Small-Sample SAR Image Target Recognition Method Based on Deep Brownian Distance

Abstract

The present invention discloses a small-sample SAR image target recognition method based on the deep Brown distance, which relates to the technical field of radar signal processing and includes: obtaining a synthetic aperture radar image and dividing it into a training sample set and a test sample set; constructing a deep Brown distance covariance module - prototype network; wherein, the deep Brown distance covariance module - prototype network includes a deep residual neural network, a deep Brown distance covariance module, and an Euclidean distance classifier; using the training sample set to perform small-sample training on the deep Brown distance covariance module - prototype network to obtain a trained deep Brown distance covariance module - prototype network; inputting the test set samples into the trained deep Brown distance covariance module - prototype network to obtain the predicted labels of the test query set. This application can improve the recognition accuracy of SAR image targets.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and particularly relates to a small-sample SAR image target recognition method based on deep Brownian distance. Background Art

[0002] Synthetic Aperture Radar (SAR) is an active microwave radar that can be installed on a flying platform to achieve all-weather and all-day real-time observation of the ground, and has a certain ability to penetrate the ground surface and vegetation. Synthetic Aperture Radar has high resolution in both the range direction and the azimuth direction, and can obtain high-resolution radar images of targets under extremely low visibility meteorological conditions. Therefore, it is widely used in fields such as electronic reconnaissance and anti-reconnaissance, disaster detection, and ocean detection, and is an indispensable technical means in the current observation field.

[0003] Automatic Target Recognition (ATR) is a technology for determining the category of a target image by extracting image feature information, and it is widely used in many sub-fields such as image processing, target recognition, unmanned driving, and anomaly detection. Since the images obtained in the real environment are affected by noise and clutter, and the texture information of the target images is not obvious, it increases the difficulty of feature extraction and target recognition for SAR images.

[0004] Therefore, it is urgent to improve the ability of feature extraction and target recognition for SAR images. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a small-sample SAR image target recognition method based on deep Brownian distance. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] In a first aspect, the present application provides a small-sample SAR image target recognition method based on deep Brownian distance, including:

[0007] Obtain a synthetic aperture radar image and divide it into a training sample set and a test sample set; wherein, the training sample set includes a training support set and a training query set, and the test sample set includes a test support set and a test query set;

[0008] Construct a deep Brownian distance covariance module - prototype network; wherein, the deep Brownian distance covariance module - prototype network includes a deep residual neural network, a deep Brownian distance covariance module, and an Euclidean distance classifier;

[0009] Use the training sample set to perform small-sample training on the deep Brownian distance covariance module - prototype network to obtain a trained deep Brownian distance covariance module - prototype network;

[0010] Input the test set samples into the trained deep Brown distance covariance module - prototype network to obtain the predicted labels of the test query set.

[0011] Advantages of the present invention:

[0012] A small - sample SAR image target recognition method based on deep Brown distance provided by the present invention adopts a deep Brown distance covariance module, which can enhance the image features extracted by a deep residual neural network; adopting a deep Brown distance covariance module - prototype network can obtain embedding vectors with richer image features, and can make full use of a single SAR image sample, so as to achieve accurate recognition of SAR image targets under the condition of extremely few labeled samples.

[0013] The following will further elaborate on the present invention in conjunction with the drawings and embodiments. Description of the Drawings

[0014] Figure 1 is a flowchart of a small - sample SAR image target recognition method based on deep Brown distance provided by an embodiment of the present invention;

[0015] Figure 2 is a schematic structural diagram of a deep residual - deep Brown distance covariance module - Euclidean classifier provided by an embodiment of the present invention;

[0016] Figure 3 is an implementation framework diagram of the training and testing of a deep Brown distance covariance module - prototype network provided by an embodiment of the present invention;

[0017] Figure 4 is a schematic structural diagram of a deep Brown distance covariance module - prototype network provided by an embodiment of the present invention;

[0018] Figure 5 is a schematic structural diagram of a residual block provided by an embodiment of the present invention. Detailed Embodiments

[0019] The following further describes the present invention in detail with specific embodiments, but the implementation manners of the present invention are not limited thereto.

