Small sample SAR image target recognition method and system based on uncertainty

Abstract

The application belongs to the technical field of image recognition, and discloses a small sample SAR image automatic target recognition method and system based on uncertainty, which utilizes Dirichlet distribution to model classification results; combines Dempster-Shafer theory and Dirichlet distribution, and deduces a loss function of evidence deep learning; combines prior information from a source domain, and deduces a loss function suitable for target recognition and uncertainty estimation of passive FSDA; adopts a teacher-student network structure to fine-tune the model by using the loss function of passive FSDA and combining a small amount of target domain labeled data, and finally realizes small sample automatic target recognition and uncertainty estimation of SAR. The application uses passive FSDA for small sample automatic target recognition of SAR, solves the limitation problem of traditional FSDA, and provides a new method for reliable small sample automatic target recognition technology of SAR.

Description

Technical Field

[0001] The present invention belongs to the technical field of image recognition, and in particular relates to an automatic target recognition method for small sample SAR images based on uncertainty. Background Art

[0002] Synthetic Aperture Radar (SAR) is a sensor that actively transmits electromagnetic waves and receives echoes. Unlike optical sensors, SAR systems are unaffected by weather conditions, making them widely used in military, agricultural, and other fields. With the improvement of SAR image resolution, key technologies, such as SAR automatic target recognition (ATR), have become crucial for military applications such as situational reconnaissance and intelligence interpretation. The backscattering characteristics of targets in SAR images are affected by various factors. Variations in imaging conditions, such as acquired training data and real-world test data, can no longer satisfy the independent and identically distributed (IID) condition. Research on domain adaptation is crucial to addressing this issue. However, SAR images are less intuitive than optical images, making target identification difficult. Furthermore, military backgrounds offer fewer samples, resulting in a shortage of labeled data in the target domain. Consequently, few-shot domain adaptation (FSDA) has been proposed for SAR automatic target recognition (SAR ATR). Most FSDA methods require access to source domain data. In the military context, SAR imagery data from various types of equipment is confidential. This means that when using data from other sensors or simulations as source data for FSDA, the data itself is inaccessible. Furthermore, source data can be large and stored across multiple devices. Accessing this data can create data transmission bottlenecks or risk data leakage. Therefore, it is necessary to implement FSDA without accessing the source data, known as passive FSDA.

[0003] Passive FSDA for SAR ATR presents two major challenges. The first challenge is how to represent transferable knowledge between the target and source domains using a given source domain classifier. Approaches to this problem include data generation and model fine-tuning. Data generation methods include domain image generation and domain distribution generation. For example, in passive FSDA for optical images, Haoang Chi et al. proposed the Target-Oriented Hypothesis Adaptation Network (TOHAN), which gradually transfers data knowledge to the target domain by generating highly compatible unlabeled data. The second challenge is that the scarcity of labeled samples in the target domain leads to high model uncertainty and unreliable predictions. To ensure the reliability of model predictions, many machine learning-based methods have been proposed to quantify or estimate uncertainty. The main methods for uncertainty estimation include MC-Dropout, Deep Ensemble, PBP, and models based on Dirichlet distribution. However, these methods are designed for uncertainty estimation in natural image object recognition and are based on big data, without addressing uncertainty estimation under small sample sizes.

[0004] Through the above analysis, the problems and defects of the existing technology are as follows:

[0005] Research on passive FSDA methods is urgently needed in SAR ATR. However, currently available research focuses solely on the challenges of using inaccessible source data, neglecting the importance of uncertainty estimation. In summary, no SAR small-sample automatic target recognition method has been developed that combines target recognition performance and uncertainty estimation within a single framework. Summary of the Invention

[0006] In view of the problems existing in the prior art, the present invention provides an automatic target recognition method for small sample SAR images based on uncertainty.

[0007] The present invention is implemented as follows: a method for automatic target recognition of small-sample SAR images based on uncertainty, first, the SAR image is preprocessed, including operations such as denoising and filtering; then, a target detection algorithm is used to detect targets in the image, and the detection results are used as input to model the classification probability using Dirichlet distribution; then, the Dempster-Shafer evidence theory (DS evidence theory) and Dirichlet distribution are combined to derive a loss function for evidence deep learning, and the target recognition and uncertainty estimation loss function suitable for passive FSDA is derived in combination with prior information from the source domain; finally, a teacher-student network structure is adopted, and the model is fine-tuned using the loss function of passive FSDA and a small amount of target domain annotated data to achieve small-sample automatic target recognition and uncertainty estimation of SAR.

