Zero-Shot SAR Target Recognition Method Based on Optimal Transport Distance Function

Abstract

A zero-shot synthetic aperture radar (SAR) target recognition method based on the optimal transport distance function, which mainly solves the problems that the existing zero-shot SAR target recognition methods cannot recognize new targets of unknown categories and have a low recognition accuracy for easily confused targets. The implementation steps are as follows: extract the feature information of SAR images and optical images; calculate the class centers of SAR images in the source domain and the target domain; calculate the class centers of optical images; construct a target loss function using the mean square error function and the optimal transport distance function; and perform image recognition using the optimal transport distance function. In the present invention, the extracted feature information of the optical image is used as the semantic attribute defined in zero-shot learning, and the optimal transport distance function is used to align the class centers of unknown categories in the target domain, effectively improving the accuracy of zero-shot SAR target recognition.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, and further relates to a zero-shot synthetic aperture radar (SAR) target recognition method based on an optimal transport distance function in the field of target recognition technology. The present invention proposes a distance metric method combining optimal transport for SAR images, which can be used to recognize new targets of unknown classes in SAR images. Background Art

[0002] Synthetic Aperture Radar (SAR) has the characteristics of all-weather, all-time, high resolution, and strong penetration, and has been widely used in many fields such as topographic mapping, geological exploration, ocean observation, and military missions. SAR images can provide unique information by capturing the electromagnetic scattering characteristics of targets, which is of great significance for the recognition of SAR images. However, due to the limitations of background clutter and resolution, SAR images have the characteristics of blurred edges and strong anisotropy, which increases the difficulty of SAR image target recognition. In addition, in actual application scenarios, it is difficult to obtain SAR images with labels, especially in non-cooperative situations, resulting in SAR target recognition under small-sample or even zero-sample conditions. Currently, all zero-shot SAR target recognition methods optimize the training network model by combining simulation data and real data, and the target categories for training and testing are the same. However, new targets of unknown classes often appear in actual scenarios. For the recognition of new targets in optical image recognition tasks, zero-shot recognition is usually based on language information such as semantic attributes. Different from the semantic attributes defined in optical images, the semantic descriptions in SAR images are difficult to visually capture, which is the main problem faced by zero-shot SAR target recognition.

[0003] Xidian University proposed a zero-shot SAR target recognition method that hierarchically fuses CNN and image similarity in its patent document "Zero-shot SAR Target Recognition Method Combining CNN and Image Similarity" (Patent Application No.: CN 202111188558.3, Publication No.: CN 113902969 A). This method aims at the zero-shot SAR image target recognition problem, uses simulation data to recognize real data of the same category, constructs a two-step classifier, uses a convolutional neural network as a pre-classifier, and a multi-similarity fusion classifier as a fine-classifier, alleviating the phenomenon of low recognition accuracy caused by the distribution difference between simulation data and real data, and significantly improving the recognition accuracy. However, the disadvantage of this method is that the recognition target category of real data during testing is restricted by the category of simulation data during training, and it is unable to recognize new targets of unknown classes that appear during testing, limiting the recognition performance of the model.

[0004] Fei Gao, Jieqiong Zhao, Chong Lin et al. proposed a SAR image recognition method based on distance metric learning in their published paper "A SAR Image Recognition Method Based on Distance Metric Learning" (Transactions of Beijing Institute of Technology, 2021). This method uses a CNN network to obtain the feature distribution of images, uses an LSTM network to strengthen the correlation between images, calculates the matching degree between images based on the cosine similarity distance metric method, and classifies the target through an attention mechanism. In addition, in the case of limited data samples, combined with the training method of data in few-shot learning, the training set is divided proportionally, and a pre-training strategy is adopted for model training to obtain the classification and recognition results of test images. However, the disadvantage of this method is that when using the cosine similarity distance metric method, it is difficult to extract distinguishable image feature information for easily confused targets of the same category but different models, resulting in a low recognition accuracy for easily confused targets. Summary of the Invention

[0005] The object of the present invention is to address the deficiencies of the above-mentioned prior art and propose a zero-shot synthetic aperture radar (SAR) target recognition method based on the optimal transport distance function, aiming to solve the problems that the existing zero-shot SAR target recognition method based on the fusion of CNN and image similarity cannot recognize new targets of unknown categories, and the SAR target recognition method based on the cosine similarity distance metric has a low recognition accuracy for easily confused targets.

