Semi-supervised lpi radar signal modulation recognition system and method based on entropy-aware pseudo-label

Abstract

The application discloses a semi-supervised LPI radar signal modulation recognition system and method based on entropy-aware pseudo-labels, and relates to the technical fields of radar signal processing and pattern recognition. The system comprises a preprocessing module, a multi-scale reconstruction enhancer, a classification backbone network and a semi-supervised training module. The multi-scale reconstruction enhancer separates and enhances discriminative features in a noisy environment through a high-frequency detail enhancement and a low-frequency structure reconstruction dual-channel. The classification backbone network introduces an adaptive shrinkage unit to realize channel-level noise suppression. The semi-supervised training module adopts an entropy-aware mechanism to dynamically evaluate the uncertainty of unlabeled samples, generates weighted pseudo-labels and performs consistency regularization training. The method realizes signal modulation recognition based on the above system. The application solves the feature masking problem under the condition of low signal-to-noise ratio, reduces the dependence of the model on labeled data through a reliable pseudo-label generation mechanism, and still realizes stable and efficient modulation recognition in a harsh channel environment with scarce labeled data.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, specifically to a semi-supervised LPI radar signal modulation identification system and method based on entropy-aware pseudo-tags. Background Technology

[0002] Radar signal modulation identification is a key technology in the field of signal processing, aiming to automatically determine the modulation type of received signals. It is of great significance for civilian applications such as spectrum monitoring and environmental sensing. Early identification methods heavily relied on expert prior knowledge, constructing classifiers by manually designing time-frequency analysis or statistical features. While such methods may be effective in ideal simulation environments, in complex real-world electromagnetic environments, especially under low signal-to-noise ratio conditions, the essential characteristics of the signal are easily submerged by background noise, leading to a significant decrease in the generalization ability and robustness of artificial features.

[0003] To overcome the limitations of manual features, deep learning technology has been introduced into this field. Models such as convolutional neural networks can automatically learn hierarchical features directly from time-frequency images, reducing reliance on feature engineering. However, the full potential of deep learning models depends on massive amounts of high-quality labeled data, which is extremely costly to acquire in radar signal recognition scenarios, leading to a severe "data hunger" problem. Furthermore, existing general-purpose network architectures are not specifically designed for low signal-to-noise ratio environments and lack robustness to noise interference, limiting their practical application under harsh channel conditions.

[0004] To reduce reliance on labeled data, semi-supervised learning has been proposed as a solution, which improves model performance by combining a small number of labeled samples with a large amount of unlabeled data. However, this approach still suffers from the following drawbacks in low signal-to-noise ratio scenarios:

[0005] First, at the feature extraction level, noise has a significant masking effect on the signal. It not only obscures transient details such as phase jumps and frequency agility, but also destroys global structural information such as modulation profiles, resulting in a severe decrease in feature discriminativeness.

[0006] Secondly, at the network architecture level, existing models lack targeted design for noise. While convolutional neural networks excel at local feature extraction, they struggle to capture global dependencies; while Transformers can model long-range context, they lack local inductive bias and are sensitive to noise. More importantly, existing networks generally lack built-in adaptive noise suppression mechanisms, making it impossible to achieve intelligent denoising during feature propagation.

[0007] Finally, at the training mechanism level, the reliability of the pseudo-label generation stage is insufficient. Traditional methods use a fixed confidence threshold for screening, which is extremely sensitive to prediction confidence distortion caused by noise, easily generating a large number of erroneous pseudo-labels. Once these noisy labels are injected into the training process, they will cause error propagation and training instability, severely limiting the practical performance of semi-supervised learning under low signal-to-noise ratio conditions. Summary of the Invention

[0008] This invention proposes a semi-supervised LPI radar signal modulation recognition system and method based on entropy-aware pseudo-labels. Its purpose is to: alleviate the problem of decreased discriminative power of transient signal details and global structural features caused by noise masking in low signal-to-noise ratio environments; construct a noise-robust network architecture that, while achieving local feature extraction and global dependency modeling, introduces an adaptive noise suppression mechanism to improve feature purity; and establish a reliable pseudo-label generation mechanism within a semi-supervised learning framework to avoid erroneous label injection and training instability caused by fixed threshold selection, thereby achieving stable and efficient learning under conditions of low annotation resources.

[0009] The technical solution of this invention is as follows:

[0010] A semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels includes a preprocessing module, a multi-scale reconstruction enhancer, and a classification backbone network, as well as a semi-supervised training module based on entropy-aware pseudo-labels.

[0011] The preprocessing module is used to receive the original radar signal time series data and convert it into a time-frequency image through time-frequency transformation;

[0012] The multi-scale reconstruction enhancer is used for time-frequency images. Feature enhancement is performed to separate and enhance the discriminative features of the signal from noise;

[0013] The classification backbone network is used to process the enhanced feature maps output by the multi-scale reconstruction enhancer. Deep feature extraction and encoding are performed, and the final modulation category probability distribution, i.e., the classification result, is output. The classification backbone network introduces an adaptive shrinking unit to achieve channel-level adaptive noise suppression.

[0014] The semi-supervised training module is used to train the recognition system based on labeled and unlabeled samples. Its core is to use an entropy-aware mechanism to dynamically evaluate the uncertainty of the prediction of unlabeled samples and generate weighted pseudo-labels for consistency regularization.

[0015] As a further improvement to the semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels: the multi-scale reconstruction enhancer includes a multi-scale feature extraction module, a high-frequency detail enhancement module, a low-frequency structure reconstruction module, and an axial sensing attention unit.

[0016] The multi-scale reconstruction enhancer process is as follows: the multi-scale feature extraction module uses depth-separable convolutional kernels of different scales to process the input time-frequency image. Perform convolution operations sequentially, and then sum the feature maps obtained from the first and last convolution operations to obtain the primary feature map. Then from the primary feature map Extracting low-frequency features and residual high frequency characteristics low-frequency features and residual high frequency characteristics The input high-frequency detail enhancement module extracts and enhances high-frequency detail information in the feature map, while low-frequency features are... The input low-frequency structure reconstruction module extracts and reconstructs deep structural information from the low-frequency components of the feature map. Finally, the output feature maps from the high-frequency detail enhancement module and the low-frequency structure reconstruction module are fused at the pixel level, and then further refined by the axial perception attention unit to obtain the enhanced feature map. That is, the output feature map of the multi-scale reconstruction enhancer.