[0008] Further, the method specifically includes the following steps:

[0009] S101, modeling the classification result with Dirichlet distribution;

[0010] S102, combining DS evidence theory and Dirichlet distribution to derive the loss function of evidence deep learning;

[0011] S103, combining prior information from the source domain, derive the loss function suitable for target recognition and uncertainty estimation of source-free FSDA;

[0012] S104, using the teacher-student network structure to fine-tune the model using the loss function of source-free FSDA combined with a small amount of target domain labeled data, and finally realize small sample automatic target recognition and uncertainty estimation of SAR.

[0013] Further, the modeling method in S101 is:

[0014] In the K-classification problem, the Dirichlet distribution with parameter α is used to model the classification probability p

[0015]

[0016] Further, the method in S102 is:

[0017] Use subjective logic to formalize the evidence (e) of evidence theory on the recognition framework as Dirichlet distribution, as shown in formula (6). Through the neural network with parameter Θ, realize evidence search and Dirichlet parameter estimation, and finally realize uncertainty estimation:

[0018] Model the uncertainty with subjective logic as follows, where u represents uncertainty, b represents belief mass, and S represents Dirichlet intensity.

[0019]

[0020] Formalize the evidence distribution on the recognition framework as Dirichlet distribution to obtain formula (6), where α k =e k +1

[0021]

[0022] Through the neural network f(·) with parameter Θ, realize the evidence search of sample x k , and obtain the estimation of Dirichlet parameter α k .

[0023] α k =e k+1=f(x k |Θ)+1. (7)

[0024] Combining formula (5) with formula (4), we can get formula (8), which can directly calculate the uncertainty u

[0025]

[0026] According to the properties of Dirichlet distribution, the probability after calibration is:

[0027]

[0028] Considering MSE loss during classification and using KL divergence enables the network to express "I don't know", and obtains the loss function L(Θ) in evidence deep learning:

[0029]

[0030] λ t =min(1.0,t / 10)∈[0,1] (11)

[0031]

[0032] Among them, λ t represents the annealing coefficient, and y represents the one-hot label corresponding to the true value.

[0033] Furthermore, the method in S103 is:

[0034] The prior knowledge that is beneficial to target recognition is introduced into formula (10) to achieve SAR image target recognition and uncertainty estimation under passive FSDA.

[0035] First, use the label distribution q that contains more negative information i Replacing the one-hot label as prior information makes the loss function corresponding to formula (10) adaptable to small sample target recognition, and obtains formula (14).

[0036]

[0037] Some parameters in formula (14) can be converted into:

[0038]

[0039] Based on the shared domain attributes, the loss function of passive FSDA is finally determined:

[0040]

[0041] Some parameters in formula (16) can be converted to formula (17). Among them, if and only if the prediction results of the same data on different models are the same, there are samples in the shared domain, and there is β i =<1,…,1>

[0042]

[0043] Furthermore, the method in S104 is:

[0044] A fixed CNN classifier is trained using simulated SAR data as the teacher model, and another CNN model with the same structure is initialized with the weights of this model as the student model. Then, the student model is fine-tuned using the measured SAR data; due to the distribution offset between the source and target domains, only data in the shared domain can be transferred from the source to the student model. For the same input sample, when the prediction results of the teacher model and the student model are consistent, the sample is considered to belong to the shared domain, and the label distribution q corresponding to formula (17) is i The logits value s obtained by the distillation temperature τ and the model input i (x i ) can be expressed by formula (18).

[0045]

[0046] Another object of the present invention is to provide an uncertainty-based small sample SAR image automatic target recognition system, comprising:

[0047] 1) Preprocessing module: Preprocess the input SAR image, including denoising, filtering and other operations, to improve image quality and reduce the impact of noise on subsequent processing.

[0048] 2) Target Detection Module: Targets in the preprocessed SAR image are detected using a target detection algorithm. This target detection algorithm can be selected from existing mature algorithms such as Faster R-CNN, YOLO, or SSD.