[0006] The technical idea for achieving the object of the present invention is as follows: The present invention replaces the semantic attributes defined in conventional zero-shot learning by introducing the feature information of optical images to connect the relationship between the known target categories in the source domain and the unknown new categories in the target domain, and recognizes the new category SAR images in the target domain, thereby solving the problem that the target categories recognized during testing in the prior art are restricted by the target categories during training and cannot recognize new targets of unknown categories. The present invention adopts the optimal transport distance function to align the category centers of unknown categories in the target domain and measure and find the synthetic center closest to the image samples in the visual space, aiming to solve the problem of low recognition accuracy for easily confused SAR image targets in the prior art.

[0007] The specific steps of the present invention are as follows:

[0008] Step 1, extract the feature information of SAR images and optical images:

[0009] Step 1.1: Use a deep neural network model as the feature extraction network for SAR images to extract the feature information in each SAR image;

[0010] Step 1.2: Use the same deep neural network model as in Step 1.1 as the feature extraction network for optical images to extract the feature information in each optical image;

[0011] Step 2: Calculate the class centers of SAR images in the source domain and the target domain:

[0012] Step 2.1: According to the class label information of the known target-class SAR images in the source domain, calculate the class centers of the SAR images of the same class in the source domain;

[0013] Step 2.2: Use the K-Means unsupervised clustering algorithm to approximately calculate the class centers of the SAR images of unknown classes in the target domain;

[0014] Step 3: Calculate the class centers of optical images:

[0015] Input the feature information of the optical images into a two-layer trained embedding network to output the class centers of the optical images;

[0016] Step 4: Construct the target loss function using the mean squared error function and the optimal transport distance function:

[0017] Step 4.1: Use the mean squared error function formula to calculate the distance between the class centers of the SAR images in the source domain and the class centers of the optical images;

[0018] Step 4.2: Use the optimal transport distance function formula to calculate the distance between the class centers of the SAR images in the target domain and the class centers of the optical images;

[0019] Step 4.3: Add the two distance function formulas in Step 4.1 and Step 4.2 to obtain the distance between all the class centers of the SAR images and all the class centers of the optical images;

[0020] Step 4.4: Use the gradient descent method to minimize the distance between all the class centers of the SAR images and all the class centers of the optical images to obtain the class centers of the SAR images of unknown classes in the target domain;

[0021] Step 5: Use the optimal transport distance function for image recognition:

[0022] Use the optimal transport distance function to find the class center closest to the SAR images of unknown classes in the target domain in the visual space, and obtain the class information of the zero-shot synthetic aperture radar (SAR) images of unknown classes in the target domain according to the label of the found class center.

[0023] The present invention has the following advantages compared with the prior art:

[0024] First, the present invention uses the feature information of optical images to replace the semantic attributes defined in conventional zero-shot learning, which is used to connect the relationship between known target categories in the source domain and unknown new categories in the target domain, making the SAR zero-shot target recognition task possible. When performing SAR zero-shot target recognition, it overcomes the defect in the prior art that new targets of unknown categories cannot be recognized, enabling the present invention to directly utilize optical images to achieve SAR zero-shot target recognition without defining corresponding semantic attributes, thus expanding the application scope of SAR target recognition.

