A radar non-uniform target category recognition method based on constraint and optimization

Abstract

The application discloses a SAR non-equilibrium target category recognition method based on constraint and optimization. Firstly, a focal loss is used to balance the contribution of minority classes and majority classes to model optimization. Then, a focal loss with first-order flatness constraint is designed to find the minimum of high generalization error. Finally, a gradient norm perception minimization algorithm is used to integrate the first-order flatness into the optimization process, so as to realize the recognition and classification of minority classes and majority classes. The method constructs a SAR non-equilibrium target category model and solves the model. In the solving process, the focal loss is fully utilized to optimize the non-equilibrium categories, and on this basis, a functional constraint based on the first-order flatness is designed, and the GAM algorithm is fused to optimize the category recognition, so that good performance is achieved in the SAR non-equilibrium target category recognition, and the problems of existing target recognition classification imbalance and performance decline are solved.

Description

Technical Field

[0001] This invention belongs to the field of radar target recognition, and specifically relates to a method for radar non-equilibrium target category recognition based on constraints and optimization. Background Technology

[0002] Automatic Target Recognition (ATR) plays a crucial role in radar image interpretation. Thanks to continuous breakthroughs and the adoption of deep learning methods, ATR performance has been significantly improved. Most existing radar target recognition methods are data-driven. Specifically, the accuracy, robustness, and generalization capabilities of radar target recognition methods highly depend on a sufficient and balanced distribution of training samples across all classes. However, obtaining radar datasets with balanced classifications is a challenge in actual reconnaissance operations, severely impacting the performance of radar target recognition models. This is mainly because the model tends to focus more on the majority class with more samples, while neglecting the minority class with fewer samples. Therefore, accurately identifying radar targets under imbalanced classification has become one of the key challenges in current radar target recognition tasks.

[0003] The core of solving the target recognition problem under imbalanced class distribution is to balance the weights of the minority and majority classes. Currently, methods for solving radar target recognition problems with an imbalanced number of classes can be broadly categorized into data-based and algorithm-based approaches. Data-based methods primarily utilize oversampling or undersampling to ensure a balanced distribution of samples across each class, effectively transforming the target recognition problem from an imbalanced state to a balanced state. However, oversampling can lead to overfitting of the minority classes, while undersampling can result in the loss of samples containing important information, inevitably leading to poor generalization and expressive power.

[0004] Algorithm-based methods primarily correct the discriminatory bias of target recognition models towards the majority class through algorithmic design. Cost-sensitive learning methods effectively address the problem of insufficient minority class learning by adjusting the weights of the minority and majority classes. On the other hand, ensemble learning transforms the imbalance problem into a comprehensive recognition result from multiple training sets with varying degrees of imbalance. Compared to data-based methods, algorithm-based methods focus more on the essence of the imbalance problem. However, most existing algorithm-based methods prioritize improving the recognition performance of the minority class while neglecting the overall performance, including the majority class. Therefore, it is necessary to develop a novel algorithm-based method for imbalanced radar target recognition. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a constrained and optimized method for radar non-equilibrium target category identification. This invention introduces a first-order flatness-constrained focal loss (FL) to prevent the loss function from converging to a saddle point during optimization, thereby balancing the contributions of the minority and majority classes to the model's identification and enhancing the model's generalization ability. Furthermore, it utilizes the Gradient Norm Aware Minimization (GAM) algorithm to incorporate the first-order flatness-constrained FL into the optimization process, achieving non-equilibrium identification of radar targets.

[0006] The objective of this invention is achieved through the following technical solution: a radar non-equilibrium target category identification method based on constraints and optimization, comprising the following steps:

[0007] S1. Acquire the original radar image, use center cropping to crop the acquired radar scene image sample into image slices of the same size with the target located in the center of the image, and perform normalization operation on the sliced ​​sample.

[0008] S2. Construct an imbalanced radar target dataset: Randomly select k classes from the dataset as the minority classes, where k satisfies... C represents the total number of classes; based on the original dataset, an imbalance factor η is introduced to calculate the proportion of samples from the k randomly selected minority classes; then, samples are selected at equal intervals from the sample set of the k minority classes, with the number of selected samples being ηN. ck N ck Let ηN be the number of samples in the sample set of the k-th minority class; using the selected ηN ck One sample replaces the original N. ck A number of samples are added to the dataset to form an imbalanced dataset; the imbalance degree η is calculated as follows:

[0009]

[0010] Where E(·) is the mean operation, N c Minority(N) represents the number of samples of radar targets of type c. c ) and majiroly(N c () represent the sample size for the minority and majority categories, respectively;

[0011] S3. Construct a radar target recognition network. Construct three typical radar target recognition networks: Net in Net, Vgg, or AlexNet, as the recognition network. Train the image target recognition network using an imbalanced radar target dataset.