[0049] 3) Uncertainty Modeling Module: Based on the detected targets, the classification probability is modeled using Dirichlet distribution. This step will provide the basis for subsequent uncertainty estimation.

[0050] 4) Loss Function Derivation Module: This module combines DS evidence theory with the Dirichlet distribution to derive a loss function for evidence-based deep learning. Furthermore, it incorporates prior information from the source domain to derive target recognition and uncertainty estimation loss functions suitable for passive FSDA.

[0051] 5) Teacher-Student Network Structure Module: This module uses a teacher-student network structure to fine-tune the model using the passive FSDA loss function and a small amount of labeled target domain data. This structure can accelerate model training and improve learning outcomes.

[0052] 6) Automatic Target Recognition and Uncertainty Estimation Module: This module applies the fine-tuned model to automatic target recognition and uncertainty estimation in SAR images. The output includes the target category, location information, and uncertainty.

[0053] The entire system is designed to achieve automatic target recognition and uncertainty estimation of small sample SAR images, and to improve the accuracy and reliability of target recognition.

[0054] Another object of the present invention is to provide a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the uncertainty-based small sample SAR image automatic target recognition method.

[0055] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the uncertainty-based small sample SAR image automatic target recognition method.

[0056] Another object of the present invention is to provide an information data processing terminal, which is used to implement the SAR-based small sample automatic target recognition system.

[0057] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0058] First, there are few labeled samples in SAR Automatic Target Recognition (SAR ATR), and changes in imaging pitch angle, imaging band, and imaging background will cause data distribution to shift. Therefore, FSDA is a key issue in SARATR. In FSDA, most methods require access to source domain data, which is often limited in actual scenarios due to factors such as privacy protection, data storage and transmission costs, especially in SAR ATR. For example, in the military field, imaging data from various types of equipment are confidential, which means that when data from other sensors or simulation data are used as source domain data for FSDA, the data is inaccessible; the source domain data may be large in scale and exist on multiple devices. Accessing the source domain data will bring about data transmission bottlenecks or the risk of data leakage. The SAR small sample automatic target recognition of the present invention uses passive FSDA, which solves the limitation problem when only accessing the source domain model, and provides a new method for SAR ATR technology.

[0059] Second, existing SAR ATR methods focus on accuracy and ignore uncertainty, resulting in unreliable predictions. This paper studies a SAR small-sample automatic target recognition method that simultaneously studies target recognition and uncertainty estimation within a teacher-student network, creating a new approach for SAR reliable target recognition technology.

[0060] Specifically, the source domain model is used to obtain the similarity relationships between categories inherent in the sample as prior information. This prior information is then selectively introduced into the EDL to achieve small-sample object recognition and uncertainty estimation. To better express and utilize this prior information, a teacher-student network is employed. The source domain model serves as the teacher network to express the prior information, while the target domain model to be fine-tuned serves as the student network to leverage this prior information.

[0061] Third, in SARATR, using simulated data to assist in target recognition with small samples of measured data is a key research difficulty and focus. This invention learns prior knowledge from simulated data and partially incorporates it into target recognition using measured data, addressing the issues of simulated data being difficult to use and not being used effectively. Furthermore, this invention only addresses the model corresponding to the simulated data, not the simulated data itself, effectively preventing data leakage.

[0062] Fourth, here are the specific technological advancements for each step:

[0063] S101, use Dirichlet distribution to model the classification results:

[0064] Significant technical advancement: Application of the Dirichlet distribution to small-sample image classification. The Dirichlet distribution is a multivariate distribution commonly used in probabilistic modeling. By applying it to object classification, it can better handle uncertainty in small-sample situations. This approach provides more accurate and reliable classification probability estimates, facilitating better understanding and interpretation of object recognition results.

[0065] S102, combining DS evidence theory and Dirichlet distribution, derives the loss function of evidence-based deep learning:

[0066] Significant technical advancement: Loss function for evidence-based deep learning. Combining DS evidence theory and the Dirichlet distribution, a more accurate and comprehensive loss function for target recognition can be developed. This loss function effectively utilizes multi-source information and uncertainty, improving the model's target recognition performance in small-sample SAR images.

