Feature fusion-based complex-valued polarized synthetic aperture radar ground feature classification method

Abstract

The invention discloses a complex-valued polarized synthetic aperture radar ground feature classification method based on feature fusion. The method comprises the following steps: firstly, carrying out dimension reduction processing on polarization characteristics of original PolSAR data by utilizing a principal component analysis method to generate an optimal characteristic subset; and then designing a hybrid random data enhancement module combining space-level enhancement and pixel-level enhancement, and performing data enhancement in a random extraction mode. Then, the FCN-16s network is subjected to complex-valued modification, a complex-valued CGeLU activation function is introduced, a complex-valued full convolutional network CV-FCN is obtained, the network is trained by using an enhanced training sample, and the performance of the network for processing a pixel-level terrain classification task is evaluated. According to the method, phase information and amplitude information in PolSAR complex value data can be fully utilized, the expression ability of real number features is combined, and the PolSAR ground feature classification detection performance is improved by adopting a strategy of a space enhancement mode and a pixel enhancement mode.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar target detection, and particularly relates to a method for classifying ground objects of a complex-valued polarimetric synthetic aperture radar based on feature fusion. Background Art

[0002] Synthetic Aperture Radar (SAR) is an advanced active microwave sensor. Compared with other remote sensing tools such as optical, infrared, and hyperspectral, it has the characteristics of all-weather and all-time ground observation without being restricted by illumination and climate conditions, and is widely used in geological exploration, disaster rescue, ocean surveillance and other scenarios. Polarimetric Synthetic Aperture Radar (PolSAR) is an important branch of SAR technology, which can obtain the polarization feature information of target objects. Compared with traditional single-polarization SAR, PolSAR includes horizontal polarization HH, vertical polarization VV, and cross polarizations HV and VH. By transmitting and receiving electromagnetic waves of different polarization states, it provides more comprehensive electromagnetic scattering information for ground object targets, which is of great significance for ground object classification tasks. However, the high-dimensional complex-valued data characteristics of PolSAR pose high requirements for algorithm design and computing resources. How to achieve efficient processing under limited computing power and make full use of the complex-valued information of PolSAR is an important issue. On the other hand, the scattering characteristics of targets in complex scenes are highly uncertain and random, which poses higher requirements for the physical interpretation of polarization features and the robustness of algorithms.

[0003] In the existing technology for ground object classification tasks, traditional methods and deep learning technologies each have their own advantages and complement each other. Traditional methods such as Maximum Likelihood Classification (MLC), Support Vector Machine (SVM), and Markov Random Field (MRF) rely on statistical features or spatial context modeling, and are suitable for small-scale data and the analysis of physical properties, but have limited effects when dealing with high-dimensional complex data. In recent years, methods based on deep learning have developed rapidly. Models represented by Convolutional Neural Network (CNN) can effectively extract high-level features of ground objects. For example, ResNet and DenseNet capture global patterns through deep structures, while Fully Convolutional Network (FCN) and DeepLab achieve pixel-level classification through semantic segmentation. The above methods often use optical data or SAR data alone, unable to make full use of the complementarity of multimodal information, and easily ignoring low-level texture, geometric structure, and polarization information, with insufficient feature expression and missing classification details, resulting in limited ability to distinguish complex ground objects. In complex scenes, the target boundaries of SAR images often become blurred due to clutter interference or weak scattering phenomena, leading to false alarms and missed alarms in target classification. Summary of the Invention

[0004] Aiming at the deficiencies of the existing technology, the present invention proposes a method for classifying ground objects of complex-valued polarimetric synthetic aperture radar based on feature fusion. By extracting polarimetric features from the original data and selecting appropriate feature subsets, it supplements the low-level polarimetric scattering characteristics and geometric edge information. After fusing the original complex-valued data with the feature subsets, data augmentation of the random enhancement space is performed and then input into the improved complex-valued FCN network. At the same time, a complex-valued GeLU activation function is introduced to improve the detection performance.

[0005] The method for classifying ground objects of complex-valued polarimetric synthetic aperture radar based on feature fusion specifically includes the following steps:

[0006] Step 1: Process the original PolSAR data, extract the polarimetric feature set in the dataset, perform dimensionality reduction processing on the extracted features using the principal component analysis method (PCA), and select the k features with the largest proportion according to the contribution rate as the optimal feature subset. Concatenate and fuse the original complex-valued data with the optimal feature subset as the fusion feature.

