ISAR small sample fast imaging method and system based on stacked complex neural network
By stacking complex neural networks and utilizing various heterogeneous machine learning algorithms and Fourier feature mapping, the imaging blur problem under small sample data in ISAR imaging was solved, and high-precision ISAR imaging was achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF POSTS & TELECOMM
- Filing Date
- 2026-02-02
- Publication Date
- 2026-05-12
AI Technical Summary
Traditional ISAR imaging algorithms perform poorly under sparse data conditions, existing machine learning methods cannot effectively handle complex data, and deep learning models have poor generalization ability in small sample situations, resulting in blurry or distorted imaging results.
Stacked complex neural networks are employed. By constructing a base model library containing various heterogeneous machine learning algorithms, K-fold cross-validation is used to generate meta-features. Combined with Fourier feature mapping and a hybrid loss function, a fully complex neural network is constructed for training, maintaining phase coupling and fitting high-frequency oscillation components.
It significantly improves imaging accuracy with small sample sizes, avoids phase distortion, eliminates imaging artifacts, and enhances image focus.
Smart Images
Figure CN122017837A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a method and system for rapid ISAR small-sample imaging based on stacked complex neural networks. Background Technology
[0002] Inverse Synthetic Aperture Radar (ISAR) is an all-weather, all-time high-resolution microwave imaging technology that can acquire two-dimensional high-resolution images of non-cooperative moving targets. It has important application value in fields such as space surveillance, target identification, and missile defense.
[0003] Traditional ISAR imaging algorithms, such as Range-Doppler (RD) and Back-Projection (BP) algorithms, are typically based on Fast Fourier Transform (FFT) or coherent accumulation principles. These methods can achieve good imaging results when the echo data is complete and the signal-to-noise ratio is high. However, in real-world complex electromagnetic environments, limitations in radar system measurement time, storage capacity, or enemy interference often result in only sparse aperture or small sample echo data. Under such incomplete data conditions, traditional imaging algorithms suffer from severe sidelobe interference, grating lobe effects, or resolution degradation, making it difficult to form a clear, focused target image.
[0004] To address the imaging challenges posed by sparse data, data-driven machine learning and deep learning methods have been introduced into the field of radar signal processing in recent years. However, existing technologies still suffer from the following significant drawbacks in practical applications: 1) Limitations of traditional machine learning methods: While traditional algorithms such as Support Vector Machines (SVM) or Random Forests (RF) exhibit good robustness with small sample sizes, they typically cannot directly handle complex data. Current practices often treat the real and imaginary parts of radar echoes as two independent real scalars for training. This approach disrupts the inherent phase coupling of complex signals, leading to phase distortion in the prediction results and consequently affecting the azimuth focusing performance of ISAR imaging. 2) The "Spectral Bias" Problem of Deep Neural Networks: While deep learning methods based on Multilayer Perceptrons (MLPs) or Convolutional Neural Networks (CNNs) possess powerful nonlinear fitting capabilities, they generally suffer from "spectral bias," meaning that neural networks tend to prioritize learning low-frequency smooth components, making it difficult to fit high-frequency oscillating details. Radar echo signals are essentially typical high-frequency oscillating signals. Ordinary network predictions often lose high-frequency texture, resulting in blurred imaging results, manifesting as a detail-less "bright spot" in the target area, making it impossible to distinguish the scattering center. Deep learning models typically rely on massive amounts of data for training. In ISAR imaging missions, acquiring large amounts of labeled electromagnetic simulation data or measured data is extremely costly. With only a small number of samples (e.g., 20% sparsity), complex deep neural networks are prone to overfitting, resulting in poor generalization ability and an inability to accurately predict echoes from unseen angles. Summary of the Invention
[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method and system for rapid ISAR imaging with small samples based on stacked complex neural networks, thereby solving the problems in existing technologies.
[0006] The objective of this invention can be achieved through the following technical solutions: A fast ISAR imaging method for small samples based on stacked complex neural networks includes the following steps: Obtain raw ISAR radar echo data, construct a sample set and divide it into a training set and a test set; perform multi-dimensional feature extraction on the sample set, and construct an enhanced feature vector containing physical coordinate features and local spatial statistical features; A stacked ensemble strategy is adopted to build a base model library containing multiple heterogeneous machine learning algorithms; the training set is divided using K-fold cross-validation, and the base model is trained by K-fold cross-validation on the real and imaginary parts of the echo, generating out-of-bag prediction values, which are used as meta-features. A fully complex neural network including a Fourier feature mapping module is constructed as a meta-model; the physical coordinate features are mapped to high-frequency phase features through the Fourier feature mapping module, and then concatenated with the meta-features and input into the meta-model; A hybrid loss function is constructed, which includes a data-driven term for constraining the numerical errors of the real and imaginary parts of the complex echo, and a physical-driven term for constraining the consistency of the echo amplitude energy distribution. The meta-model is trained on the training set using the hybrid loss function, and the meta-model parameters are updated through backpropagation. The base model is retrained using the training set data, and the test set data is input into the trained base model and meta-model to output the final complex echo prediction value and perform ISAR imaging.