[0067] In step S103, the target recognition and uncertainty estimation loss function suitable for passive FSDA is derived by combining the prior information from the source domain:

[0068] Significant technical advancement: A loss function for passive FSDA. By incorporating prior information from the source domain, it combines target recognition with uncertainty estimation, enabling better handling of target recognition in small sample sizes. This loss function provides more accurate and reliable target recognition results and uncertainty estimation in the context of passive FSDA, significantly improving automatic target recognition in SAR imagery.

[0069] In S104, a teacher-student network structure is used to fine-tune the model using the passive FSDA loss function and a small amount of target domain annotated data, ultimately achieving small-sample automatic target recognition and uncertainty estimation for SAR.

[0070] Significant technical advancement: Application of a teacher-student network architecture. This architecture enables fine-tuning of the model using a small amount of labeled target domain data and the passive FSDA loss function, enabling small-sample automatic target recognition and uncertainty estimation in SAR images. This approach fully utilizes limited labeled data in small-sample situations, improving target recognition performance and robustness.

[0071] In summary, this uncertainty-based automatic target recognition method for small-sample SAR images combines multiple advanced techniques, such as the Dirichlet distribution, evidence-based deep learning, and a teacher-student network structure, to achieve significant technical advancements in SAR image target recognition performance. By fully leveraging multi-source information and prior knowledge, this method achieves more accurate and reliable target recognition and uncertainty estimation in small sample sizes. This will bring significant progress to the field of SAR image applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 This is a flow chart of a small sample automatic target recognition and uncertainty estimation method based on SAR provided by an embodiment of the present invention.

[0073] Figure 2 This is an example diagram of the relationship between the α parameter and the uncertainty estimate in a three-classification problem provided by an embodiment of the present invention.

[0074] Figure 3 This is a target recognition and uncertainty estimation framework diagram of a passive FSDA based on a teacher-student network provided by an embodiment of the present invention.

[0075] Figure 4 The embodiment of the present invention provides the comparison results (empirical CDF) of different methods on OOD data with a pitch angle of 15°.

[0076] Figure 5 The embodiment of the present invention provides the comparison results (empirical CDF) of different methods on OOD data with a pitch angle of 17°.

[0077] Figure 6 The embodiments of the present invention provide comparison results (uncertainty distribution density) of different methods on OOD data with a pitch angle of 15°.

[0078] Figure 7 The embodiments of the present invention provide comparison results (uncertainty distribution density) of different methods on OOD data with a pitch angle of 14°.

[0079] Figure 8 An embodiment of the present invention provides an example of uncertainty estimation and calibration probability on OOD data. DETAILED DESCRIPTION

[0080] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0081] S101, use Dirichlet distribution to model the classification results:

[0082] In the K classification problem, the classification probability p is modeled using the Dirichlet distribution with parameter α.

[0083]

[0084] S102, combining DS evidence theory and Dirichlet distribution, derives the loss function of evidence-based deep learning:

[0085] The evidence (e) of evidence theory is distributed in the recognition framework using subjective logic and formalized as Dirichlet distribution, as shown in formula (24). Evidence search and Dirichlet parameter estimation are realized through a neural network with parameter Θ, and finally uncertainty estimation is realized:

[0086] Modeling uncertainty using subjective logic is shown below, where u represents uncertainty, b represents belief mass, and S represents Dirichlet strength.

[0087]

[0088] The evidence distribution is formalized as Dirichlet distribution in the recognition framework, and formula (24) is obtained, where α k =e k +1

[0089]

[0090] The neural network f(·) with parameter Θ is used to realize the sample x k Evidence search for the Dirichlet parameter α k Estimates.

[0091] α k =e k+1 =f(x k |Θ)+1. (25)

[0092] Formula (26) can be obtained by transforming formula (22), and the uncertainty u can be directly calculated:

[0093]

[0094] An example of the relationship between the α parameter and the uncertainty estimate in the three-classification problem is as follows Figure 2 .

[0095] According to the properties of Dirichlet distribution, the probability after calibration is:

[0096]

[0097] Considering MSE loss during classification and using KL divergence enables the network to express "I don't know", and obtains the loss function L(Θ) in evidence deep learning:

[0098]

[0099] λ t =min(1.0,t / 10)∈[0,1] (29)

[0100]

[0101] Among them, λ t represents the annealing coefficient, and y represents the one-hot label corresponding to the true value.