[0007] Step 2: Adopt a hybrid random data augmentation module that combines spatial-level augmentation and pixel-level augmentation. Among them, the spatial-level data augmentation includes 6 augmentation operations, and the pixel-level data augmentation includes 7 augmentation operations. Input the fusion feature into the hybrid random data augmentation module, and then perform slicing processing. The obtained samples are used as the training original dataset.

[0008] Step 3: In view of the particularity of complex-valued data, perform complex-valued modification on the original FCN-16s network to construct a complex-valued fully convolutional network (CV-FCN), including convolutional operations, batch normalization, activation functions, and pooling operations. And replace the ReLU activation function of the original network with a complex-valued GeLU activation function to obtain an improved CV-FCN model.

[0009] Step 4: Input the training samples obtained in Step 2 into the improved CV-FCN model constructed in Step 3 for training, and evaluate its performance in processing pixel-level ground object classification tasks.

[0010] The present invention has the following beneficial effects:

[0011] 1. It can make full use of the phase information and amplitude information in the complex-valued data of PolSAR, and at the same time combine the expression ability of real-valued features to achieve more accurate target detection, effectively improving the sensitivity of the model to targets, especially improving the detection accuracy in complex environments.

[0012] 2. By combining the strategies of spatial and pixel enhancement methods, the complexity of the image enhancement operation can be controlled, ensuring the effectiveness of data augmentation, improving the generalization ability of the model, ensuring its robustness to various complex situations in practical applications, and enabling the model to better learn the effective features of complex-valued data during the training process.

[0013] 3. The improved CV-FCN network can learn more accurate patterns from richer features by introducing complex-valued operations, thereby improving the accuracy and robustness of the ground object classification task. Brief Description of the Drawings

[0014] Figure 1 It is a flowchart of a complex-valued polarimetric synthetic aperture radar ground object classification method based on feature fusion;

[0015] Figure 2 It is a flowchart of the complex-valued data and real-valued feature fusion strategy in the embodiment;

[0016] Figure 3 It is a schematic diagram of a hybrid random data augmentation module combining spatial-level enhancement and pixel-level enhancement in the embodiment;

[0017] Figure 4 It is a schematic diagram of the structure of the complex-valued fully convolutional network (CV-FCN) in the embodiment;

[0018] Figure 5 It is a structural diagram of the downsampling module of CV-FCN in the embodiment;

[0019] Figure 6 It is a structural diagram of the upsampling module of CV-FCN in the embodiment;

[0020] Figure 7 It is a schematic diagram of the CGeLU activation function in the embodiment;

[0021] Figure 8 It is a comparison chart of the detection results of multiple schemes in the embodiment. Detailed Embodiment

[0022] The present invention will be further explained below with reference to the accompanying drawings;

[0023] The complex-valued polarimetric synthetic aperture radar ground object method based on feature fusion, as Figure 1 shown, specifically includes the following steps:

[0024] Step 1. For the PolSAR raw data to be processed, perform polarimetric decomposition on it, and extract the polarimetric features shown in Table 1 as the total polarimetric feature set Φ 0 .

[0025] Table 1

[0026]

[0027] Use PCA to perform dimensionality reduction on Φ 0 For the n-dimensional data P l composed of m polarization parameters p n×m = [p 1 , p 2 , p 3 .... p m , perform centering processing:

[0028]

[0029] where n represents the length of the polarization parameter x i . Calculate the covariance matrix C:

[0030]

[0031] The superscript T represents transpose. Perform eigenvalue decomposition on the covariance matrix C to obtain the eigenmatrix, and take the first k columns to form the matrix Q n×k . Project the original data P onto the Q coordinate system to obtain the dimensionality-reduced data P' k×m :

[0032]

[0033] P' k×m The data in is the selected k features with the largest proportion, and they are re-stitched to generate the optimal feature subset

[0034] In order to make full use of the phase information and amplitude information in the complex-valued data, and at the same time combine the expression ability of real-valued features, a strategy of fusing original complex-valued data and real-valued features is proposed, aiming to effectively fuse complex-valued data and real-valued polarization features. As Figure 2 shown, normalize the polarization features in the optimal feature subset , and stitch and fuse them with the original complex-valued data S = {S HH , S HV , S VV} of size M×N×3 in the third dimension to form the fused feature Φ of size M×N×(k + 3).