[0025] Second, according to the optimal transport theory, the present invention uses the optimal transport distance, i.e., the Wasserstein distance, to align the category centers of unknown categories in the target domain, and measures to find the synthetic center closest to the image samples in the visual space, overcoming the deficiency in the prior art that the recognition accuracy of confusing SAR image targets is relatively low, and enabling the present invention to improve the recognition accuracy of SAR targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flowchart of the present invention;

[0027] Figure 2 is a visualization diagram of the target recognition method based on the mean square error function in the simulation experiment of the present invention;

[0028] Figure 3 is a visualization diagram of the target recognition method based on the optimal transport distance function in the simulation experiment of the present invention; DETAILED DESCRIPTION OF THE INVENTION

[0029] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described below in conjunction with the drawings and embodiments.

[0030] Refer to Figure 1 and the embodiments to further describe the specific steps for implementing the present invention.

[0031] Step 1: Extract the feature information of the SAR image and the optical image.

[0032] Step 1.1, The deep neural network model with a convolutional structure not only has high fault tolerance but also has efficient computing power, and is widely used in important fields such as target recognition. Network models such as Alexnet, Vggnet, Googlenet, and Resnet are all the most direct methods for extracting image characterization features and can quickly extract the most effective feature information in the image. Therefore, in the embodiments of the present invention, the Resnet-101 network model is used as the feature extraction network for SAR images to extract the feature information in each SAR image.

[0033] Use the following formula to extract the feature information of each SAR image:

[0034] φ(x i ) = Resnet-101(x i )

[0035] Where, φ(x i ) represents the feature information extracted from the i-th SAR image x i , i represents the serial number of the SAR image, i = 1, 2, 3...I, I represents the total number of SAR images, and in the embodiments of the present invention, I takes the value of 2673, and Resnet-101(·) represents the operation of the network model to extract feature information.

[0036] Step 1.2, Use the Resnet-101 network model as the feature extraction network for optical images in the embodiments of the present invention to extract the feature information in each optical image and replace the semantic attributes defined in conventional zero-shot learning.

[0037] Use the following formula to extract the feature information of each optical image:

[0038]

[0039] Where, represents the optical image feature information extracted from the j-th optical image , j represents the serial number of the optical image, j = 1, 2, 3...J, J represents the total number of optical images, and in the embodiments of the present invention, J takes the value of 10, and Resnet-101(·) represents the operation of the network model to extract feature information.

[0040] Step 2, Calculate the class centers of SAR images in the source domain and the target domain.

[0041] Step 2.1, Since the SAR images with known target class labels in the source domain have corresponding class label information. Therefore, according to the class label information of the SAR images with known target classes in the source domain, calculate the class centers of the SAR images of the same class in the source domain.

[0042] Calculate the class center of SAR images of the same class with known target classes in the source domain using the following formula:

[0043]

[0044] where represents the class center of the p-th SAR image of the same class with known target classes in the source domain. p represents the serial number of the class center of SAR images in the source domain, p = 1, 2, 3...P, and P represents the total number of class centers of SAR images in the source domain. In the embodiments of the present invention, P takes the value of 7. M represents the total number of SAR images of the same class in the source domain. In the embodiments of the present invention, M takes the value of 233. ∑ represents the summation operation, and m represents the serial number of SAR images of the same class in the source domain, m = 1, 2, 3...M, represents the SAR images of the same class in the source domain extracted feature information.

[0045] Step 2.2. Since the SAR images of unknown classes in the target domain lack corresponding class label information, the class centers of the SAR images of unknown classes in the target domain cannot be calculated through class label information. Therefore, in the embodiments of the present invention, the K-Means unsupervised clustering algorithm is used to approximately calculate the class centers of the SAR images of unknown classes in the target domain.

[0046] Calculate the class centers of the SAR images of unknown classes in the target domain using the following formula:

[0047]

[0048] where represents the class center of the q-th SAR image of the same class with unknown classes in the target domain. q represents the serial number of the class center of SAR images in the target domain, q = 1, 2, 3...Q, and Q represents the total number of class centers of SAR images in the target domain. In the embodiments of the present invention, Q takes the value of 3. K-means(·) represents the clustering algorithm operation, represents all the SAR images in the target domain extracted feature information. n represents the serial number of SAR images in the target domain, n = 1, 2, 3...N, and N represents the total number of SAR images in the target domain. In the embodiments of the present invention, Q takes the value of 822.