[0102] In step S103, the target recognition and uncertainty estimation loss function suitable for passive FSDA is derived by combining the prior information from the source domain:

[0103] First, use the label distribution q that contains more negative information i Replacing the one-hot label as prior information makes the loss function corresponding to formula (28) adaptable to small sample target recognition, and obtains formula (32).

[0104]

[0105] Some parameters in formula (32) can be converted to:

[0106]

[0107] Based on the shared domain attributes, the loss function of passive FSDA is finally determined:

[0108]

[0109] Some parameters in formula (34) can be converted to formula (35). Among them, if and only if the prediction results of the same data on different models are the same, there are samples in the shared domain, and there is β i =<1,…,1>

[0110]

[0111] S104: Use the teacher-student network structure to fine-tune the model using the passive FSDA loss function and a small amount of target domain labeled data:

[0112] A fixed CNN classifier is trained using simulated SAR data as the teacher model, and another CNN model with the same structure is initialized with the weights of this model as the student model. Then, the student model is fine-tuned using the measured SAR data; due to the distribution offset between the source and target domains, only data in the shared domain can be transferred from the source to the student model. For the same input sample, when the prediction results of the teacher model and the student model are consistent, the sample is considered to belong to the shared domain, and the label distribution q corresponding to formula (35) is i The logits value s obtained by the distillation temperature τ and the model input i (x i ), can be expressed by the following formula (36)

[0113]

[0114] The automatic target recognition method for small sample SAR images based on uncertainty provided by the application embodiment of the present application is applied to a computer device, the computer device comprising a memory and a processor, the memory storing a computer program, the computer program being executed by the processor to enable the processor to execute the steps of the automatic target recognition method for small sample SAR images based on uncertainty.

[0115] The automatic target recognition method for small sample SAR images based on uncertainty provided by the application embodiment of the present application is applied to an information data processing terminal, the information data processing terminal being used to implement the automatic target recognition system for small sample SAR.

[0116] Two specific embodiments of the present application are:

[0117] Embodiment one:

[0118] (1) Dirichlet distribution is used to model the classification results. Dirichlet distribution is widely used in multi-class problems and is the conjugate prior of multinomial distribution, which is used to represent the uncertainty of the class.

[0119] (2) Dempster-Shafer theory (also known as DS evidence theory) and Dirichlet distribution are combined. DS evidence theory is a method for combining incomplete or conflicting evidence, which is suitable for handling uncertainty and ambiguity. We use it in combination with Dirichlet distribution to derive a new deep learning loss function for measuring the uncertainty of the prediction results.

[0120] (3) Prior information of the source domain is introduced, which is a way of transfer learning and can help the model to better generalize in the small sample learning environment. By combining this information, a target recognition and uncertainty estimation loss function suitable for source-free Few-Shot Domain Adaptation (FSDA) is further derived.

[0121] (4) The teacher-student network (Teacher-Student Network) is used to fine-tune the model using the loss function of source-free FSDA and a small amount of target domain labeled data. The teacher-student network is a particularly effective model fine-tuning technique that allows a trained (“teacher”) model to guide the training process of a new (“student”) model, helping it to learn quickly and effectively.

[0122] Embodiment two:

[0123] S101: Use Dirichlet distribution to model the classification results, which is used to calculate the probability of different categories appearing in the classification problem, and then realize uncertainty estimation.

[0124] S102: We combine DS evidence theory with the Dirichlet distribution to derive a new deep learning loss function. DS evidence theory is a well-known information fusion framework for handling uncertainty and ambiguity, providing more robust predictions in the face of incomplete evidence.

[0125] S103: Introducing prior information from the source domain helps the model generalize better. This approach leverages the characteristics of the source domain to improve object recognition and uncertainty estimation. This prior information is then incorporated into the loss function to derive a target recognition and uncertainty estimation loss function suitable for passive FSDA.

[0126] S104: In this phase, we will use the distillation learning framework to discover and utilize prior information, thereby unifying prior-guided object recognition and uncertainty estimation. First, we will adopt a teacher-student network structure and fine-tune the model using the passive FSDA loss function and a small amount of target domain labeled data.