[0035] Step 2. This example proposes a hybrid random data augmentation module that combines spatial-level enhancement and pixel-level enhancement to increase data diversity and enhance the robustness and generalization ability of the model. As Figure 3 shown, the spatial-level data augmentation focuses on the geometric transformation of images. This example selects 5 enhancement operations and 1 no-modification operation, including S 0 no modification, S 1Horizontal flip, S 2 Vertical Flip, S 3 Rotate 90 degrees clockwise, S 4 Rotate 180 degrees clockwise, S 5 Rotate 270 degrees clockwise. Pixel-level data enhancement focuses on adjusting the pixel-level features of the data. This example selects 6 enhancement operations and 1 non-modification operation, including A 0 No modification, A 1 Frequency domain low-pass filtering, A 2 Frequency domain high pass filter, A 3 Frequency domain homomorphic filtering, A 4 Contrast enhancement, A 5 Add Gaussian noise, A 6 Add salt and pepper noise.

[0036] For frequency domain filtering, due to the particularity of the input data being complex-valued data, each pixel contains both real and imaginary data, so the frequency domain filtering operation must act independently on the real and imaginary parts of the complex-valued data. Specifically, the frequency domain low-pass filtering and high-pass filtering process the real and imaginary parts of the data in the frequency domain, respectively, and then restore them to the time domain. At the same time, the amplitude and phase processing of the filtering operation needs to be performed in the real and imaginary parts, respectively, to ensure that the integrity of the complex data is not destroyed. For each complex-valued pixel Z=X+iY of the input image, the frequency domain low-pass filter H LP The low-frequency part in the frequency domain is retained, while the high-frequency part is suppressed. For complex-valued data, the low-pass filter will act on both the real and imaginary spectrum:

[0037] Z Low =F -1 [F(X)·H LP +iF(Y)·H LP ]

[0038] Where F(X) and F(Y) represent the Fourier transform of the real part X and the imaginary part Y respectively. -1 is the inverse Fourier transform.

[0039] Frequency domain high pass filter H HP The high frequency part in the frequency domain is enhanced, while the low frequency part is suppressed. The complex-valued high-pass filter also acts on the real and imaginary frequency domain data separately:

[0040] Z High =F -1 [F(X)·H HP +iF(Y)·H HP ]

[0041] The purpose of homomorphic filtering is to enhance the high frequency part and suppress the low frequency part, thereby improving the contrast and details of the image. The workflow of the complex-valued homomorphic filter can be described as:

[0042] Z Homomorphic =F -1 [F(X)·Z enhanced +iF(Y)·Z enhanced ]

[0043] Where Z enhanced is the frequency enhancement function in homomorphic filtering and can be calculated by the following formula:

[0044]

[0045] Among them, rh and rl are the enhancement factors of high frequency and low frequency respectively, D is the distance from the center of the spectrum to the frequency point, and d0 is the distance constant, which controls the influence of the low frequency area.

[0046] Perform spatial data enhancement on the fusion features Φ of all samples, and then select some of the features for pixel-level data enhancement to obtain an enhanced data set. By setting a pixel data enhancement ratio θ, the pixel-level enhancement can be flexibly controlled, that is, a random sampling of the data with a ratio of θ in the total data set is performed. 1 To A 6 The pixel level enhancement is based on the 1-θ scale. 0 No modification operation. When θ is large, the proportion of pixel-level enhancement operations is high, which helps the model learn richer detail features; when θ is small, the model relies more on spatial-level transformations, thereby improving the model's robustness to geometric transformations. By flexibly adjusting θ, we can find the most suitable enhancement strategy for data and tasks, further improving the performance of the model.

[0047] Through two different spatial enhancement strategies, the complexity of image enhancement operations is controlled and conflicting operations are avoided, while the effectiveness of data enhancement is ensured, so that the model can better learn the effective features of complex-valued data during training.

[0048] For the enhanced data set, it is cropped into slices of size 32×32 in an overlapping sliding window manner. The number of slices after enhancement is 10395 in total, which is used as the data set required for training. Take 80% of them as training set, 10% as validation set, and 10% as test set.

[0049] Step 3: Construct a complex-valued fully convolutional network (CV-FCN). The traditional FCN network usually consists of a series of real-valued operations, including convolutional operations, batch normalization, activation functions, and pooling operations. In this example, due to the particularity of complex-valued data, the original FCN-16s network is modified to be complex-valued, and the ReLU activation function of the original network is replaced with a complex-valued GeLU activation function. After the improvement, the CV-FCN model is obtained. As Figure 4 shown, the CV-FCN network includes a downsampling module, a Bottleneck module, and an upsampling module to achieve end-to-end complex-valued feature extraction and restoration.