[0017] As a further improvement to the semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels, from the primary feature map Extracting low-frequency features and residual high frequency characteristics The processing procedure is as follows: for the primary feature map Low-frequency features are obtained by average pooling downsampling. Then, the low-frequency characteristics The upsampled low-frequency features are obtained by upsampling back to the original size using bilinear interpolation. Then from the primary feature map Subtracting upsampled low-frequency features High-frequency characteristics of the residuals were obtained. .

[0018] As a further improvement to the semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels, the high-frequency detail enhancement module includes an edge-aware feature enhancer and a frequency-domain attention gate. The processing procedure is as follows: the first input feature map is the residual high-frequency feature. High-frequency features are initially enhanced using an edge-aware feature enhancer. Then high-frequency features Features are obtained by inputting into a frequency domain attention gate. The second input feature map is the low-frequency feature. Features are obtained by inputting into a frequency domain attention gate. Then the features With features Subtraction yields the characteristics Then the features High-frequency characteristics of residuals Matrix multiplication is performed, and the result is then subjected to a 1×1 convolution operation to obtain the output feature map of the high-frequency detail enhancement module. ;

[0019] In the edge-aware feature enhancer, the high-frequency features of the residual are calculated first. Results of 3×3 average pooling and high-frequency characteristics of residuals The difference between the values ​​is used to extract edge features. This difference is then input into a weight generation network consisting of 1×1 convolutions and a sigmoid function to obtain an edge-aware weight map. This edge-aware weight map is then compared with the residual high-frequency features. By fusing the matrices, a preliminary enhanced high-frequency feature is obtained. ;

[0020] In the frequency domain attention gate, the input features are subjected to global average pooling and global max pooling in parallel. Then, the two pooling results are added together to obtain the features output by the frequency domain attention gate.

[0021] As a further improvement to the semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags: the low-frequency structure reconstruction module includes three encoders with identical structures and two decoders with identical structures;

[0022] The processing procedure of the low-frequency structure reconstruction module is as follows: the input feature map of the low-frequency structure reconstruction module is the low-frequency feature map. The first-stage encoder extracts features, and then average pooling is performed on the extracted feature maps. The features after the first-stage average pooling are... Figure 1 On one hand, the input is passed to the corresponding first-level decoder; on the other hand, it is used as input to the second-level encoder. The second-level encoder extracts the input feature map and also performs average pooling. The feature map after second-level average pooling... Figure 1 The feature map is passed to the corresponding second-level decoder on one hand, and continues to be input to the third-level encoder on the other. The feature map extracted by the third-level encoder is directly passed to the second-level decoder. Subsequently, the second-level decoder fuses the feature map from the third-level encoder with the feature map after second-level average pooling, and the output feature map is passed to the first-level decoder. The first-level decoder fuses the feature map from the second-level decoder with the feature map after first-level average pooling. Finally, the output feature map of the first-level decoder is fused with the input feature map of the low-frequency structure reconstruction module through matrix addition to obtain the output feature map of the low-frequency structure reconstruction module.

[0023] As a further improvement to the semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels, the encoder's processing procedure is as follows: the input feature map of the encoder first undergoes preliminary feature transformation through the first convolutional layer, and the resulting feature map is then split into query vectors. Key vector Sum value vector ; query vector With key vector After performing matrix transformations and then matrix multiplication, the product is normalized using Softmax to obtain the attention weights; these attention weights are then compared with the value vector. The matrix transformation result is multiplied by matrix to obtain the sequence features that incorporate the global context; this sequence feature is then convolved by 1×1 and added to the input feature map of the encoder. The result of the matrix addition is passed through a second convolutional layer to obtain the convolutional feature map. The result of the activation function processing of this convolutional feature map is then multiplied by matrix, and the result of the multiplication is added to the input feature map of the encoder to obtain the output feature map of the encoder.

[0024] The decoder's processing procedure is as follows: The decoder receives two input feature maps. The first input feature map is the output of the previous level decoder or encoder, and the second input feature map is the feature map after average pooling at the same level. First, the second input feature map is decomposed into four sub-bands by discrete wavelet transform: low-frequency sub-band, horizontal high-frequency sub-band, vertical high-frequency sub-band, and diagonal high-frequency sub-band. The low-frequency sub-band is concatenated with the first input feature map, and the concatenated result is subjected to 1×1 convolution to adjust the number of channels to obtain the first convolutional feature. The horizontal high-frequency sub-band, vertical high-frequency sub-band, and diagonal high-frequency sub-band are concatenated, and the concatenated result is subjected to 1×1 convolution to obtain the second convolutional feature. The first convolutional feature and the second convolutional feature are concatenated, and the concatenated result is then subjected to inverse discrete wavelet transform to reconstruct a high-resolution feature map, which is the output feature map of the decoder.

[0025] As a further improvement to the semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels, the pixel-level fusion process of the output feature map of the high-frequency detail enhancement module and the output feature map of the low-frequency structure reconstruction module is as follows: the output feature map of the low-frequency structure reconstruction module is upsampled and then concatenated with the output feature map of the high-frequency detail enhancement module. The concatenated result is then subjected to average pooling, 1×1 convolution, and 3×3 convolution in sequence, and then combined with the primary feature map. Matrix addition yields pixel-level fusion results;

[0026] The process of refining features using the axial sensing attention unit is as follows: the pixel-level fusion result is input into the axial sensing attention unit to obtain a spatial attention map, and then the spatial attention map is multiplied by the pixel-level fusion result to obtain the enhanced feature map. ;

[0027] The processing procedure of the axial sensing attention unit is as follows: the input of the axial sensing attention unit is first compressed spatially by average pooling, and then the number of channels is adjusted by 1×1 convolution operation. The features obtained by convolution are first captured by 1×11 depthwise convolution to capture long-range dependencies in the horizontal direction. The result of the first depthwise convolution is then captured by 11×1 depthwise convolution to capture long-range dependencies in the vertical direction. The result of the second depthwise convolution is used to obtain the spatial attention map, i.e., the output of the axial sensing attention unit, by 1×1 convolution and sigmoid activation function.