[0020] The main methods of SAR image target recognition are: template matching, target modeling, and deep learning. Among them, the template - based method requires designing a dedicated template and comparing the similarity between a certain region in the image and the template according to a certain similarity principle, but this method does not have rotational invariance and has limitations in the recognition of target images; the target modeling method depends on the quality of model establishment, and it is very difficult to realize real - time recognition of target images using this method in a complex electromagnetic environment.

[0021] Most of the existing few-shot object recognition techniques are based on meta-learning. The basic idea is as follows: The training set is divided into a support set and a query set. During multiple iterative training processes, based on a certain similarity metric, the representations of all training samples are learned. The cross-entropy loss function between the prediction of the query samples and the true labels is calculated, and the network parameters are updated using an optimization model algorithm. Finally, the trained model is used to complete the label prediction of the test samples. Specifically, J. Snell et al. proposed the concept of prototypical networks in the literature "J. Snell, K. Swersky, and R. S. Zemel, "Prototypical networks for few-shot learning," in Proc. Int. Conf. Neural Inf. Process. Syst., 2017, pp. 4080-4090." By using the support set samples to calculate prototypes, and then calculating the error based on the prototypes and the embedding vectors of the query set samples to update the network parameters, and adopting the way of diversity training can well avoid the overfitting phenomenon.

[0022] However, when there are few support set samples in the existing technology, such as only one support set sample, the model cannot accurately extract the features of the image samples, resulting in poor final test performance of the model. The recognition performance of the prototypical network still needs to be improved in the case of extremely few labeled samples.

[0023] In view of this, a few-shot SAR image object recognition method based on deep Brownian distance provided by this application uses a deep residual neural network to extract features from SAR images, and learns image representations by measuring the difference between the joint feature function and the marginal product of image features, so that the model can obtain richer image features and maintain a high recognition accuracy for test samples even when there are few support set samples.

[0024] Please refer to Figure 1 and Figure 2 shown in Figure 1 is a flowchart of a few-shot SAR image object recognition method based on deep Brownian distance provided by an embodiment of the present invention. Figure 2 is a schematic structural diagram of a deep residual - deep Brownian distance covariance module - Euclidean classifier provided by an embodiment of the present invention. A few-shot SAR image object recognition method based on deep Brownian distance provided by this application includes:

[0025] S101. Obtain synthetic aperture radar images and divide them into a training sample set and a test sample set; wherein, the training sample set includes a training support set and a training query set, and the test sample set includes a test support set and a test query set;

[0026] S102. Construct a deep Brown distance covariance module - prototype network, where the deep Brown distance covariance module - prototype network includes a deep residual neural network, a deep Brown distance covariance module, and an Euclidean distance classifier;

[0027] S103. Use the training sample set to perform few - shot training on the deep Brown distance covariance module - prototype network to obtain a trained deep Brown distance covariance module - prototype network;

[0028] S104. Input the test set samples into the trained deep Brown distance covariance module - prototype network to obtain the predicted labels of the test query set.

[0029] Specifically, a few - shot SAR image target recognition method based on deep Brown distance provided in this embodiment adopts a deep Brown distance covariance module, which can enhance the image features extracted by the deep residual neural network; adopting a deep Brown distance covariance module - prototype network can obtain embedding vectors with richer image features, and can make full use of a single SAR image sample, so as to accurately recognize SAR image targets under the condition of extremely few labeled samples.

[0030] Please refer to Figure 3 and Figure 4 as shown, Figure 3 is an implementation framework diagram for the training and testing of the deep Brown distance covariance module - prototype network provided by an embodiment of the present invention, Figure 4 is a structural schematic diagram of the deep Brown distance covariance module - prototype network provided by an embodiment of the present invention. In an optional embodiment of the present application, the process of using the training sample set to perform few - shot training on the deep Brown distance covariance module - prototype network to obtain a trained deep Brown distance covariance module - prototype network includes:

[0031] Adopt a deep residual neural network to map the samples in the training support set S train into a high - dimensional space to obtain the features of the SAR image. Among them, the mapping function is:

[0032]

[0033] where x j ∈R C×H×W is a sample, x j is the j - th image sample, j is the subscript corresponding to the image, C is the number of image channels, H is the image height, W is the image width, is the trainable parameter of the deep residual neural network, is the mapping function, X ∈ R 128×8×8 is the image feature map extracted by the deep residual neural network; it can be understood that the initial input is R1×60×60 , after passing through the deep residual neural network, it becomes R 128×8×8 , including 128 channels, and each channel is an 8×8 matrix;