[0050] s3.1: The downsampling module includes 4 consecutive convolutional and pooling units. Each unit contains a complex-valued convolutional layer, a complex-valued batch normalization layer, a complex-valued activation layer, and a complex-valued pooling layer, as Figure 5 shown.

[0051] In the convolutional operation, the original real-valued convolution is replaced with a complex-valued convolution. For each input enhanced complex-valued pixel Z′ = X′ + iY′, independent convolutions are performed on the real and imaginary parts respectively, and then the convolution results of the real and imaginary parts are combined. The basic form of the complex-valued convolution is:

[0052] Z Con = X Con + iY Con = (X′ * K real - Y′ * K imag ) + i(X′ * K imag + Y′ * K real )

[0053] where K real and K imag are the real and imaginary parts of the convolution kernel respectively, and X′ and Y′ are the real and imaginary parts of the input pixel respectively, and * represents the convolution operation.

[0054] The original batch normalization operation is improved to a complex-valued batch normalization layer. The means μ X and μ Y , as well as the standard deviations σ X and σ Y of the input data are calculated separately for the real and imaginary parts. The input feature Z Con is normalized according to the following formula:

[0055]

[0056] The learnable complex-valued parameters γ = γ real + γ imag and offset β = β real + β imag are used to transform the normalization result:

[0057] Z out = γZ norm + β

[0058] Traditional activation functions are invalid for complex-valued data. Therefore, CV-FCN uses complex-valued activation functions to introduce non-linear expressive ability. In this example, the CGeLU activation function is adopted, which is obtained by extending the CGeLU activation function from the real number domain to the complex number domain. The images of the GeLU activation function and its derivative are as Figure 7 shown and are continuously differentiable on the complex plane:

[0059] CGeLU(z) = GeLU(Re(z)) + i·GeLU(Im(z))

[0060] = Re(z)·Φ(Re(z)) + i·Im(z)·Φ(Im(z))

[0061] The complex-valued max pooling layer is used to reduce the size of the feature map in the downsampling stage, while retaining the significance of the complex-valued features and selecting the maximum value of the input amplitude.

[0062] s3.2. The Bottleneck module in CV-FCN is used to connect the downsampling and upsampling modules. It compresses the number of channels through 1x1 convolution operations, reduces the computational amount of the model, and retains key information at the same time.

[0063] s3.3. As Figure 6 shown, the upsampling module includes a complex-valued de-pooling layer, a complex-valued convolutional layer, a complex-valued batch normalization layer, and a complex-valued activation function. Through de-pooling and convolution operations, the upsampling module can restore the spatial information lost in the downsampling process, gradually restore the resolution of the feature map, and generate the final output feature map.

[0064] The complex-valued de-pooling layer restores the low-resolution feature map to a high-resolution feature map by recording the indices in the max pooling operation; the complex-valued convolution is used to extract the complex-valued information of the high-resolution feature map and further extract the complex-valued features after upsampling; the complex-valued batch normalization independently normalizes the real and imaginary parts of the convolution output to ensure the stability of model training; the complex-valued activation function enhances the expressive ability of the model through non-linear transformation.

[0065] To prevent overfitting, a Dropout mechanism is added to the three modules of CV-FCN respectively to enhance the generalization ability of the model by randomly discarding the activation values of some neurons.

[0066] Step 4. Input the data sets obtained in Steps 1 and 2 into the improved CV-FCN model constructed in Step 3 for network training.

[0067] The data used in this embodiment comes from the SAN_FRANCISCO_AIRSAR dataset. The software platform is the WIN10 operating system and Pytorch1.8.1, and the hardware configuration is an i9-13900K CPU and an NVIDIA GeForce RTX 3090 GPU.

[0068] Set the number of model training rounds to 50, the batch-size to 32, use the gradient descent optimization algorithm Adam to optimize the model parameters, adopt the traditional cross-entropy loss function ComplexAverageCrossEntropy after complex-valued extension, and set the learning rate lr to 0.001. To evaluate the performance of pixel-level land cover classification, Precision (P), Recall (R), Accuracy (ACC), Average Accuracy (AA), and F1 value are used as evaluation indicators:

[0069]

[0070] Among them, TP represents the number of actual positive classes predicted as positive classes; TN represents the number of actual negative classes predicted as negative classes; FP represents the number of actual negative classes predicted as positive classes; FN represents the number of actual positive classes predicted as negative classes; P represents Precision, and R represents Recall; ACC represents Accuracy, and AA represents Average Accuracy.