[0028] As a further improvement to the semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels, the classification backbone network includes N stages connected in sequence. The first N-1 stages each contain a convolutional token embedding module, a converter, and an adaptive shrinking unit connected in sequence, and the last stage contains a convolutional token embedding module and a converter connected in sequence. The output of the last stage enters the multilayer perceptron classification head to obtain the modulation category probability distribution.

[0029] The processing procedure of the adaptive shrinking unit is as follows: A soft thresholding function is applied element-by-element to the input token sequence of the adaptive shrinking unit to achieve adaptive denoising, resulting in an output token sequence; the soft thresholding function is:

[0030] ;

[0031] in, For elements in the input token sequence, yes The absolute value represents its characteristic intensity. It is a symbolic function. These are the shrunk output elements, and all output elements constitute the output token sequence; threshold Dynamically generated through a learnable function:

[0032] ;

[0033] in, yes The energy of the channel is obtained by averaging the absolute values ​​of all elements in that channel. It is a two-layer fully connected network, based on the input energy. Dynamically learn and output the most suitable threshold If the energy of a channel A higher value results in a larger threshold. If the energy of a channel If the value is lower, a smaller threshold will be generated. .

[0034] This invention also provides a semi-supervised LPI radar signal modulation identification method based on entropy-aware pseudo-tags. It is based on the aforementioned semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags, and the method includes:

[0035] Step S1: Use a semi-supervised training module to train a multi-scale reconstruction enhancer and a classification backbone network;

[0036] The specific processing steps of the semi-supervised training module are as follows:

[0037] Step S1.1: Prepare training sets for multiple training batches, each containing labeled and unlabeled samples;

[0038] Step S1.2: For each unlabeled sample Two enhanced versions are generated independently: weakly enhanced samples. and strongly enhanced samples For each labeled sample, a standard augmented sample is generated, thus obtaining an augmented sample set;

[0039] Step S1.3: Input all augmented samples in batches into the multi-scale reconstruction augmenter and the classification backbone network connected in sequence, and record the classification results obtained from the standard augmented samples as follows: The classification result corresponding to the weakly enhanced sample is denoted as The classification result corresponding to the strongly enhanced sample is denoted as ;

[0040] For each batch of samples input, calculate the loss once according to steps S1.4 and S1.5, and update the network parameters of the multi-scale reconstruction enhancer and the classification backbone network according to the loss;

[0041] Step S1.4: Generate weights and pseudo-labels for unlabeled samples;

[0042] Step S1.5: Calculate the loss corresponding to the unlabeled sample based on the weights and pseudo-labels, and then weight the loss of the labeled sample with the loss of the unlabeled sample to obtain the total loss;

[0043] Step S2: Input the time series data of the radar signal to be identified into the semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels after training. The system processes the data sequentially through a preprocessing module, a multi-scale reconstruction enhancer, and a classification backbone network, and finally outputs the modulation category probability distribution of the radar signal. The category with the highest probability is taken as the recognition result.

[0044] As a further improvement to the semi-supervised LPI radar signal modulation identification method based on entropy-aware pseudo-tags, step S1.4 specifically includes:

[0045] Step S1.4.1: Classification result for any weakly enhanced sample Calculate its entropy value:

[0046] ;

[0047] In the above formula, for The Middle The element, i.e., the th element The predicted probabilities of each category; Number of categories;

[0048] Step S1.4.2: Calculate the weight of each unlabeled sample based on the entropy value. :

[0049] ;

[0050] Step S1.4.3: For Apply sharpening to generate pseudo-labels for the corresponding unlabeled samples. :

[0051] ;

[0052] In the above formula, For temperature parameters, ;

[0053] In step S1.5:

[0054] Calculate the standard cross-entropy loss for the standard augmented samples. :

[0055] ;

[0056] in This represents the number of standard enhanced samples in the current batch. For the first In the one-hot encoding of the true labels of the standard augmented sample, the first... The element value corresponding to the class, For the first In the classification results of the standard augmented samples, the first... The predicted probability of a class;

[0057] For strongly augmented samples, use the corresponding pseudo-labels. and classification results Calculate consistency loss And weighted by weights:

[0058] ;

[0059] in This represents the number of unlabeled samples in the current batch. For the first The weights corresponding to each unlabeled sample For the first The pseudo-label of the unlabeled sample corresponding to the strongly enhanced sample. The element value corresponding to the class, For the first In the classification results of the strongly enhanced samples, the first The predicted probability of a class;

[0060] Finally, the total loss is calculated by combining supervised loss and unsupervised loss. :

[0061] ;

[0062] in To balance the weights.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] 1. This invention employs a multi-scale reconstruction enhancer to perform path-splitting processing on time-frequency images, effectively mitigating the problem of noise masking signal features in low signal-to-noise ratio (SNR) environments. Furthermore, the high-frequency detail enhancement module utilizes an edge-aware feature enhancer and a frequency-domain attention gate to extract and enhance transient details such as phase jumps and frequency agility from the residual high-frequency features; the low-frequency structure reconstruction module, through a multi-level encoder-decoder structure combined with discrete wavelet transform and an attention mechanism, restores global structural information such as modulation contours destroyed by noise. This divide-and-conquer feature processing strategy enables the model to maintain high feature discriminative power even at SNRs as low as -10dB, providing a robust feature representation foundation for subsequent classification.

[0065] 2. In the design of the classification backbone network, this invention extracts local features through a convolutional token embedding module and then uses a Transformer encoder to establish global contextual dependencies, achieving collaborative modeling of local features and global relationships. Furthermore, an adaptive shrinking unit is embedded in the network. This unit dynamically generates soft thresholds based on channel energy and performs channel-level shrinking on feature responses, thereby achieving adaptive noise suppression in deep networks. This architecture not only overcomes the shortcomings of traditional convolutional neural networks in long-range dependency modeling but also improves the Transformer's weak perception of local structure and sensitivity to noise, significantly enhancing the model's feature purity and representational ability under low signal-to-noise ratio conditions.