[0012] S4. The radar target recognition network is optimized and trained using a first-order constrained focusing loss function. This loss function introduces weighting factors and focusing parameters to balance the unbalanced categories.

[0013] S5. Solve the loss function described in S4 using the GAM optimization algorithm to optimize the radar target recognition network model;

[0014] S6. Input the radar image into the radar target recognition network trained in step S5.

[0015] Step S4 specifically includes the following sub-steps:

[0016] S41. By introducing a weighting factor and a focusing parameter into the focusing loss, the weights between the majority and minority classes are balanced, specifically as follows:

[0017] FL=-α t (1-pt) γ log(pt)

[0018] Where FL represents the focusing loss; α t γ≥0 represent the weighting factor and focusing parameter, respectively; pt is the probability predicted by the model.

[0019] S42. Enhancing the generalization ability of the model using first-order flatness regularization: Let ω∈Ξ represent the parameters of the radar target recognition network, where Ξ represents the global parameter space; the open sphere in Euclidean space centered on the model parameter ω with radius σ>0 is represented as Ω(ω,σ), and its expression is:

[0020] Ω(ω,σ)={ω′:||ω-ω′||<σ}

[0021] Where ω′ represents the model parameters in the open sphere space Ω(ω,σ), and ||·|| represents the distance operator between the parameters;

[0022] For a model, its empirical loss function is related to the model parameters and is denoted as L(ω);

[0023] First-order flatness is defined as:

[0024] Therefore, the overall loss function for radar unbalanced target identification is defined as the focusing loss with first-order flatness constraints, expressed as:

[0025]

[0026] Where λ represents the hyperparameter that determines the regularization strength.

[0027] The specific implementation method of step S5 is as follows: The specific algorithm solution process is as follows:

[0028]

[0029] Here, ▽ represents the gradient operator; the gradient function is solved using Hessian vector operations.

[0030] The beneficial effects of this invention are as follows: Compared with existing algorithms, the method of this invention alleviates the challenge caused by the imbalance of sample numbers in different categories during radar target recognition. By introducing a first-order constraint FL loss function, it converges to a saddle point during the optimization process, thereby enhancing the model's generalization ability. Furthermore, by utilizing the GAM algorithm, the first-order FL is incorporated into the optimization process, achieving imbalanced recognition of radar targets. This results in better recognition performance for both minority and overall categories in the radar target recognition network. Attached Figure Description

[0031] Figure 1 Algorithm flowchart of the method of this invention;

[0032] Figure 2 In a specific embodiment of the present invention, a comparison curve of the overall performance of the optimized Alex and the conventional Alex within the range of η being 0.1 to 0.7 is shown.

[0033] Figure 3 In a specific embodiment of the present invention, t-distributed random neighbor embedding (t-SNE) visualizes the target features extracted by Alex. Detailed Implementation

[0034] This invention is primarily verified using simulation experiments. All steps and conclusions have been verified correctly on the Windows 10 operating system platform using Python 3.9. The technical solution of this invention is further described below with reference to the accompanying drawings.

[0035] like Figure 1 As shown, the present invention provides a radar non-equilibrium target category identification method based on constraints and optimization, comprising the following steps:

[0036] S1. Acquire raw radar images. Using center cropping, crop the acquired radar scene image samples into image slices of the same size with the target located at the center of the image. Normalize the sliced ​​samples to obtain the radar image dataset. In this embodiment, each image slice is 128×128 pixels. Let X represent the sample data before normalization, where the pixel value at position (i,j) can be represented as X(i,j), and X′ represent the sample data after normalization. Where min[X] represents the minimum value of the sample pixel before normalization, and max[X] represents the maximum value of the sample pixel before normalization.

[0037] S2. Construct an imbalanced radar target dataset: Randomly select k classes from the dataset as the minority classes. To better simulate the actual imbalanced class situation, k satisfies... C represents the total number of classes. Based on the original dataset, an imbalance factor η is introduced to calculate the proportion of samples from the k randomly selected minority classes. Then, samples are selected at equal intervals from the set of k minority classes, with the number of selected samples being ηN. ck N ck Let ηN be the number of samples in the sample set of the k-th minority class; using the selected ηN ck One sample replaces the original N. ck A number of samples are added to the dataset to form an imbalanced dataset, which is then used to train the model. The imbalance degree η is calculated as follows:

[0038]

[0039] Where E(·) is the mean operation, N c Minority(N) represents the number of samples of radar targets of type c. c ) and majiroly(N c () represent the sample size for the minority and majority categories, respectively;

[0040] Table 1 provides a detailed description of the dataset used in this embodiment. The original dataset contains ten categories. Four categories are randomly selected from the dataset as the minority class to construct an imbalanced dataset.