[0071] Extract the total polarization feature set Φ of the original data 0 Perform PCA feature dimensionality reduction, and the results are shown in Table 2:

[0072] Table 2

[0073]

[0074] The smaller the contribution rate of the principal component, the less the contribution of the principal component to the total variance of the data. The total contribution rate of the first 7 principal components is about 99%. In this example, the first 7 feature combinations with a contribution rate greater than 0.001 are combined into a feature subset For subsequent training.

[0075] Fuse the original complex-valued data S = {S HH , S HV , S VV} and the new feature subset Set the pixel data enhancement ratio θ to 0.25, and use the enhanced dataset For training, and compare the training effects of the fused feature data obtained by random sampling of the two groups after enhancement As shown in Table 3:

[0076] Table 3

[0077]

[0078]

[0079] Among them, PCA selects the feature subset r2, H, Cameron, RF3, A, alpha, RF1;

[0080] Feature combination alpha, RF1, YPd, YPv, H, Span, A;

[0081] Feature combination Pv, A, RF5, RF2, Cameron, YPc, Span;

[0082] It can be seen from the data in Table 3 that after fusing the polarization features, the classification effects of various feature combination schemes are significantly improved compared with those without fused features. In addition, the feature subset selected by PCA performs the best, and all indicators are better than other feature combinations, showing the effectiveness of selecting the feature subset by PCA.

[0083] To verify the effectiveness of this method, in this embodiment, the real-valued networks FCN, CNN, the complex-valued network CV-CNN, and the CV-FCN proposed in this example are selected for comparative experiments. Among them, the training of the real-valued network replaces the complex-valued original data S fused in the input data set with the real and imaginary parts of the data {S HH_real , S HH_imag , S HV_real , S HV_imag , S VV_real , S VV_imag}, and at the same time, both are fused with the feature subset selected by PCA , and the fused data is input into the enhancement module of this method, and the pixel data enhancement ratio θ is set to 0.25.

[0084] Using the enhanced data set for training, the detection results are visualized on the test images, as Figure 8 shown, and the comparison results of the performance indicators are shown in Table 4:

[0085] Table 4

[0086]

[0087] As the results show, compared with the real-valued network FCN, the proposed method for classifying ground objects in complex-valued polarimetric synthetic aperture radar based on feature fusion has significantly improved in all indicators. The CNN and CV-CNN networks perform poorly in detecting small targets and boundary regions, while the FCN network also outperforms the CNN network in all aspects when dealing with the task of classifying ground objects with higher-dimensional data. This indicates that the fully convolutional nature of the FCN network is more suitable for global feature capture and classification of high-dimensional complex data, and the feature fusion strategy further improves the segmentation accuracy and robustness of the complex-valued network.

Claims

1. A complex-valued polarimetric synthetic aperture radar object classification method based on feature fusion, characterized by: The specific steps include: Step 1: Process the original PolSAR data, extract the polarization feature set Φ0 in the data set, perform dimensionality reduction, select the optimal feature subset, and concatenate and fuse the original complex-valued data with the optimal feature subset as the fusion feature; Step 2: Design a hybrid random data enhancement module, including spatial-level data enhancement and pixel-level data enhancement; The fused features are input into the data enhancement module, followed by slicing, and the obtained data is used as training samples; Step 3: Modify the FCN-16s network to a complex value and replace the ReLU activation function with the complex-valued GeLU activation function to obtain the complex-valued fully convolutional network CV-FCN. Step 4: Input the training samples obtained in step 2 into the complex-valued fully convolutional network CV-FCN constructed in step 3, and use the cross entropy loss function to train the network parameters to achieve pixel-level ground object classification of complex-valued polarimetric synthetic aperture radar.

2. The complex-valued polarimetric synthetic aperture radar object classification method based on feature fusion as claimed in claim 1, characterized in that: PCA is used to reduce the dimension of the polarization feature set Φ0, and the k features with the largest contribution rate are selected as the optimal feature subset.