[0066] 3. To address the low reliability of pseudo-labels in semi-supervised training, this invention introduces an entropy-aware mechanism. By calculating the entropy value of the prediction results of weakly enhanced samples, its uncertainty is dynamically assessed, and weighted pseudo-labels are generated for consistency regularization. This approach abandons the traditional fixed threshold screening mechanism and instead adopts continuous weight allocation, effectively reducing the injection of erroneous labels caused by prediction confidence distortion due to noise. This allows the model to stably and efficiently utilize a large number of unlabeled samples for training even with only a very small amount of labeled data, significantly reducing dependence on labeled data and improving learning robustness and generalization performance in low signal-to-noise ratio semi-supervised scenarios. Attached Figure Description

[0067] Figure 1 This is an architecture diagram of a semi-supervised LPI radar signal modulation and identification system based on entropy-aware pseudo-tags in a specific implementation.

[0068] Figure 2 This is an architecture diagram of the high-frequency detail enhancement module.

[0069] Figure 3 This is the architecture diagram of the low-frequency structure reconstruction module.

[0070] Figure 4 This is an architecture diagram of the encoder in the low-frequency structure reconstruction module.

[0071] Figure 5 This is an architecture diagram of the decoder in the low-frequency structure reconstruction module.

[0072] Figure 6 This is an architecture diagram of the axial sensing attention unit. Detailed Implementation

[0073] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0074] A semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags, such as Figure 1 As shown, it includes a preprocessing module, a multi-scale reconstruction enhancer, and a classification backbone network, as well as a semi-supervised training module based on entropy-aware pseudo-labels.

[0075] (1) Preprocessing module.

[0076] The preprocessing module receives the raw radar signal time-series data and converts it into a standardized time-frequency image through time-frequency transformation. In this embodiment, the Chirp-Wigner distribution is used for transformation, and the transformation formula is as follows:

[0077] ;

[0078] in, This is the original radar signal timing data. This represents the time-frequency kernel function. Subsequently, the resulting time-frequency image is processed... Normalization and size cropping are performed to obtain a standardized time-frequency image. .

[0079] (2) Multiscale reconstruction enhancer.

[0080] The multi-scale reconstruction enhancer is used to process the normalized time-frequency image. Feature enhancement is performed to separate and enhance the discriminative features of the signal from noise.

[0081] The multi-scale reconstruction enhancer internally includes a multi-scale feature extraction module, a high-frequency detail enhancement module, a low-frequency structure reconstruction module, and an axis-aware attention unit. The processing flow of the multi-scale reconstruction enhancer is as follows: the multi-scale feature extraction module is based on the input normalized time-frequency image... Obtain the primary feature map Then from the primary feature map Extracting low-frequency features and residual high frequency characteristics low-frequency features and residual high frequency characteristics The input high-frequency detail enhancement module extracts and enhances high-frequency detail information in the feature map, while low-frequency features are... The low-frequency structure reconstruction module extracts and reconstructs deep structural information from the low-frequency components of the feature map. Finally, the output feature maps from the high-frequency detail enhancement module and the low-frequency structure reconstruction module are fused at the pixel level, and then further refined by the axial perception attention unit to obtain the enhanced feature map. That is, the output feature map of the multi-scale reconstruction enhancer.

[0082] (2.1) Multi-scale feature extraction module.

[0083] The multi-scale feature extraction module uses depthwise separable convolutional kernels of three different scales (3×3, 5×5, and 7×7) to extract the input normalized time-frequency image. Perform convolution operations sequentially, and then sum the feature maps obtained from the first and last convolution operations to obtain the primary feature map. .

[0084] (2.2) Extraction of low-frequency features and high-frequency features of residuals.

[0085] like Figure 1 As shown, from the primary feature map Extracting low-frequency features and residual high frequency characteristics The processing procedure is as follows: for the primary feature map Low-frequency features are obtained by performing average pooling downsampling (kernel_size=2, stride=2). Then, the low-frequency characteristics The upsampled low-frequency features are obtained by upsampling back to the original size using bilinear interpolation. Then from the primary feature map Subtracting upsampled low-frequency features High-frequency characteristics of the residuals were obtained. .

[0086] (2.3) High-frequency detail enhancement module.

[0087] like Figure 2 The high-frequency detail enhancement module includes an edge-aware feature enhancer and a frequency-domain attention gate. The processing procedure is as follows: the first input feature map is the residual high-frequency feature. High-frequency features are initially enhanced using an edge-aware feature enhancer. Then high-frequency features Features are obtained by inputting into a frequency domain attention gate. The second input feature map is the low-frequency feature. Features are obtained by inputting into a frequency domain attention gate. Then the features With features Subtraction yields the characteristics Then the features High-frequency characteristics of residuals Matrix multiplication is performed, and the result is then subjected to a 1×1 convolution operation to obtain the output feature map of the high-frequency detail enhancement module. .

[0088] (2.3.1) Edge-aware feature enhancer.

[0089] In the edge-aware feature enhancer, the high-frequency features of the residual are calculated first. Results of 3×3 average pooling and high-frequency characteristics of residuals The difference between the values ​​is used to extract edge features. This difference is then input into a weight generation network consisting of 1×1 convolutions and a sigmoid function to obtain an edge-aware weight map. This edge-aware weight map is then compared with the residual high-frequency features. By fusing the matrices, a preliminary enhanced high-frequency feature is obtained. .

[0090] (2.3.2) Frequency domain attention gate.

[0091] In the frequency domain attention gate, the input features are subjected to global average pooling and global max pooling in parallel. Then, the two pooling results are added together to obtain the features output by the frequency domain attention gate.

[0092] (2.4) Low-frequency structure reconstruction module.

[0093] like Figure 3 As shown, the low-frequency structure reconstruction module adopts a Transformer-based U-Net structure, which includes three identical encoders and two identical decoders. The encoders are used to downsample the input features and capture multi-scale contextual information, while the decoders are used to progressively restore spatial resolution and fuse details. Features are passed between the encoders and decoders via skip connections.