[0041] Table 1. Number of training samples in the original data and the imbalanced dataset.

[0042]

[0043]

[0044] S3. Construct a radar target recognition network. Construct three typical radar target recognition networks: Net in Net (NiN), Vgg, or AlexNet (Alex) as recognition networks; and train the image target recognition network using an imbalanced radar target dataset.

[0045] S4. The radar target recognition network is optimized and trained using a first-order constrained focusing loss function. This loss function introduces weighting factors and focusing parameters to balance the various unbalanced categories. Specifically, this includes the following steps:

[0046] S41. By introducing weighting factors and focusing parameters into the Focal Loss (FL) to balance the weights between the majority and minority classes, the problem of ignoring the limited number of classes in the training samples is alleviated. FL reduces the influence of easily classified samples while amplifying the contribution of difficult-to-classify samples to the overall loss function. Specifically, it is expressed as follows:

[0047] FL=-α t (1-pt) γ log(pt)

[0048] Where FL represents the focusing loss; α t γ≥0 represent the weighting factor and focusing parameter, respectively; set α t This is used to adjust the loss ratio between the majority and minority classes; pt is the probability predicted by the model. When pt approaches 1, the sample belongs to the easily distinguishable majority class, the modulation factor (1-pt) approaches 0, and its complement approaches 1. This is achieved by adjusting α. t γ can balance the contributions of majority and minority class samples, thus improving the overall recognition performance.

[0049] S42. Enhancing the model's generalization ability using first-order flatness regularization: By considering first-order derivative information, the smoothness of the model in the parameter space is ensured, thereby preventing the model from getting stuck in saddle points during optimization and enhancing the model's generalization ability. Let ω∈Ξ represent the parameters of the radar target recognition network in S3, where Ξ represents the overall parameter space; the open sphere in Euclidean space centered on the model parameter ω with radius σ>0 can be represented as Ω(ω,σ), and its expression is:

[0050] Ω(ω,σ)={ω′:||ω-ω′||<σ}

[0051] Here, ω′ represents the model parameters in the open sphere Ω(ω,σ), and ||·|| represents the distance operator between the parameters.

[0052] For a model, its empirical loss function is related to the model parameters and is denoted as L(ω), where L represents the empirical loss function and ω represents the model parameters;

[0053] First-order flatness is defined as:

[0054] Therefore, the overall loss function for radar unbalanced target identification is defined as the focusing loss with first-order flatness constraints, expressed as:

[0055]

[0056] Here, λ represents the hyperparameter that determines the regularization strength. This means that the loss function FL should not change drastically in the neighborhood of ω, thus limiting the maximum gradient norm.

[0057] Therefore, using first-order flatness constraints for model optimization can not only improve the recognition performance of minority classes, but also improve the overall recognition and generalization performance of the model.

[0058] S5. Utilize the GAM optimization algorithm to optimize the overall loss function L described in step S4. all (ω) is solved to optimize the radar target recognition network model; the specific algorithm solution process is as follows:

[0059]

[0060] Here, ▽ represents the gradient operator. This gradient function can be solved using Hessian vector operations. A method combining first-order flatness constraints (FL) and the GAM optimization algorithm can improve the recognition performance of typical radar target recognition networks in both minority and majority categories.

[0061] S6. Input the radar image into the radar target recognition network trained in step S5 to obtain the target recognition result.

[0062] This invention uses four evaluation metrics—Precision, Recall, G-mean, and F1-score—to assess the recognition performance of the object recognition network. The formulas for calculating Precision, Recall, G-mean, and F1-score are as follows:

[0063]

[0064] Here, TP represents the number of samples accurately identified as belonging to the minority class; FP and FN represent the number of misclassified majority class samples and misclassified minority class samples, respectively. Precision and Recall represent the proportion of accurately predicted minority class samples out of all predicted and actual minority class samples, respectively. G-mean and F1-score are the harmonic mean and geometric mean of Precision and Recall, respectively, providing a comprehensive evaluation of the minority and majority class identification performance. The values ​​of these four evaluation metrics range from [0,1], with higher values ​​indicating better performance of the proposed method.