[0049] Step 3. Calculate the class centers of the optical images.

[0050] Since the feature information of the optical images extracted in Step 1.2 cannot be directly used as the class centers of the optical images. Therefore, the feature information of the optical images is input into a two-layer trained embedding network to output the class centers of the optical images.

[0051] According to the following formula, calculate the class center of the k-th same class based on the class label information of the j-th optical image:

[0052]

[0053] where represents the k-th class center of the same class of the j-th optical image, k represents the serial number of the class center, k = 1, 2, 3...K, K represents the total number of class centers, in the embodiment of the present invention, K takes the value of 10, j represents the serial number of the optical image, j = 1, 2, 3...J, J represents the total number of optical images, in the embodiment of the present invention, J takes the value of 10, σ(·) represents a non-linear operation, and w1 and w2 respectively represent the weights of two fully connected layers to be learned. represents the optical image feature information extracted from the j-th optical image represents the j-th optical image

[0054] Step 4, construct an objective loss function using the mean square error function and the optimal transport distance function.

[0055] Step 4.1, since both the SAR images and the optical images in the source domain have corresponding class label information. Therefore, directly adopt the mean square error function formula to calculate the distance between the class center of the SAR images in the source domain obtained in Step 2.1 and the class center of the optical images obtained in Step 3.

[0056] According to the following formula, calculate the distance between the class center of the SAR images in the source domain and the class center of the optical images:

[0057]

[0058] where L M represents the distance between the class center of the SAR images in the source domain and the class center of the optical images, S represents the total number of class centers of the SAR images in the source domain, in the embodiment of the present invention, S takes the value of 7, s represents the serial number of the class center of the SAR images in the source domain, s = 1, 2, 3...S, represents the class center of the s-th SAR image in the source domain, represents the class center of the s * -th optical image, s * represents the serial number of the class center of the optical images, s * = 1, 2, 3...S * , S * represents the total number of class centers of the optical images, in the embodiment of the present invention, S *The value is 7, λ represents the regularization coefficient. According to the simulation experiment results, in the embodiments of the present invention, the value of λ is 0.0005. Ψ(·) represents the parameter regularization operation of the L2 norm, which is used to reduce the complexity of the model.

[0059] Step 4.2: Since the SAR images in the target domain lack corresponding class label information, the optimal transport distance function formula is used to calculate the distance between the class centers of the SAR images in the target domain obtained in Step 2.2 and the class centers of the optical images obtained in Step 3.

[0060] Use the following formula to calculate the distance between the class centers of the SAR images in the target domain and the class centers of the optical images:

[0061]

[0062] Among them, L W represents the distance between the class centers of the SAR images in the target domain and the class centers of the optical images. T represents the total number of class centers of the SAR images in the target domain. In the embodiments of the present invention, the value of T is 3. t represents the serial number of the class centers of the SAR images in the target domain, t = 1, 2, 3...T. represents the class center of the t-th SAR image in the target domain. represents the t * -th class center of the optical images. t * represents the serial number of the class centers of the optical images. t * = 1, 2, 3...T * , T * represents the total number of class centers of the optical images. In the embodiments of the present invention, T * takes the value of 3. Z represents the matching relationship matrix between the class centers of the SAR images and the optical images in the target domain. ε represents the regularization coefficient. According to the simulation experiment results, in the embodiments of the present invention, the value of ε is 0.0005. log represents the logarithm operation with base 10.

[0063] Step 4.3: Add the two distance function formulas in Step 4.1 and Step 4.2 to obtain the distance between all the class centers of the SAR images and all the class centers of the optical images.

[0064] Use the following formula to calculate the distance between all the class centers of the SAR images and all the class centers of the optical images:

[0065] L = L M + β·L 单

[0066] Among them, L represents the distance between the centers of all SAR image categories and the centers of all optical image categories, β represents the weight coefficient, and according to the simulation experiment results, β is taken as 0.0001 in the embodiments of the present invention.