[0094] The processing procedure of the low-frequency structure reconstruction module is as follows: the input feature map of the low-frequency structure reconstruction module is the low-frequency feature map. The first-stage encoder extracts features, and then average pooling is performed on the extracted feature maps. The features after the first-stage average pooling are... Figure 1 On one hand, the input is passed to the corresponding first-level decoder; on the other hand, it is used as input to the second-level encoder. The second-level encoder extracts the input feature map and also performs average pooling. The feature map after second-level average pooling... Figure 1 The feature map is simultaneously passed to the corresponding second-level decoder and to the third-level encoder. The feature map extracted by the third-level encoder is directly passed to the second-level decoder. Subsequently, the second-level decoder fuses the feature map from the third-level encoder with the feature map obtained from the second-level average pooling, and the output feature map is passed to the first-level decoder. The first-level decoder then fuses the feature map from the second-level decoder with the feature map obtained from the first-level average pooling. Finally, the output feature map of the first-level decoder is fused with the input feature map of the low-frequency structure reconstruction module through matrix addition to obtain the output feature map of the low-frequency structure reconstruction module.

[0095] (2.4.1) Encoder.

[0096] like Figure 4 As shown, the encoder's processing procedure is as follows: the encoder's input feature map first undergoes preliminary feature transformation through the first convolutional layer, and the resulting feature map is then split into query vectors. Key vector Sum value vector Query vector With key vector After performing matrix transformations and then matrix multiplication, the product is normalized using Softmax to obtain the attention weights. Higher weights indicate stronger structural correlation. These attention weights are then compared with the value vector. The transformed matrix is ​​multiplied to obtain sequence features that incorporate the global context. This sequence feature is then convolved with a 1×1 convolution and added to the encoder's input feature map. The result of this matrix addition is passed through a second convolutional layer to obtain a convolutional feature map. This convolutional feature map is then processed by an activation function and multiplied with the result of the activation function. This multiplication result is then added to the encoder's input feature map to obtain the encoder's output feature map.

[0097] In the second convolutional layer, 3×3 and 1×1 convolutions are performed sequentially, followed by layer normalization.

[0098] (2.4.2) Decoder.

[0099] like Figure 5 As shown, the decoder's processing procedure is as follows: The decoder receives two input feature maps. The first input feature map is the output of the previous stage decoder or encoder, and the second input feature map is the feature map after average pooling at the same stage. First, the second input feature map is decomposed into four sub-bands using discrete wavelet transform: low-frequency sub-band (LL), horizontal high-frequency sub-band (LH), vertical high-frequency sub-band (HL), and diagonal high-frequency sub-band (HH). The low-frequency sub-band is concatenated with the first input feature map, and the concatenated result is subjected to 1×1 convolution to adjust the number of channels, resulting in the first convolutional feature. The horizontal high-frequency sub-band, vertical high-frequency sub-band, and diagonal high-frequency sub-band are concatenated, and the concatenated result is subjected to 1×1 convolution to obtain the second convolutional feature. The first and second convolutional features are concatenated, and the concatenated result is then subjected to inverse discrete wavelet transform to reconstruct a high-resolution feature map, obtaining the decoder's output feature map.

[0100] The wavelet decomposition-based feature fusion mechanism between the encoder and decoder in the low-frequency structure reconstruction module further optimizes the reconstruction quality of multi-scale structural information.

[0101] (2.5) Pixel-level fusion.

[0102] like Figure 1 The pixel-level fusion process of the output feature maps of the high-frequency detail enhancement module and the low-frequency structure reconstruction module is as follows: the output feature map of the low-frequency structure reconstruction module is upsampled and then concatenated with the output feature map of the high-frequency detail enhancement module. The concatenated result is then subjected to average pooling, 1×1 convolution, and 3×3 convolution to compress the number of channels back to the original dimension, and then combined with the primary feature map. Matrix addition yields pixel-level fusion results.

[0103] (2.6) Axial perception attention unit.

[0104] The process of refining features using the axial sensing attention unit is as follows: the pixel-level fusion result is input into the axial sensing attention unit to obtain a spatial attention map, and then the spatial attention map is multiplied by the pixel-level fusion result to obtain the enhanced feature map. .

[0105] Furthermore, such as Figure 6 As shown, the processing procedure of the axial sensing attention unit is as follows: the input of the axial sensing attention unit is first compressed spatially through average pooling, and then the number of channels is adjusted through 1×1 convolution. The features obtained by convolution are first captured by 1×11 depthwise convolution to capture long-range dependencies in the horizontal direction. The result of the first depthwise convolution is then captured by 11×1 depthwise convolution to capture long-range dependencies in the vertical direction. The result of the second depthwise convolution is used to obtain the spatial attention map, i.e., the output of the axial sensing attention unit, through 1×1 convolution and the Sigmoid activation function.

[0106] Axial perception attention units capture long-range dependencies in the horizontal and vertical directions by using asymmetric depth convolutions, thereby enhancing the discriminative power of spatial features without introducing excessive computational complexity.

[0107] The aforementioned modules of the multi-scale reconstruction enhancer work together to improve the overall recognition performance of the system from multiple levels, including feature extraction, structural reconstruction and spatial refinement.

[0108] (3) Classification backbone network.

[0109] like Figure 1 As shown, the classification backbone network is used to enhance the feature maps output by the multi-scale reconstruction enhancer. Deep feature extraction and encoding are performed, and the final modulation category probability distribution, i.e., the classification result, is output. The classification backbone network introduces adaptive shrinking units to achieve channel-level adaptive noise suppression.

[0110] Specifically, the classification backbone network consists of three sequentially connected stages. The first two stages each contain a convolutional token embedding module, a transformer (Transformer encoding module), and an adaptive shrinking unit, all connected sequentially. The third stage contains a convolutional token embedding module and a transformer, connected sequentially. The output of the third stage is fed into the multilayer perceptron classification head to obtain the modulated class probability distribution.

[0111] The convolutional token embedding module maps the input feature map to a series of image patch embeddings through convolutional layers and incorporates positional encoding. Specifically, the feature map output from the convolutional layers is transformed into a token sequence through a rearrangement operation, and layer normalization is applied. The convolutional token embedding module leverages the local receptive field of convolution to aggregate neighboring pixel information during token embedding generation, providing the Transformer with a locally correlated input sequence.

[0112] The converter, or Transformer encoding module, uses the standard Transformer architecture to process the input token sequence. Perform global context modeling and output the token sequence after global modeling. Its dimensions and same.