[0065] Table 2 shows the recognition results of three typical radar target recognition networks using the η=0.2 method. It can be seen that the proposed method can achieve effective radar target recognition results under imbalanced classification. Specifically, the accuracy of Vgg reaches 98.10%, indicating that the method can effectively classify a minority of categories. Furthermore, both the F1-score and G-mean exceed 92%, demonstrating that the radar target recognition network optimized by the proposed method has better recognition performance for both minority and overall categories compared to radar target recognition networks optimized by traditional methods.

[0066] Table 2 shows the identification results of this method, indicating that the imbalance η = 0.2.

[0067]

[0068] To further verify the effectiveness of the proposed method, a comparison curve of the combined performance of the optimized Alex and the conventional Alex when η is in the range of 0.1 to 0.7 was plotted, as shown below. Figure 2 As shown, (a) is the F1-score curve and (b) is the G-mean curve.

[0069] It is worth noting that the traditional Alex represents the Alex optimized using general cross-entropy LF and the Adam optimizer. It can be seen that when η = 0.1, the F1-score and G-mean of the traditional Alex can only reach 45%, while the F1-score and G-mean of the method in this invention can both reach 85%. As the value of η decreases, both the F1-score and G-mean improve, and at an η value of 0.7, it outperforms the conventional optimization method, reaching over 95%. This verifies the effectiveness and robustness of this method in identifying different levels of imbalance.

[0070] The distribution of target features extracted by Alex is visualized using t-distributed random neighbor embeddings (t-SNE), such as... Figure 3 As shown. Figure 3 (a) Features extracted by Alex after optimization using the general cross-entropy loss function and Adam optimizer. Figure 3 (b) shows the features extracted by Alex after training using the method presented in this paper. It can be seen that in... Figure 3 In (a), there is overlap between the features of the minority and majority classes, especially in the BTR70 class, where almost all features are mixed with those of the majority class. In contrast, in Figure 3 In (b), the clustering and separability of each category feature are significantly improved, which further highlights the comprehensive enhancement of the proposed method in both minority and majority categories.

[0071] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A radar non-equilibrium target category identification method based on constraints and optimization, characterized in that, Includes the following steps: S1. Acquire the original radar image, use center cropping to crop the acquired radar scene image sample into image slices of the same size with the target located in the center of the image, and perform normalization operation on the sliced ​​sample. S2. Construct an imbalanced radar target dataset: Randomly select k classes from the dataset as the minority classes. satisfy , The total number of categories; an imbalance is introduced into the original dataset. Calculate the randomly selected The proportion of samples in the minority categories; then... Samples are selected at equal intervals from a sample set of a minority category, and the number of samples selected is [number missing]. , Let be the number of samples in the sample set of the k-th minority class; using the selected One sample replaces the original A number of samples are added to the dataset, forming an imbalanced dataset; the degree of imbalance... The calculation method is as follows: ； in, For mean calculation, Indicates the first Number of radar-like target samples, and These represent the sample size for the minority and majority categories, respectively. S3. Construct a radar target recognition network, using three typical radar target recognition networks: Net in Net, Vgg, and AlexNet as recognition networks; and train the image target recognition network using an imbalanced radar target dataset. S4. The radar target recognition network is optimized and trained using a first-order constrained focusing loss function. This loss function introduces weighting factors and focusing parameters to balance the various unbalanced categories. Specifically, this includes the following steps: S41. By introducing a weighting factor and a focusing parameter into the focusing loss, the weights between the majority and minority classes are balanced, specifically as follows: ； in, This indicates a focus on losses; and These represent the weighting factor and the focusing parameter, respectively. The probability predicted by the model; S42. Enhance the generalization ability of the model using first-order flatness regularization: Let... The parameters represent the radar target recognition network, where Represents the overall parameter space; in Euclidean space, model parameters are represented. Centered on, radius The kickoff is represented as Its expression is: ； in, Overall, it represents the space at the start of the game. The model parameters in the data, Distance operators between parameters; For a given model, its empirical loss function is related to the model parameters, and is expressed as follows: ; First-order flatness is defined as: ; Therefore, the overall loss function for radar unbalanced target identification is defined as the focusing loss with first-order flatness constraints, expressed as: ； in, This represents the hyperparameter that determines the strength of regularization; S5. Solve the loss function described in S4 using the GAM optimization algorithm to optimize the radar target recognition network model; the specific implementation method is as follows: the specific algorithm solution process is as follows: ； in, This represents the gradient operator; the gradient operator is solved using Hessian vector operations. S6. Input the radar image into the radar target recognition network trained in step S5.

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