[0067] Step 4.4: Use the gradient descent method to minimize the distance between the centers of all SAR image categories and the centers of all optical image categories in Step 4.3, and obtain the category centers of SAR images of unknown categories in the target domain.

[0068] Step 5: Use the optimal transport distance function for image recognition:

[0069] Use the optimal transport distance function to find the category center closest to the SAR image of the unknown category in the target domain in the visual space, and obtain the category information of the zero-shot synthetic aperture radar (SAR) image of the unknown category in the target domain according to the label of the found category center.

[0070] Use the following formula to calculate the category information of the SAR image of the unknown category in the target domain:

[0071]

[0072] Among them, V * represents the category information of the SAR image of the unknown category in the target domain, U represents the total number of SAR images of the unknown category in the target domain, and U is taken as 822 in the embodiments of the present invention. u represents the serial number of the SAR image of the unknown category in the target domain, u = 1, 2, 3... U, φ(x u ) represents the feature information extracted from the u-th SAR image x u of the unknown category in the target domain, and V represents the matching relationship matrix between the SAR image of the unknown category in the target domain and the SAR image category center.

[0073] The effects of the present invention will be further described below in combination with simulation experiments.

[0074] 1. Simulation experiment conditions:

[0075] The hardware platform for the simulation experiment of the present invention is: the processor is an Intel(R) Core(TM) i7-10700K CPU with a main frequency of 2.9 GHz, the memory is 64 GB, and the graphics card is an NVIDIA GeForce RTX 3090.

[0076] The software platform for the simulation experiment of the present invention is: Ubuntu 20.04 operating system, Anaconda3 (64-bit) compilation environment, Pycharm 2021 software, Python 3.7 version, and Pytorch deep learning framework.

[0077] 2. Simulation Content and Result Analysis:

[0078] The data used in the simulation experiment of the present invention is selected from the publicly available "Moving and Stationary Target Acquisition and Recognition MSTAR" dataset. This dataset includes ten types of military ground targets at radar pitch angles of 15° and 17°. These ten types of targets are: armored transport vehicle BTR70, infantry fighting vehicle BMP2, tank T72, self-propelled howitzer 2S1, armored reconnaissance vehicle BRDM2, BTR60 armored transport vehicle, bulldozer D7, tank T62, freight truck ZIL131, and self-propelled anti-aircraft gun ZSU234. Seven types of SAR image targets (BTR60, BTR70, T62, T72, BMP2, D7, and ZIL131) at a radar pitch angle of 17° and their corresponding class labels are selected as the training samples in the source domain, and three types of SAR image targets (2S1, BRDM2, and ZSU234) at a radar pitch angle of 15° and their corresponding class labels are selected as the test samples in the target domain. The size of all sample images is 128×128 pixels.

[0079] The simulation experiment of the present invention uses the synthetic aperture radar (SAR) target recognition methods of the present invention and three existing technologies to classify the SAR images of the above-mentioned ten types of military ground targets respectively, and obtain the classification results.

[0080] In the simulation experiment of the present invention, the synthetic aperture radar (SAR) target recognition methods of the three existing technologies are respectively: the target recognition method based on the mean square error function, the target recognition method based on the chamfer distance function, and the target recognition method based on the bipartite graph matching function. Among them, the target recognition method based on the mean square error function means directly using the mean square error function to optimize the model parameters for classification; the target recognition method based on the chamfer distance function means combining the mean square error function and the chamfer distance function to optimize the model parameters for classification; the target recognition method based on the bipartite graph matching function means combining the mean square error function and the bipartite graph matching function to optimize the model parameters for classification.

[0081] In order to evaluate the recognition effects of the method of the present invention and the two existing technology methods, according to the following formula, the recognition rate of the test samples of each method in the simulation experiment is calculated respectively:

[0082]

[0083] Among them, Accuracy represents the recognition rate of the test samples, M represents the number of samples correctly classified for the MSTAR test samples, N represents the total number of MSTAR test samples, and the larger the value of the recognition rate Accuracy, the better the recognition performance.