[0113] The adaptive shrinking unit processes the following: A soft thresholding function is applied element-by-element to the input token sequence to achieve adaptive denoising, resulting in the output token sequence. The soft thresholding function is:

[0114] ;

[0115] in, For elements in the input token sequence, yes The absolute value represents its characteristic intensity. It is a symbolic function. These are the shrunk output elements, and all output elements form an output token sequence. Threshold It is not a fixed value, but is dynamically generated through a learnable function:

[0116] ;

[0117] in, yes The energy of the channel is obtained by averaging the absolute values ​​of all elements in that channel. It is a two-layer fully connected network, based on the input energy. Dynamically learn and output the most suitable threshold If the energy of a channel A higher value results in a larger threshold. It performs a strong contraction to filter out noise; if the energy of a channel... If the value is lower, a smaller threshold will be generated. Perform gentle contraction to avoid accidentally damaging weak signals.

[0118] The multilayer perceptron classification head is used to process the global feature representation output from the third stage. It outputs the predicted probability of each modulation category through a fully connected layer and a Softmax function, forming a probability distribution.

[0119] (4) Semi-supervised training module.

[0120] Furthermore, the semi-supervised training module is used to train the recognition system based on labeled and unlabeled samples. Its core is to use an entropy-aware mechanism to dynamically evaluate the uncertainty of the prediction of unlabeled samples and generate weighted pseudo-labels for consistency regularization.

[0121] A semi-supervised LPI radar signal modulation identification method based on entropy-aware pseudo-tags includes:

[0122] Step S1: Use a semi-supervised training module to train the multi-scale reconstruction enhancer and classification backbone network in a semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels.

[0123] The specific processing steps of the semi-supervised training module are as follows:

[0124] Step S1.1: Prepare training sets for multiple training batches, which contain labeled samples and unlabeled samples.

[0125] The received radar signals are converted into time-frequency images using a Chirp-Wigner distribution and then standardized to a uniform size. The training set is obtained by performing Min-Max normalization. The training set contains labeled and unlabeled samples, and the proportion of labeled samples can be set to 10%, 5%, 1%, or 0.5%.

[0126] Batch size ,in It is the number of labeled samples. It is the ratio of unlabeled samples to labeled samples, for example, when , At that time, the batch size was 8.

[0127] Step S1.2: For each unlabeled sample Two enhanced versions are generated independently: weakly enhanced samples. and strongly enhanced samples For each labeled sample, a standard augmented sample is generated, thus obtaining an augmented sample set.

[0128] Weak enhancement for unlabeled samples refers to applying slight enhancement operations (such as small-angle rotation or slight translation) to the original unlabeled samples, while strong enhancement refers to applying stronger enhancement operations (such as large-angle rotation, noise injection, or color jitter). Labeled samples are only enhanced with standard enhancements (such as random rotation, translation, and horizontal flipping).

[0129] Step S1.3: Input all enhanced samples (standard enhanced samples, weakly enhanced samples, and strongly enhanced samples) into the multi-scale reconstruction enhancer and the classification backbone network connected in sequence in batches. Record the classification result obtained from the standard enhanced samples as... The classification result corresponding to the weakly enhanced sample is denoted as The classification result corresponding to the strongly enhanced sample is denoted as For each batch of samples input, the loss is calculated once according to steps S1.4 and S1.5, and the network parameters of the multi-scale reconstruction enhancer and the classification backbone network are updated according to the loss.

[0130] Step S1.4: Generate weights and pseudo-labels for unlabeled samples. Specifically, this includes:

[0131] Step S1.4.1: Classification result for any weakly enhanced sample Calculate its entropy value:

[0132] ;

[0133] In the above formula, for The Middle The element, i.e., the th element The predicted probabilities of each category; This represents the number of categories.

[0134] Step S1.4.2: Calculate the weight of each unlabeled sample based on the entropy value. :

[0135] .

[0136] The weights range from 0 to 1, with low-entropy (high-confidence) samples having a weight close to 1 and high-entropy (low-confidence) samples having a weight close to 0.

[0137] Step S1.4.3: For Apply sharpening to generate pseudo-labels for the corresponding unlabeled samples. :

[0138] ;

[0139] In the above formula, For temperature parameters, This is used to reduce the entropy of the predicted distribution, making the pseudo-labels more confident.

[0140] Step S1.5: Calculate the loss corresponding to the unlabeled sample based on the weights and pseudo-labels, and then weight the loss of the labeled sample with the loss of the unlabeled sample to obtain the total loss.

[0141] Calculate the standard cross-entropy loss for the standard augmented samples. :

[0142] ;

[0143] in This represents the number of standard enhanced samples in the current batch. For the first In the one-hot encoding of the true labels of the standard augmented sample, the first... The element value corresponding to the class, For the first In the classification results of the standard augmented samples, the first... The predicted probability of a class.

[0144] For strongly augmented samples, use the corresponding pseudo-labels. and classification results Calculate consistency loss And weighted by weights:

[0145] ;

[0146] in This represents the number of unlabeled samples in the current batch. For the first The weights corresponding to each unlabeled sample For the first The pseudo-label of the unlabeled sample corresponding to the strongly enhanced sample. The element value corresponding to the class, For the first In the classification results of the strongly enhanced samples, the first The predicted probability of a class.

[0147] Finally, the total loss is calculated by combining supervised loss and unsupervised loss. :

[0148] ;

[0149] in To balance the weights, this embodiment sets it to 1.2.

[0150] During training, the optimizer used AdamW with an initial learning rate of 0.001, cosine decay scheduling, a total of 300 training epochs, and stable updates using exponential moving average (EMA).

[0151] Step S2: Input the time series data of the radar signal to be identified into the semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels after training. The system processes the data sequentially through a preprocessing module, a multi-scale reconstruction enhancer, and a classification backbone network, and finally outputs the modulation category probability distribution of the radar signal. The category with the highest probability is taken as the recognition result.

[0152] This invention effectively separates and enhances signal features against noisy backgrounds through a multi-scale reconstruction enhancer. It combines the local feature extraction advantages of convolution with the global modeling capabilities of Transformer through a ShrinkCvT classification backbone network, and incorporates an adaptive noise suppression mechanism. Furthermore, by introducing a semi-supervised training framework with entropy-aware pseudo-labels, it efficiently utilizes a large amount of unlabeled data, significantly reducing the dependence on labeled data. This enables the system to achieve high-precision LPI radar signal modulation recognition even under conditions of low signal-to-noise ratio and scarce labeled data.