[0034] Regarding each row x of the image feature map X extracted by the deep residual neural network i as the observed value, the squared Euclidean distance between each row is obtained, and its calculation formula is:

[0035]

[0036] where is the Hadamard product, "1" is the matrix of weight 1, I is the identity matrix, X is the image feature extracted by the deep residual neural network, and X T is the transpose of the image feature extracted by the deep residual neural network. It is set that then the Euclidean distance between each row is:

[0037]

[0038] where is the squared Euclidean distance between each row;

[0039] Based on the Euclidean distance between each row, the deep Brown distance covariance matrix of the samples in the training support set is obtained, and its calculation formula is:

[0040]

[0041] where is the Euclidean distance between the observed values of each row of the sample feature map X in the training support set, D is the number of channels of the sample feature map in the training support set, and D×D is the size of the obtained deep Brown distance covariance matrix;

[0042] Set the negative elements in the deep Brown distance covariance matrix to zero, and take out the upper triangular elements and flatten them as the embedding vector of the samples in the training support set. Its expression is:

[0043]

[0044] where A θ (·) is the mapping function of the deep residual neural network and the deep Brown distance covariance module, and A θ (x j ) is the embedding vector of the samples in the training support set, and θ is the trainable parameter of the deep residual network and the deep Brown distance covariance module;

[0045] Based on the embedding vectors of C×k samples in the training support set S train , C class prototypes are obtained, and its calculation formula is:

[0046]

[0047] Among them, P i is the i-th class prototype, is the i-th class training support set, k is the number of samples in each class of the training support set, and x j is the j-th input image, and y j is the true label of the j-th image. A θ (x j ) is the embedding vector of the input image passing through the deep residual neural network and the deep Brown distance covariance module;

[0048] Using the same method, input the samples in the training query set Q train into the deep residual neural network and the deep Brown distance covariance module to obtain the embedding vectors of the training query samples Calculate the Euclidean distance between the embedding vectors of the training query samples and the C class prototypes, obtain the class prototype with the shortest distance, and use the corresponding class as the predicted label pred of the training query set j ; among them, the calculation formula of the Euclidean distance is:

[0049] Among them, is the Euclidean distance between the query sample embedding vector and the class prototype, and ||·||2 is the vector two-norm;

[0050] Obtain the true labels of the training query samples, and based on the predicted labels and true labels of the training query samples, obtain the current cross-entropy loss function. Use the stochastic gradient descent algorithm to iteratively optimize the deep Brown distance covariance module-prototype network to obtain the trained deep Brown distance covariance module-prototype network.

[0051] In an optional embodiment of the present application, before using the training sample set to perform few-shot training on the deep Brown distance covariance module-prototype network to obtain the trained deep Brown distance covariance module-prototype network, it further includes:

[0052] Initialize the deep Brown distance covariance module-prototype network, set the number of training iterations to T, T≥1000, and initialize the iteration number t = 0.

[0053] In an optional embodiment of the present application, it further includes:

[0054] The training query samples pass through the Deep Brown Distance Covariance Module - Prototype Network to obtain the predicted labels of the training query samples. Calculate the cross - entropy loss function between the true labels and the predicted labels of the training query samples, and use it as the training error. Utilize the Stochastic Gradient Descent algorithm to backpropagate the error and update the trainable parameters θ in the Deep Residual Neural Network and the Deep Brown Distance Covariance Module, obtaining a Deep Brown Distance Covariance Module - Prototype Network that can accurately identify the training query samples. The training error is:

[0055]

[0056]

[0057] where, is the sample in the training query set, y j is the true label of the training query set sample, is the classification prediction probability of identifying the training query sample as the y j th class, |Q train | is the total number of samples in the training query set, is the Euclidean distance between the embedding vector of the sample in the j - th training query set and the k - th class prototype. C is the number of classes set in the iterative training.