[0084] After calculating the recognition rates of the recognition results of the three methods used in the simulation experiment of the present invention respectively, the calculation results are listed in Table 1.

[0085] MSE in Table 1 represents the target recognition method based on the mean square error function using the prior art. CD in Table 1 represents the target recognition method based on the chamfer distance function using the prior art. BM in Table 1 represents the target recognition method based on the bipartite graph matching function using the prior art.

[0086] Table 1 Comparison table of recognition rates of MSTAR test samples corresponding to different recognition methods

[0087] Experimental method The method of the present invention MSE CD BM Recognition rate 93％ 56％ 89％ 91％

[0088] As can be seen from Table 1, for the data of "Acquisition and Recognition of Moving and Stationary Targets MSTAR" used in the experiment of the present invention, the recognition rate of the zero-shot SAR target recognition method based on the optimal transport distance function proposed by the present invention can reach 93%. Compared with the prior art methods, the method of the present invention has the highest recognition rate. The method of the present invention makes full use of the features of optical images, optimizes the model parameters through the optimal transport distance function, and aligns the class centers of unknown new classes, so that the class centers obtained by the present invention are better, the classification ability of images is stronger, and the performance of zero-shot SAR target recognition is improved.

[0089] Figure 2 is the experimental result of the target recognition method based on the mean square error function using the prior art. Figure 2 The abscissa and ordinate in represent the two dimensions of the data, where the dot (·), star point (*), and plus point (+) represent the 3 types of SAR image targets of 2S1, BRDM2, and ZSU234 respectively, and the 3 multiplication sign points (×) represent the 3 synthesized class centers. It can be seen from Figure 2 that the class centers synthesized by directly optimizing the model parameters using the mean square error function will deviate from the true class centers, resulting in poor classification results. Figure 3 is the experimental result of the method of the present invention. Figure 3 The abscissa and ordinate in represent the two dimensions of the data, where the dot (·), star point (*), and plus point (+) represent the 3 types of SAR image targets of 2S1, BRDM2, and ZSU234 respectively, and the 3 multiplication sign points (×) represent the 3 synthesized class centers. It can be seen from Figure 3 that the method of the present invention combines the mean square error function and the optimal transport distance function, and the synthesized class centers are better, and good classification results can be further obtained.

[0090] In summary, the recognition rate of the zero-shot SAR target recognition method based on the optimal transport distance function proposed by the present invention reaches 93%. Compared with the existing technical methods, it has a higher recognition rate. It can be seen that the method of the present invention is an effective zero-shot SAR target recognition method with better performance.

Claims

1. A zero-sample synthetic aperture radar (SAR) target recognition method based on the optimal transport distance function, characterized in that Use the feature information of the extracted optical image as the semantic attributes defined in zero-shot learning, and align the class centers of unknown classes in the target domain using the optimal transport distance function. The steps of this target recognition method are as follows: Step 1, extract the feature information of SAR images and optical images: Step 1.1, use a deep neural network model as the feature extraction network for SAR images, and extract the feature information in each SAR image; Step 1.2, use the same deep neural network model as in Step 1.1 as the feature extraction network for optical images, and extract the feature information in each optical image; Step 2, calculate the class centers of SAR images in the source domain and the target domain: Step 2.1, according to the class label information of the known target-class SAR images in the source domain, calculate the class centers of the SAR images of the same class in the source domain; Step 2.2, use the K-Means unsupervised clustering algorithm to approximately calculate the class centers of the unknown-class SAR images in the target domain; Step 3, calculate the class centers of optical images: Input the feature information of the optical image into a two-layer trained embedding network, and output the class centers of the optical images; Step 4, construct the target loss function using the mean square error function and the optimal transport distance function: Step 4.1, use the mean square error function formula to calculate the distance between the class centers of SAR images in the source domain and the class centers of optical images; Step 4.2, use the optimal transport distance function formula to calculate the distance between the class centers of SAR images in the target domain and the class centers of optical images; Step 4.3, add the two distance function formulas in Step 4.1 and Step 4.2 to obtain the distance between all SAR image class centers and all optical image class centers; Step 4.4, use the gradient descent method to minimize the distance between all SAR image class centers and all optical image class centers to obtain the class centers of the unknown-class SAR images in the target domain; Step 5, perform image recognition using the optimal transport distance function: Use the optimal transport distance function to find the class center closest to the unknown-class SAR images in the target domain in the visual space, and obtain the class information of the zero-shot synthetic aperture radar (SAR) images of the unknown classes in the target domain according to the found class center labels.