[0153] It should be noted that, as will be apparent to those skilled in the art, the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics thereof. The scope of the present invention is defined by the claims rather than the foregoing description.

Claims

1. A semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags, characterized in that: It includes a preprocessing module, a multi-scale reconstruction enhancer, and a classification backbone network, as well as a semi-supervised training module based on entropy-aware pseudo-labels; The preprocessing module is used to receive the original radar signal time series data and convert it into a time-frequency image through time-frequency transformation; The multi-scale reconstruction enhancer is used for time-frequency images. Feature enhancement is performed to separate and enhance the discriminative features of the signal from noise; The classification backbone network is used to process the enhanced feature maps output by the multi-scale reconstruction enhancer. Perform deep feature extraction and encoding, and output the final modulation category probability distribution, i.e., the classification result; The classification backbone network introduces adaptive shrinking units to achieve channel-level adaptive noise suppression; The semi-supervised training module is used to train the recognition system based on labeled and unlabeled samples. Its core is to use an entropy-aware mechanism to dynamically evaluate the uncertainty of the prediction of unlabeled samples and generate weighted pseudo-labels for consistency regularization.

2. The semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags as described in claim 1, characterized in that: The multi-scale reconstruction enhancer includes a multi-scale feature extraction module, a high-frequency detail enhancement module, a low-frequency structure reconstruction module, and an axial awareness attention unit. The multi-scale reconstruction enhancer process is as follows: the multi-scale feature extraction module uses depth-separable convolutional kernels of different scales to process the input time-frequency image. Perform convolution operations sequentially, and then sum the feature maps obtained from the first and last convolution operations to obtain the primary feature map. Then from the primary feature map Extracting low-frequency features and residual high frequency characteristics low-frequency features and residual high frequency characteristics The input high-frequency detail enhancement module extracts and enhances high-frequency detail information in the feature map, while low-frequency features are... The input low-frequency structure reconstruction module extracts and reconstructs deep structural information from the low-frequency components of the feature map. Finally, the output feature maps from the high-frequency detail enhancement module and the low-frequency structure reconstruction module are fused at the pixel level, and then further refined by the axial perception attention unit to obtain the enhanced feature map. That is, the output feature map of the multi-scale reconstruction enhancer.

3. The semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags as described in claim 2, characterized in that, From primary feature maps Extracting low-frequency features and residual high frequency characteristics The processing procedure is as follows: for the primary feature map Low-frequency features are obtained by average pooling downsampling. Then, the low-frequency characteristics The upsampled low-frequency features are obtained by upsampling back to the original size using bilinear interpolation. Then from the primary feature map Subtracting upsampled low-frequency features High-frequency characteristics of the residuals were obtained. .

4. The semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags as described in claim 2, characterized in that, The high-frequency detail enhancement module includes an edge-aware feature enhancer and a frequency-domain attention gate. The processing procedure is as follows: the first input feature map is the residual high-frequency feature. High-frequency features are initially enhanced using an edge-aware feature enhancer. Then high-frequency features Features are obtained by inputting into a frequency domain attention gate. The second input feature map is the low-frequency feature. Features are obtained by inputting into a frequency domain attention gate. Then the features With features Subtraction yields the characteristics Then the features High-frequency characteristics of residuals Matrix multiplication is performed, and the result is then subjected to a 1×1 convolution operation to obtain the output feature map of the high-frequency detail enhancement module. ; In the edge-aware feature enhancer, the high-frequency features of the residual are calculated first. Results of 3×3 average pooling and high-frequency characteristics of residuals The difference between the values ​​is used to extract edge features. This difference is then input into a weight generation network consisting of 1×1 convolutions and a sigmoid function to obtain an edge-aware weight map. This edge-aware weight map is then compared with the residual high-frequency features. By fusing the matrices, a preliminary enhanced high-frequency feature is obtained. ; In the frequency domain attention gate, the input features are subjected to global average pooling and global max pooling in parallel. Then, the two pooling results are added together to obtain the features output by the frequency domain attention gate.

5. The semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags as described in claim 2, characterized in that: The low-frequency structure reconstruction module includes three encoders with identical structures and two decoders with identical structures; The processing procedure of the low-frequency structure reconstruction module is as follows: the input feature map of the low-frequency structure reconstruction module is the low-frequency feature map. The first-level encoder performs feature extraction, and then the extracted feature map is averaged. The feature map after the first-level average pooling is passed to the corresponding first-level decoder on one hand, and as input to the second-level encoder on the other hand. The second-level encoder extracts the input feature map and performs average pooling. The feature map after second-level average pooling is passed to the corresponding second-level decoder and then input to the third-level encoder. The feature map extracted by the third-level encoder is directly passed to the second-level decoder; Subsequently, the second-level decoder fuses the feature map from the third-level encoder with the feature map after the second-level average pooling, and the output feature map is passed to the first-level decoder. The first-level decoder fuses the feature map from the second-level decoder with the feature map after the first-level average pooling. Finally, the output feature map of the first-level decoder is fused with the input feature map of the low-frequency structure reconstruction module through matrix addition to obtain the output feature map of the low-frequency structure reconstruction module.

6. The semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags as described in claim 5, characterized in that, The encoder's processing procedure is as follows: the input feature map of the encoder first undergoes preliminary feature transformation through the first convolutional layer, and the resulting feature map is then split into query vectors. Key vector Sum value vector ; query vector With key vector After performing matrix transformations, the matrices are multiplied together, and the product is normalized using Softmax to obtain the attention weights. The attention weights and value vector The matrix transformation result is multiplied by matrix to obtain the sequence features that incorporate the global context; this sequence feature is then convolved by 1×1 and added to the input feature map of the encoder. The result of the matrix addition is passed through a second convolutional layer to obtain the convolutional feature map. The result of the activation function processing of this convolutional feature map is then multiplied by matrix, and the result of the multiplication is added to the input feature map of the encoder to obtain the output feature map of the encoder. The decoder's processing procedure is as follows: The decoder receives two input feature maps. The first input feature map is the output of the previous level decoder or encoder, and the second input feature map is the feature map after average pooling at the same level. First, the second input feature map is decomposed into four sub-bands by discrete wavelet transform: low-frequency sub-band, horizontal high-frequency sub-band, vertical high-frequency sub-band, and diagonal high-frequency sub-band. The low-frequency sub-band is concatenated with the first input feature map, and the concatenated result is subjected to 1×1 convolution to adjust the number of channels to obtain the first convolutional feature. The horizontal high-frequency sub-band, vertical high-frequency sub-band, and diagonal high-frequency sub-band are concatenated, and the concatenated result is subjected to 1×1 convolution to obtain the second convolutional feature. The first convolutional feature and the second convolutional feature are concatenated, and the concatenated result is then subjected to inverse discrete wavelet transform to reconstruct a high-resolution feature map, which is the output feature map of the decoder.