[0058] In an optional embodiment of the present application, the process of inputting the test set samples into the trained Deep Brown Distance Covariance Module - Prototype Network to obtain the predicted labels of the test query set includes:

[0059] Input the samples x test in the test support set S j into the trained Deep Brown Distance Covariance Module - Prototype Network to obtain the embedding vectors A θ (x j ) of the samples in the test support set, and obtain the mean of the embedding vectors of the same - class samples in the test support set in each dimension as the class prototype in the test process. The calculation formula is:

[0060]

[0061] where, P i is the i - th class prototype, is the i - th class test support set, and k is the number of samples in each class of the test support set;

[0062] Input the samples test in the test query set Q into the trained Deep Brown Distance Covariance Module - Prototype Network to obtain the embedding vectors Calculate the minimum distance between the embedding vector of a sample in the test query set and the class prototype to obtain the predicted label of the test query sample. The calculation formula is as follows:

[0063]

[0064] where d(·) is the Euclidean distance, is the Euclidean distance between the query sample embedding vector and the class prototype;

[0065] Compare the predicted labels and the true labels of all test query samples of the trained Deep Brown Distance Covariance Module - Prototype Network to obtain the recognition accuracy. The calculation formula is as follows:

[0066]

[0067] where I(·) is the exponential function, if it holds, the recognition accuracy is 1, otherwise it is 0; is the predicted label of the model for the query sample, y j is the true label of the query sample, |Q test | is the number of samples in the test query set, and Acc is the test accuracy of the model.

[0068] Please refer to Figure 5 as shown in Figure 5 which is a schematic structural diagram of the residual block provided by an embodiment of the present invention. In an optional embodiment of the present application, the Deep Brown Distance Covariance Module - Prototype Network includes a first convolutional layer, a first residual block, a second residual block, a third residual block, a fourth residual block, a fifth residual block, a sixth residual block, a seventh residual block, an eighth residual block, a Deep Brown Distance Covariance Module, and an Euclidean classifier;

[0069] where each residual block includes a second convolutional layer, a first batch normalization layer, a first ReLU activation layer, a third convolutional layer, and a second batch normalization layer.

[0070] In an optional embodiment of the present application, when the number of input and output channels of each residual block is not equal, the input of the residual block is subjected to convolutional operation and batch normalization operation, and then added to the output of the residual block as the final output of the residual block.

[0071] In an optional embodiment of the present application, it further includes: performing target segmentation on the synthetic aperture radar image.

[0072] In an optional embodiment of the present application, the recognition of the detection target is achieved through the following steps: specifically:

[0073] S101. Obtain the training sample set and the test sample set of the SAR image.

[0074] The training samples are taken from the training samples of 7 classes of MSTAR datasets with a pitch angle of 17°, and the test samples are taken from the test samples of another 3 classes of MSTAR datasets with pitch angles of 15° and 17° respectively; the original SAR image size is 128×128. In order to remove the picture noise and the environmental features around the target, morphological SAR target segmentation is performed on the original SAR image, and the image center is cropped into a 60×60 size picture, only retaining the target features.

[0075] S102. Construct a deep Brown distance covariance module - prototype network.

[0076] Construct a deep Brown distance covariance module - prototype network including a deep residual neural network, a deep Brown distance covariance module, and an Euclidean distance classifier; the specific structure includes the first convolutional layer → the first residual block → the second residual block → the third residual block → the fourth residual block → the fifth residual block → the sixth residual block → the seventh residual block → the eighth residual block → the deep Brown distance covariance module → the Euclidean classifier; the specific structure of each residual block includes the second convolutional layer → the first batch normalization layer → the first ReLU activation layer → the third convolutional layer → the second batch normalization layer.

[0077] Among them, in the convolutional operations within the first convolutional layer, the first residual block, the second residual block, the fourth residual block, the sixth residual block, and the eighth residual block, the convolutional kernel size is 3×3, the sliding step is 1, and the Padding filling parameter is also 1; in the first convolutional operation within the third residual block, the fifth residual block, and the seventh residual block, the convolutional kernel size is 3×3, the sliding step is 1, and the Padding parameter is 1, and in the second convolutional operation, the convolutional kernel size is 3×3, the sliding step is 2, and the Padding parameter is 1; in the convolutional operation within the additional layer, the convolutional kernel size is 1×1, and the sliding step is 2.

[0078] It should be noted that when the number of channels of the input and output of the residual block is not equal, the input needs to go through an additional convolutional operation and a batch normalization operation, and then be added to the output as the final output of the residual block.

[0079] S103. Use the training support set and the training query set to perform few - shot training on the deep Brown distance covariance module - prototype network to obtain a model that can accurately identify the training query samples.