2. The zero-sample synthetic aperture radar (SAR) target recognition method based on the optimal transmission distance function according to claim 1, wherein: The deep neural network model mentioned in Step 1.1 refers to any one of the Alexnet, Vggnet, Googlenet, and Resnet network models.

3. The zero-sample synthetic aperture radar (SAR) target recognition method based on the optimal transmission distance function according to claim 1, characterized in that: The structure of the two-layer trained embedding network mentioned in Step 3 is: concatenate two convolutional neural networks with the same network structure but different network parameters to form a two-layer embedding network, and output the class centers of the optical images.

4. The zero-sample synthetic aperture radar (SAR) target recognition method based on the optimal transmission distance function according to claim 1, wherein: The mean square error function formula mentioned in Step 4.1 is as follows: Among them, L M represents the distance between the class center of the SAR image in the source domain and the class center of the optical image. S represents the total number of class centers of the SAR images in the source domain. ∑ represents the summation operation. s represents the serial number of the class center of the SAR image in the source domain, s = 1, 2, 3... S, represents the class center of the sth SAR image in the source domain, represents the class center of the sth * optical image, and s * represents the serial number of the class center of the optical image, and s * = 1, 2, 3... S * and S * represents the total number of class centers of the optical images. λ represents the regularization coefficient. Ψ(·) represents the parameter regularization operation of the L2 norm, which is used to reduce the complexity of the model. w1 and w2 respectively represent the weights of the two fully connected layers to be learned.

5. The zero-sample synthetic aperture radar (SAR) target recognition method based on the optimal transmission distance function according to claim 1, characterized in that: The optimal transport distance function formula mentioned in Step 4.2 is as follows: Among them, L W represents the distance between the class center of the SAR image and the class center of the optical image in the target domain. T represents the total number of class centers of the SAR images in the target domain, t represents the serial number of the class center of the SAR image in the target domain, and t = 1, 2, 3... T. represents the class center of the t-th SAR image in the target domain. represents the class center of the * t-th * optical image, and t * = 1, 2, 3... T * , and T * represents the total number of class centers of the optical images. Z represents the matching relationship matrix between the class centers of the SAR images and the optical images in the target domain, ε represents the regularization coefficient, and log represents the logarithm operation with base 10.

6. The zero-sample synthetic aperture radar (SAR) target recognition method based on the optimal transmission distance function according to claim 1, characterized in that: The formula for calculating the class information of the unknown-class SAR images in the target domain mentioned in Step 5 is as follows: Among them, V * represents the class information of the SAR images of unknown classes in the target domain, U represents the total number of SAR images of unknown classes in the target domain, u represents the serial number of the SAR images of unknown classes in the target domain, u = 1, 2, 3... U, φ(x u ) represents the feature information extracted from the u-th SAR image x u of unknown classes in the target domain, represents the class center of the t-th class of SAR images of unknown classes in the target domain, t represents the serial number of the class centers of the SAR images of unknown classes in the target domain, t = 1, 2, 3... T, T represents the total number of class centers of the SAR images of unknown classes in the target domain, and V represents the matching relationship matrix between the SAR images of unknown classes in the target domain and the SAR image class centers.

Images