[0127] The embodiments of the present invention have achieved some positive results during the development or use process, and indeed have great advantages over the existing technology. The following content describes them in conjunction with data, charts, etc. from the experimental process.

[0128] Experiments are conducted on the MSTAR data, where the data division of MSTAR is shown in Table 1:

[0129] Table 2 MSTAR data partition table

[0130]

[0131] Recognition results are expressed as Accuracy; larger Accuracy values ​​indicate better model performance. Uncertainty estimation performance is evaluated using Expected Calibrated Error (ECE); smaller ECE values ​​indicate better uncertainty estimation performance. Our method (Prior-EDL) is compared with direct testing without fine-tuning (WA), data-based fine-tuning (FT), DeepEnsemble, MC-Dropout, and EDL. Experimental results on ID data are shown in Table 2.

[0132] Table 2 Comparison of SARATR performance of different methods under source-free FSDA

[0133]

[0134] The results in Table 2 show that our method achieves higher recognition accuracy and uncertainty estimation performance in small-sample conditions under various settings, especially when the elevation angle difference between the source and target domains is small. This demonstrates that the label distribution effectively learns the inter-class similarity relationships of the targets, and thus, its prior information can assist in classifying measured data with small samples. Furthermore, uncertainty estimation performance improves to a certain extent when the elevation angle difference between the source and target domains is small. This indicates that, guided by prior information, the evidence distribution in small-sample conditions is more reasonable, leading to more reliable predictions. However, when the elevation angle difference between the source and target domains is large, our method (Prior-EDL) performs worse than EDL. Because SAR images are sensitive to imaging angle, targets exhibit different scattering characteristics at different elevation angles, and these differences in scattering characteristics become more pronounced with larger elevation angle differences. Consequently, the prior information obtained at an elevation angle of 15° does not generalize well to an elevation angle of 45°.

[0135] To further verify the uncertainty estimation performance on out-of-domain (OOD) data, the empirical cumulative distribution function (Empirical CDF) and the density histogram of the distribution of uncertainty estimates are used to further represent it.

[0136] Depend on Figures 4 to 7 It can be seen that on OOD data, our method can give higher uncertainty when targeting out-of-domain data, and its prediction is more reliable, especially in the 4-way 5-shot, 4-way 10-shot, and 4-way 20-shot settings. In addition, the uncertainty estimates on some OOD data are compared with the calibrated probability examples as shown in Figure 2. Figure 8 shown.

[0137] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0138] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A method for automatic target recognition in small sample SAR images based on uncertainty, characterized by: Preprocess the SAR image, including denoising and filtering operations; Detecting objects in an image using an object detection algorithm and using the detection result as input; the method includes: S101, modeling the classification results using Dirichlet distribution; S102, combining Dempster–Shafer theory with Dirichlet distribution to derive the loss function for evidence-based deep learning; In step S103, the target recognition and uncertainty estimation loss function suitable for passive FSDA is derived by combining the prior information from the source domain. The final loss function of passive FSDA is: Some parameters in the formula can be converted to the following formula after transformation; among them, if and only if the prediction results of the same data on different models are the same, there are samples in the shared domain, and there is β i =<1,…,1> S104 uses a teacher-student network structure to fine-tune the model using the passive FSDA loss function and a small amount of target domain annotated data, ultimately achieving small-sample automatic target recognition and uncertainty estimation for SAR. The specific implementation method of S102 is: 1) Establish an evidence framework: Convert target detection results into evidence and synthesize the evidence using the Dempster-Shafer theory; 2) Modeling uncertainty using subjective logic: Evidence distribution in the recognition framework is formalized as a Dirichlet distribution, and uncertainty is modeled using subjective logic; 3) Loss function derivation: We implement evidence search and Dirichlet parameter estimation through a neural network with parameter , and derive the loss function for evidence deep learning; The specific implementation method of S103 is: 1) Source domain data preparation: Use source domain data to train the classifier and extract the feature representation of the classifier; 2) Target domain data preparation: Passive FSDA is performed using target domain data to obtain the feature representation of the target domain; 3) Loss function derivation: Combining the prior information from the source domain, we derive the target recognition and uncertainty estimation loss functions suitable for passive FSDA.

