusion module, denoted as... The encoder consists of four stages. Each stage first performs downsampling through pixel rearrangement, reducing the feature map space size to ( The number of channels doubled. Let i be the encoder stage number. After downsampling, each stage extracts deep features through an increasing number of axis-based transformer modules. The number of axis-based transformer modules in the encoder from the first to the fourth stage is 2, 4, 8, and 16 respectively. Furthermore, the number of attention heads in the axis-based multi-head self-attention modules within each stage's axis-based transformer module is 1, 2, 4, and 8 respectively, gradually strengthening the ability to capture long-distance dependencies and complex features. The final output feature is denoted as... ; The decoder comprises three stages to decode the output features of the encoder For input, each stage is first up-sampled by a pixel rearrangement operation: the spatial size of the feature map is restored to 2 times, while the number of channels is adjusted to adapt to the dimension; after up-sampling, each stage optimizes the feature details through an increasing number of axial transformer modules, and the number of axial transformer modules of the decoder from the first stage to the third stage is 2, 4, and 8 in turn; and the number of attention heads of the axial multi-head self-attention module in each stage of the axial transformer module is 1, 2, and 4 in turn; at the same time, a weighted skip connection with a 1x1 convolution is introduced between the axial transformer module of the third stage of the encoder and the up-sampling result of the first stage of the decoder; a weighted skip connection with a 1x1 convolution is introduced between the axial transformer module of the second stage of the encoder and the up-sampling result of the second stage of the decoder; a weighted skip connection with a 1x1 convolution is introduced between the axial transformer module of the first stage of the encoder and the up-sampling result of the third stage of the decoder, for adjusting the contribution weight of the encoder and the decoder features and reducing information loss; the input feature of the encoder After the axial transformer block, the up-sampling result of the output feature of the third stage of the decoder is connected, and the finally reconstructed feature is output.

6. The transformer-based GPR image despeckling method of claim 1, wherein, In model training, a hybrid loss function is used as follows: ； wherein, = 2, = 0.005, to balance the contribution of the two loss functions; is a smoothing loss function, is an adversarial loss function, is a wavelet loss function; The smoothing loss function is defined as: ； wherein, is the i-th image input, is the predicted value for the i-th image output by the model, is the true value for the i-th image; x is the image input, and n is the number of images. The adversarial loss function is defined as: ； ； ； wherein, is a generator loss function, is a discriminator loss function, G(·) represents the output of the generator, D(·) represents the output of the discriminator, E(·) represents an averaging operation, z is a generator input latent variable, and x is an image input, is a fake sample generated by the generator, is a prior distribution of z, is a probability distribution of the generated sample learned by the generator, is a probability distribution of the real sample, is an optimization objective of the adversarial loss function, the generator G minimizes the adversarial loss, the discriminator D maximizes the adversarial loss, and the two are alternately iterated and optimized. The wavelet loss function is defined as: ； ； where x is the image input, y is the ground truth of the image, is the attenuation factor of the i-th level wavelet decomposition, is the wavelet decomposition result of the image input x on the i-th level, wavelet sub-band w, is the wavelet decomposition result of the ground truth y on the i-th level, wavelet sub-band w; denotes the four types of wavelet decomposition: LL for low-low sub-band, HL for high-low sub-band, LH for low-high sub-band, and HH for high-high sub-band, is the structural similarity loss function, is the mean of x within the local window, is the mean of y within the local window, is the variance of x within the local window, is the method of y within the local window, is the covariance of x and y within the local window, and To avoid the denominator being 0, take as 6.50, take as 58.

52.

7. The transformer-based GPR image despeckling method of claim 1, wherein, The formula of the axis-based transformer module is as follows: ； ； wherein, is the input feature of the axial transformer module, is the output feature of the axial multi-head self-attention module, is the output feature of the hybrid expert module, LN is layer normalization, represents computing the axial attention mechanism, represents the hybrid expert module.

8. The transformer-based GPR image despeckling method of claim 1, wherein, In the axis-based multi-head self-attention module, 3x3 convolution generates query Q, key K, and value V, with the expression as follows: ； ； ； wherein, denote the 1x1 convolution weights for generating the query Q, denote the weights of the 3x3 depthwise convolution for generating the query Q, denote the 1x1 convolution weights for generating the key K, denote the weights of the 3x3 depthwise convolution for generating the key K, denote the 1x1 convolution weights for generating the value V, denote the weights of the 3x3 depthwise convolution for generating the value V; denote the input feature map of the axial-based multi-head self-attention module; channel dimension of each attention head is: ； In the formula, C is the original feature channel number, is the number of attention heads; Reshape the dimensions of Q, K, V respectively, denoted as: , , ; To realize multi-head self-attention, the reshaped , , is split into k attention heads along the feature channel dimension, i.e. ; ； ； wherein, , , respectively represent , , the kth attention head of The multi-head self-attention of the jth attention head is represented as: ； In the formula, SA represents a self-attention operation; , , respectively represent the jth attention head of , , is a scaling factor, used to alleviate the gradient vanishing problem of the softmax function caused by the too large value after the dot product operation.​ The output feature formula is as follows: ； In the formula, Concat represents a concatenation operation; denotes the 1x1 convolution weight in the axis-based multi-head self-attention module, which is used for adjusting the channel dimension of the concatenated features. Finally, the dimension reshaping is performed to obtain output features of the axis-based multi-head self-attention module .​ 9. The transformer-based GPR image despeckling method of claim 1, wherein, The formula of the double-gated feedforward network is as follows: ； ； wherein, is the output feature of the axial basis multi-head self-attention module is the normalized feature as the input feature of the double-gated feed-forward network, is the weight of the 1x1 convolution in the first branch of the double-gated feed-forward network, is the weight of the 3x3 depthwise convolution in the first branch of the double-gated feed-forward network, is the weight of the 1x1 convolution in the second branch of the double-gated feed-forward network, is the weight of the 3x3 depthwise convolution in the second branch of the double-gated feed-forward network, and DG is the double-gated output of the double-gated feed-forward network, is the element-wise multiplication operation, is the GELU activation function, is the 1x1 convolution weight in the double-gated feed-forward network, is the output feature of the double-gated feed-forward network; The formula of the frequency domain enhancement feedforward network is as follows: ； ； ； ； wherein, is the output feature of the axial basis multi-head self-attention module is the normalized feature as the input feature of the frequency domain enhancement feedforward network, is the double-gated output in the frequency domain enhancement feedforward network, is the feature after block splitting, is the feature after ftt enhancement, is the weight of the first branch 1x1 convolution in the frequency domain enhancement feedforward network, is the weight of the first branch 3x3 depth convolution in the frequency domain enhancement feedforward network, is the weight of the second branch 1x1 convolution in the frequency domain enhancement feedforward network, is the weight of the second branch 3x3 depth convolution in the frequency domain enhancement feedforward network, is the element-wise multiplication operation, is the ReLU activation function, and split is the 4x4 block operation, is the two-dimensional real Fourier transform, is the two-dimensional real inverse Fourier transform, is the learnable frequency domain enhancement parameter, is the reorganization operation, is the output feature of the frequency domain enhancement feedforward network.

Images