3. The complex-valued polarimetric synthetic aperture radar object classification method based on feature fusion according to claim 1 or 2, characterized in that: The optimal feature subset The polarization characteristics in are normalized and compared with the original complex valued data S = {S HH ,S HV ,S VV }Splice and fuse in the third dimension to form the fusion feature Φ.

4. The complex-valued polarimetric synthetic aperture radar object classification method based on feature fusion as claimed in claim 1, characterized in that: The spatial data enhancement includes S0 no modification, S1 horizontal flip, S2 vertical flip, S3 clockwise rotation 90 degrees, S4 clockwise rotation 180 degrees, S5 clockwise rotation 270 degrees; the pixel level data enhancement includes A0 no modification, A1 frequency domain low-pass filtering, A2 frequency domain high-pass filtering, A3 frequency domain homomorphic filtering, A4 contrast enhancement, A5 adding Gaussian noise, A6 adding salt and pepper noise; The hybrid random data enhancement module performs spatial-level data enhancement on the fused features Φ of all samples, and then selects some of the features for pixel-level data enhancement to obtain an enhanced data set.

5. The complex-valued polarimetric synthetic aperture radar object classification method based on feature fusion as claimed in claim 4, characterized in that: The frequency domain low-pass filter H LP For the low frequency part Z in the frequency domain Low To make a reservation: Z Low =F -1 [F(X)·H LP +iF(Y)·H LP ] Where F(X) and F(Y) represent the Fourier transform of the real part X and imaginary part Y of the complex pixel Z = X + iY, respectively. -1 is the inverse Fourier transform; Frequency domain high pass filter H HP For the high frequency part Z in the frequency domain High To enhance: Z High =F -1 [F(X)·H HP +iF(Y)·H HP ] The purpose of homomorphic filtering is to enhance high frequencies and suppress low frequencies: Z Homomorphic =F -1 [F(X)·Z enhanced +iF(Y)·Z enhanced ] Where Z enhanced is the frequency enhancement function in homomorphic filtering: Among them, rh and rl are the enhancement factors of high frequency and low frequency respectively, D is the distance from the center of the spectrum to the frequency point, and d0 is the distance constant, which controls the influence of the low frequency area.

6. The complex-valued polarimetric synthetic aperture radar object classification method based on feature fusion as claimed in claim 1, characterized in that: The CV-FCN network includes a downsampling module, a bottleneck module and an upsampling module, and a Dropout mechanism is added to each of the three modules.

7. The complex-valued polarimetric synthetic aperture radar object classification method based on feature fusion as claimed in claim 6, characterized in that: The downsampling module includes 4 consecutive convolution and pooling units, each unit including a complex-valued convolution layer, a complex-valued batch normalization layer, a complex-valued activation layer and a complex-valued pooling layer; The Bottleneck module is used to connect the downsampling and upsampling modules and perform channel number compression through a 1x1 convolution operation; The upsampling module includes a complex-valued unpooling layer, a complex-valued convolution layer, a complex-valued batch normalization layer, and a complex-valued activation function; through unpooling and convolution operations, the resolution of the feature map is gradually restored to generate the final output feature map; Among them, the complex-valued activation layer adopts the CGeLU activation function.

8. The complex-valued polarimetric synthetic aperture radar object classification method based on feature fusion as claimed in claim 7, characterized in that: The complex-valued convolution layer performs independent convolution on the real and imaginary parts of the input complex-valued pixel Z′=X′+iY′, and then converts the convolution results of the real and imaginary parts X Con , Y Con Merge as the convolution result Z Con : Z Con =X Con +iY Con =(X′*K real -Y′*K imag )+i(X′*K imag +Y′*K real ) Where K real and K imag are the real and imaginary parts of the convolution kernel, X′ and Y′ are the real and imaginary parts of the input pixel, * represents the convolution operation; The complex-valued batch normalization layer calculates the mean μ for the real and imaginary parts of the input data respectively. X and μ Y , and the standard deviation σ X and σ Y , and get the normalized result Z norm : Using a learnable complex-valued parameter γ = γ real +γ imag and offset β = β real +β imag For the normalized result Z Con To transform: WITH out =γZ norm +β The CGeLU activation function is obtained by extending the GeLU activation function from the real number domain to the complex number domain: CGeLU(z)=GeLU(Re(z))+i·GeLU*Im(z)) =Re(z)·Φ(Re(z)(+i·Im(z)·Φ(Im(z)).

9. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method according to any one of claims 1 to 8.

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