[0080] S1031. Set the training iteration number as T≥1000, and initialize the iteration number t = 0.

[0081] S1032. Take the training support set S train and the training query set Q trainThe samples in T are fed into the initialized deep Brown distance covariance module - prototype network to obtain the predicted labels of the training query samples.

[0082] S10321. The deep residual neural network maps the training samples into a high-dimensional space. For a sample x j ∈R C ×H×W , this operation is equivalent to mapping and encoding the sample to obtain the features of the SAR image sample. The expression of the mapping function is:

[0083]

[0084] where x j ∈R C×H×W is the sample, x j is the j-th image sample, C is the number of image channels, H is the image height, W is the image width, are the trainable parameters of the deep residual neural network, is the mapping function, X ∈ R 128×8×8 is the image feature map extracted by the deep residual neural network;

[0085] S10322. Take each row x i of the image feature map X extracted by the deep residual neural network as the observed value, and obtain the squared Euclidean distance between each row. The calculation formula is:

[0086]

[0087] where, is the Hadamard product, "1" is the matrix of weight 1, I is the identity matrix, X is the image feature extracted by the deep residual neural network, X T is the transpose of the image feature extracted by the deep residual neural network. Let then the Euclidean distance between each row is:

[0088]

[0089] where, is the squared Euclidean distance between each row;

[0090] Based on the Euclidean distance between each row, obtain the deep Brown distance covariance matrix of the samples in the training support set. The calculation formula is:

[0091]

[0092] where, It is the Euclidean distance between the row observations of the sample feature map X in the training support set. D is the number of channels of the sample feature map in the training support set, and D×D is the size of the obtained deep Brown distance covariance matrix;

[0093] Set the negative elements in the deep Brown distance covariance matrix to zero, and take out the upper triangular elements and flatten them as the embedding vectors of the samples in the training support set. Its expression is:

[0094]

[0095] where A θ (·) is the mapping function of the deep residual neural network and the deep Brown distance covariance. A θ (x j ) is the embedding vector of the sample in the training support set, and θ is the trainable parameter of the deep residual network and the deep Brown distance covariance module;

[0096] S10323. Based on the embedding vectors of C×k samples in the training support set S train , obtain C class prototypes. Its calculation formula is:

[0097]

[0098] where P i is the i-th class prototype, is the i-th class training support set, k is the number of samples in each class of the training support set, x j is the j-th input image, y j is the true label of the j-th image, and A θ (x j ) is the embedding vector of the input image passing through the deep residual neural network and the deep Brown distance covariance module;

[0099] Using the same method, input the samples in the training query set Q train into the deep residual neural network and the deep Brown distance covariance module to obtain the embedding vectors of the training query samples Calculate the Euclidean distance between the embedding vectors of the training query samples and the C class prototypes, obtain the class prototype with the shortest distance, and use the corresponding class as the predicted label pred j of the training query set; where the calculation formula of the Euclidean distance is:

[0100] where is the Euclidean distance between the query sample embedding vector and the class prototype, and ||·||2 is the vector two-norm;

[0101] S10324. Obtain the true labels of the training query samples, and based on the predicted labels and true labels of the training query samples, obtain the current cross-entropy loss function. Use the stochastic gradient descent algorithm to iteratively optimize the deep Brown distance covariance module - prototype network to obtain a trained deep Brown distance covariance module - prototype network.

[0102] The error generated by the trained deep Brown distance covariance module - prototype network for the predicted labels of the training query samples is:

[0103]

[0104]

[0105] Among them, among them, is the sample in the training query set, y j is the true label of the training query set sample, is the predicted probability of predicting the training query sample as the y j th class, |Q train | is the total number of samples in the training query set, is the Euclidean distance between the embedding vector of the sample in the jth training query set and the kth class prototype.

[0106] S104. Feed the center-cropped test set samples into the trained deep Brown distance covariance module - prototype network to obtain the predicted labels of the test query set.