2. The method for automatic target recognition of small sample SAR images based on uncertainty according to claim 1, characterized in that: The specific implementation method of S101 is: 1) SAR image preprocessing: denoising and filtering the SAR image to improve image quality; 2) Object detection: Use the object detection algorithm to detect the object in the image and obtain the location and size information of the object; 3) Feature extraction: Extract features of the target area, including shape, texture, and grayscale; 4) Classifier training: Use Dirichlet distribution to model the classification probability and train the classifier.

3. The method for automatic target recognition of small sample SAR images based on uncertainty according to claim 1, characterized in that: The specific implementation method of S104 is: 1) Teacher-student network structure: Passive FSDA is performed using the teacher-student network structure to obtain the feature representation of the target domain; 2) Fine-tuning the model: Using a small amount of labeled data from the target domain to fine-tune the model to improve its performance and generalization ability; 3) Target recognition and uncertainty estimation: Target recognition and uncertainty estimation are performed using the fine-tuned model.

4. The method for automatic target recognition of small sample SAR images based on uncertainty according to claim 1, characterized in that: The method in S104 is: A fixed CNN classifier is trained using simulated SAR data as the teacher model, and another CNN model with the same structure is initialized with the weights of this model as the student model. Then, the student model is fine-tuned using the measured SAR data. Since there is a distribution offset between the source and target domains, only data in the shared domain can be transferred from the source to the student model. For the same input sample, when the prediction results of the teacher model and the student model are consistent, the sample is considered to belong to the shared domain, and the label distribution q corresponding to formula (53) is i The logits value s obtained by the distillation temperature τ and the model input i (x i ) can be expressed by the following formula (54):

5. An automatic target recognition system for small sample SAR images based on uncertainty, characterized by: include: 1) Preprocessing module: Preprocesses the input SAR image, including denoising and filtering operations, to improve image quality and reduce the impact of noise on subsequent processing; 2) Target detection module: Target detection algorithm is used to detect targets in the preprocessed SAR image; 3) Uncertainty modeling module: Based on the detected targets, the classification probability is modeled using Dirichlet distribution; 4) Loss function derivation module: The Dempster-Shafer theory is combined with the Dirichlet distribution to derive the loss function for evidential deep learning. At the same time, the target recognition and uncertainty estimation loss functions suitable for passive FSDA are derived by combining prior information from the source domain. The final loss function of passive FSDA is: Some parameters in the formula can be converted to the following formula after transformation; among them, if and only if the prediction results of the same data on different models are the same, there are samples in the shared domain, and there is β i =<1,…,1> Combining the Dempster–Shafer theory with the Dirichlet distribution, the specific implementation method of the loss function of evidence-based deep learning is derived as follows: 1) Establish an evidence framework: Convert target detection results into evidence and synthesize the evidence using the Dempster-Shafer theory; 2) Modeling uncertainty using subjective logic: Evidence distribution in the recognition framework is formalized as a Dirichlet distribution, and uncertainty is modeled using subjective logic; 3) Loss function derivation: We implement evidence search and Dirichlet parameter estimation through a neural network with parameter , and derive the loss function for evidence deep learning; Combining the prior information from the source domain, the specific implementation method of the target recognition and uncertainty estimation loss function suitable for passive FSDA is derived as follows: 1) Source domain data preparation: Use source domain data to train the classifier and extract the feature representation of the classifier; 2) Target domain data preparation: Passive FSDA is performed using target domain data to obtain the feature representation of the target domain; 3) Loss function derivation: Combining prior information from the source domain, we derive the target recognition and uncertainty estimation loss functions suitable for passive FSDA. 5) Teacher-student network structure module: Using the teacher-student network structure, the loss function of passive FSDA and a small amount of target domain annotated data are applied to model fine-tuning; 6) Automatic target recognition and uncertainty estimation module: The fine-tuned model is applied to automatic target recognition and uncertainty estimation of SAR images; the output includes the target category, location information and uncertainty.

6. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the uncertainty-based small sample SAR image automatic target recognition method according to any one of claims 1 to 4.

7. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the method for automatic target recognition of small sample SAR images based on uncertainty according to any one of claims 1 to 4.

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