7. The semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags as described in claim 2, characterized in that, The pixel-level fusion process of the output feature maps of the high-frequency detail enhancement module and the low-frequency structure reconstruction module is as follows: the output feature map of the low-frequency structure reconstruction module is upsampled and then concatenated with the output feature map of the high-frequency detail enhancement module. The concatenated result is then subjected to average pooling, 1×1 convolution, and 3×3 convolution in sequence, and finally fused with the primary feature map. Matrix addition yields pixel-level fusion results; The process of refining features using the axial sensing attention unit is as follows: the pixel-level fusion result is input into the axial sensing attention unit to obtain a spatial attention map, and then the spatial attention map is multiplied by the pixel-level fusion result to obtain the enhanced feature map. ; The processing procedure of the axial sensing attention unit is as follows: the input of the axial sensing attention unit is first compressed spatially by average pooling, and then the number of channels is adjusted by 1×1 convolution operation. The features obtained by convolution are first captured by 1×11 depthwise convolution to capture long-range dependencies in the horizontal direction. The result of the first depthwise convolution is then captured by 11×1 depthwise convolution to capture long-range dependencies in the vertical direction. The result of the second depthwise convolution is used to obtain the spatial attention map, i.e., the output of the axial sensing attention unit, by 1×1 convolution and sigmoid activation function.

8. The semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags as described in claim 1, characterized in that, The classification backbone network consists of N stages connected in sequence. The first N-1 stages each contain a convolutional token embedding module, a converter, and an adaptive shrinking unit connected in sequence. The last stage contains a convolutional token embedding module and a converter connected in sequence. The output of the last stage enters the multilayer perceptron classification head to obtain the modulated class probability distribution. The processing procedure of the adaptive shrinking unit is as follows: a soft threshold function is applied to each element of the input token sequence of the adaptive shrinking unit to achieve adaptive denoising and obtain the output token sequence. The soft threshold function is: ； in, For elements in the input token sequence, yes The absolute value represents its characteristic intensity. It is a symbolic function. These are the shrunk output elements, and all output elements constitute the output token sequence; threshold Dynamically generated through a learnable function: ； in, yes The energy of the channel is obtained by averaging the absolute values ​​of all elements in that channel. It is a two-layer fully connected network, based on the input energy. Dynamically learn and output the most suitable threshold If the energy of a channel A higher value results in a larger threshold. If the energy of a channel If the value is lower, a smaller threshold will be generated. .

9. A semi-supervised LPI radar signal modulation identification method based on entropy-aware pseudo-tags, characterized in that, Based on the semi-supervised LPI radar signal modulation identification system based on entropy-aware pseudo-tags as described in claim 1, the method includes: Step S1: Use a semi-supervised training module to train a multi-scale reconstruction enhancer and a classification backbone network; The specific processing steps of the semi-supervised training module are as follows: Step S1.1: Prepare training sets for multiple training batches, each containing labeled and unlabeled samples; Step S1.2: For each unlabeled sample Two enhanced versions are generated independently: weakly enhanced samples. and strongly enhanced samples For each labeled sample, a standard augmented sample is generated, thus obtaining an augmented sample set; Step S1.3: Input all augmented samples in batches into the multi-scale reconstruction augmenter and the classification backbone network connected in sequence, and record the classification results obtained from the standard augmented samples as follows: The classification result corresponding to the weakly enhanced sample is denoted as The classification result corresponding to the strongly enhanced sample is denoted as ; For each batch of samples input, calculate the loss once according to steps S1.4 and S1.5, and update the network parameters of the multi-scale reconstruction enhancer and the classification backbone network according to the loss; Step S1.4: Generate weights and pseudo-labels for unlabeled samples; Step S1.5: Calculate the loss corresponding to the unlabeled sample based on the weights and pseudo-labels, and then weight the loss of the labeled sample with the loss of the unlabeled sample to obtain the total loss; Step S2: Input the time series data of the radar signal to be identified into the semi-supervised LPI radar signal modulation recognition system based on entropy-aware pseudo-labels after training. The system processes the data sequentially through a preprocessing module, a multi-scale reconstruction enhancer, and a classification backbone network, and finally outputs the modulation category probability distribution of the radar signal. The category with the highest probability is taken as the recognition result.

10. The semi-supervised LPI radar signal modulation identification method based on entropy-aware pseudo-tags as described in claim 9, characterized in that, Step S1.4 specifically includes: Step S1.4.1: Classification result for any weakly enhanced sample Calculate its entropy value: ； In the above formula, for The Middle The element, i.e., the th element The predicted probabilities of each category; Number of categories; Step S1.4.2: Calculate the weight of each unlabeled sample based on the entropy value. : ； Step S1.4.3: For Apply sharpening to generate pseudo-labels for the corresponding unlabeled samples. : ； In the above formula, For temperature parameters, ; In step S1.5: Calculate the standard cross-entropy loss for the standard augmented samples. : ； in This represents the number of standard enhanced samples in the current batch. For the first In the one-hot encoding of the true labels of the standard augmented sample, the first... The element value corresponding to the class, For the first In the classification results of the standard augmented samples, the first... The predicted probability of a class; For strongly augmented samples, use the corresponding pseudo-labels. and classification results Calculate consistency loss And weighted by weights: ； in This represents the number of unlabeled samples in the current batch. For the first The weights corresponding to each unlabeled sample For the first The pseudo-label of the unlabeled sample corresponding to the strongly enhanced sample. The element value corresponding to the class, For the first In the classification results of the strongly enhanced samples, the first The predicted probability of a class; Finally, the total loss is calculated by combining supervised loss and unsupervised loss. : ； in To balance the weights.

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