[0107] S1041. Input the samples x test in the test support set S j into the trained deep Brown distance covariance module - prototype network to obtain the embedding vectors A θ (x j ) of the samples in the test support set, and obtain the mean value of the embedding vectors of the same-class samples in the test support set in each dimension as the class prototype during the test. Among them, the calculation formula is:

[0108]

[0109] Among them, P i is the ith class prototype, is the ith class test support set, and k is the number of samples in each class in the test support set;

[0110] S1042. Input the samples test in the test query set Q into the trained deep Brown distance covariance module - prototype network to obtain the embedding vectors Calculate the minimum distance between the embedding vector of a sample in the test query set and the class prototype to obtain the predicted label of the test query sample. The calculation formula is as follows:

[0111]

[0112] where d(·) is the Euclidean distance, is the Euclidean distance between the query sample embedding vector and the class prototype;

[0113] S1043. Compare the predicted labels and the true labels of all test query samples by the trained deep Brown distance covariance module - prototype network to obtain the recognition accuracy rate. The calculation formula is as follows:

[0114]

[0115] where I(·) is the exponential function. When holds, the recognition accuracy rate is 1, otherwise it is 0; is the predicted label of the model for the query sample, y j is the true label of the query sample, |Q test | is the number of samples in the test query set, and is the test accuracy rate of the model.

[0116] A small - sample SAR image target recognition method based on deep Brown distance provided by the present invention adopts a deep Brown distance covariance module, which can enhance the image features extracted by the deep residual neural network; adopts a deep Brown distance covariance module - prototype network, which can obtain embedding vectors with richer image features, and can make full use of a single SAR image sample, so as to accurately recognize the SAR image target under the condition of extremely few labeled samples.

[0117] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. A small-sample SAR image target recognition method based on the deep Brown distance, characterized in that Including: Obtain synthetic aperture radar images and divide them into a training sample set and a test sample set; wherein, the training sample set includes a training support set and a training query set, and the test sample set includes a test support set and a test query set; Construct a deep Brown distance covariance module - prototype network; wherein, the deep Brown distance covariance module - prototype network includes a deep residual neural network, a deep Brown distance covariance module, and an Euclidean distance classifier; Use the training sample set to perform few - shot training on the deep Brown distance covariance module - prototype network to obtain a trained deep Brown distance covariance module - prototype network; Input the test sample set into the trained deep Brown distance covariance module - prototype network to obtain the predicted labels of the test query set; wherein, the process of inputting the test sample set into the trained deep Brown distance covariance module - prototype network to obtain the predicted labels of the test query set includes: The test support set S test Sample x in j Input the trained deep Brown distance covariance module-prototype network to get the embedding vector A of the samples in the test support set θ (x j ), and obtain the mean of the embedding vectors of similar samples in the test support set in each dimension as the class prototype of the test process, where the calculation formula is: where P i is the i-th class prototype, is the i-th class test support set, and k is the number of samples in each class of the test support set; Put the test query set Q test The samples in are input into the trained deep Brown distance covariance module - prototype network to obtain the embedding vectors of the samples in the test query set Calculate the minimum value of the distance between the embedding vectors of the samples in the test query set and the class prototypes to obtain the predicted labels of the test query samples. The calculation formula is as follows: where d(·) is the Euclidean distance, which is the Euclidean distance between the query sample embedding vector and the class prototype; Compare the predicted labels and the true labels of all test query samples by the trained deep Brown distance covariance module - prototype network to obtain the recognition accuracy rate; wherein, the calculation formula is: where \(I(\cdot)\) is an exponential function. When holds, the recognition accuracy is 1; otherwise it is 0. is the predicted label of the model for the query sample, and \(y\) j is the true label of the query sample, \(|Q|\) test is the number of samples in the test query set, and Acc is the test accuracy of the model.

2. The small-sample SAR image target recognition method based on the deep Brown distance according to claim 1, wherein, The process of using the training sample set to perform few - shot training on the deep Brown distance covariance module - prototype network to obtain a trained deep Brown distance covariance module - prototype network includes: Using the deep residual neural network, map the samples in the training support set S train into a high-dimensional space to obtain the features of the SAR image; where the mapping function is: where x j ∈R C×H×W is a sample, x j is the j-th image sample, C is the number of image channels, H is the image height, and W is the image width. are the trainable parameters of the deep residual neural network, is the mapping function, X ∈ R 128×8×8 is the image feature map extracted by the deep residual neural network; For each row x of the image feature map X extracted by the deep residual neural network i As the observation value, obtain the squared Euclidean distance between each row, and its calculation formula is: Among them, is the Hadamard product, "1" is the matrix of weight 1, I is the identity matrix, X is the image feature extracted by the deep residual neural network, and X T is the transpose of the image feature extracted by the deep residual neural network. It is set that then the Euclidean distance between rows is: wherein, is the squared Euclidean distance between each row; Based on the Euclidean distance between rows, obtain the deep Brown distance covariance matrix of the samples in the training support set, and its calculation formula is: wherein, is the Euclidean distance between the row observations of the sample feature map X in the training support set, D is the number of channels of the sample feature map in the training support set, and D×D is the size of the obtained deep Brown distance covariance matrix; Set the negative elements in the deep Brown distance covariance matrix to zero, and take out and flatten its upper triangular elements as the embedding vectors of the samples in the training support set, and its expression is: Among them, A θ (·) is the mapping function of the deep residual neural network and the deep Brown distance covariance module, A θ (x j ) is the embedding vector of the sample in the training support set, and θ is the trainable parameter of the deep residual network and the deep Brown distance covariance module; Based on the training support set S train The embedding vectors of C×k samples in it are used to obtain C class prototypes, and its calculation formula is: where, P i is the i-th class prototype, is the i-th class training support set, k is the number of samples in each class of the training support set, x j is the j-th input image, y j is the true label of the j-th image, A θ (x j ) is the embedding vector obtained by passing the input image through a deep residual neural network and a deep Brown distance covariance module; Using the same method, input the samples in the training query set Q train into the deep residual neural network and the deep Brown distance covariance module to obtain the embedding vectors of the training query samples Calculate the Euclidean distance between the embedding vectors of the training query samples and the C-class prototypes, obtain the class prototype with the shortest distance, and use the corresponding class as the predicted label pred of the training query set j ; where the calculation formula of the Euclidean distance is: Among them, is the Euclidean distance between the query sample embedding vector and the class prototype, and ||·||2 is the vector two-norm; Obtain the true labels of the training query samples, and based on the predicted labels and true labels of the training query samples, obtain the current cross - entropy loss function. Use the stochastic gradient descent algorithm to iteratively optimize the deep Brown distance covariance module - prototype network to obtain a trained deep Brown distance covariance module - prototype network.

3. The small-sample SAR image target recognition method based on the deep Brown distance according to claim 2, wherein, Before using the training sample set to perform few - shot training on the deep Brown distance covariance module - prototype network to obtain a trained deep Brown distance covariance module - prototype network, it also includes: Initialize the deep Brown distance covariance module - prototype network, set the number of training iterations to T, T≥1000, and initialize the iteration number t = 0.

4. The small-sample SAR image target recognition method based on the deep Brown distance according to claim 2, wherein Also including: The training query samples pass through the deep Brown distance covariance module - prototype network to obtain the predicted labels of the training query samples. Calculate the cross - entropy loss function between the true labels and the predicted labels of the training query samples, and use it as the training error. Use the stochastic gradient descent algorithm to backpropagate the error to update the trainable parameters θ in the deep residual neural network and the deep Brown distance covariance module to obtain a deep Brown distance covariance module - prototype network that can accurately recognize the training query samples. The training error is: Among them, is a sample in the training query set, and y j is the true label of the training query set sample. is the classification prediction probability of identifying the training query sample as the y j -th class, and |Q train | is the total number of samples in the training query set. is the Euclidean distance between the embedding vector of the sample in the j-th training query set and the k-th class prototype, and C is the number of classes set in the iterative training.

5. The small-sample SAR image target recognition method based on the deep Brown distance according to claim 1, wherein The deep Brown distance covariance module - prototype network includes a first convolutional layer, a first residual block, a second residual block, a third residual block, a fourth residual block, a fifth residual block, a sixth residual block, a seventh residual block, an eighth residual block, a deep Brown distance covariance module, and an Euclidean classifier; Among them, each residual block includes a second convolutional layer, a first batch normalization layer, a first ReLU activation layer, a third convolutional layer, and a second batch normalization layer.

6. The small-sample SAR image target recognition method based on the deep Brownian distance according to claim 5, wherein When the number of channels of the input and output of each residual block is not equal, the input of the residual block is subjected to convolutional operation and batch normalization operation, and then added to the output of the residual block as the final output of the residual block.

7. The small sample SAR image target recognition method based on the deep Brown distance according to claim 1, characterized in that It further includes: Performing target segmentation on the synthetic aperture radar image.

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