[0007] Furthermore, the enhanced feature vector includes: Physical coordinate characteristics include: frequency, azimuth, the square of the frequency, the square of the azimuth, and the cross product of frequency and azimuth. Local spatial statistical features include: local mean, local variance, gradient along the frequency direction, gradient along the azimuth direction, global mean, and phase variance; Furthermore, the base models in the base model library include at least: linear regression model, support vector regression model, and random forest regression model.
[0008] Furthermore, the formula by which the Fourier feature mapping module maps physical coordinate features to high-frequency phase features is as follows: in, For normalized frequency and azimuth coordinate vectors, For a random projection matrix that follows a Gaussian distribution and is not trainable, This is the high-frequency phase eigenvector of the output.
[0009] Furthermore, the network layer weights, biases, and activation functions of the fully complex neural network are all defined in the complex domain; wherein, the weights of the complex linear layers are defined... and input Its forward propagation operation follows the rules of complex multiplication: Among them, subscript and Let represent the real and imaginary parts, respectively; W be the weight matrix; and x be the input feature vector. The bias is Output, which is the result of the linear transformation.
[0010] Furthermore, the hybrid loss function is: in, This represents the total mixed loss function value; This is a balancing coefficient used to adjust the weighting of the physics-driven terms in the total loss. This is a data-driven term used to constrain the numerical error of the real and imaginary parts of the complex echo; This is a physical driving term used to constrain the envelope distribution of the echo amplitude.
[0011] The ISAR small-sample fast imaging system based on stacked complex neural networks performs the above-mentioned method, including: Data acquisition and feature extraction module: acquire raw ISAR radar echo data, construct a sample set and divide it into training and test sets; perform multi-dimensional feature extraction on the sample set, and construct an enhanced feature vector containing physical coordinate features and local spatial statistical features; Meta-feature generation module: It adopts a stacked ensemble strategy to build a base model library containing multiple heterogeneous machine learning algorithms; it uses K-fold cross-validation to divide the training set, and performs K-fold cross-validation to train the base model for the real and imaginary parts of the echo respectively, generating out-of-bag prediction values, which are used as meta-features; Feature fusion module: Construct a fully complex neural network including a Fourier feature mapping module as a meta-model; map the physical coordinate features into high-frequency phase features through the Fourier feature mapping module, and concatenate them with the meta-features, then input them into the meta-model; Meta-model training module: Constructs a hybrid loss function, which includes a data-driven term for constraining the numerical errors of the real and imaginary parts of the complex echo, and a physical-driven term for constraining the consistency of the echo amplitude energy distribution; The meta-model is trained on the training set using the hybrid loss function, and the meta-model parameters are updated through backpropagation; Prediction module: Retrains the base model using training set data, inputs the data from the test set into the trained base model and meta-model, outputs the final complex echo prediction value, and performs ISAR imaging.
[0012] A computer storage medium storing a readable program that, when executed, instructs a computing device to perform the ISAR small-sample fast imaging method described above based on stacked complex neural networks.
[0013] An electronic device includes: a processor, a memory, a communication interface, and a communication bus, wherein the processor, the memory, and the communication interface communicate with each other through the communication bus; The memory is used to store at least one executable instruction, which causes the processor to perform operations corresponding to the ISAR small sample fast imaging method based on stacked complex neural networks described above.
[0014] A computer program product includes computer instructions that instruct a computing device to perform operations corresponding to the ISAR small-sample fast imaging method based on stacked complex neural networks described above.
[0015] The beneficial effects of this invention are: 1. This invention utilizes a stacked integrated base model to extract robust contour features and uses a complex element model to repair high-frequency details, significantly improving prediction accuracy under small sample conditions.
[0016] 2. This invention, through a fully complex network structure, strictly maintains the phase coupling relationship between the real and imaginary parts of the radar signal during propagation, thus avoiding phase distortion caused by real networks.
[0017] 3. This invention introduces Fourier feature mapping to effectively fit the high-frequency oscillation components of radar echoes. Combined with physically driven amplitude envelope constraints, it effectively eliminates artifacts and light spots in imaging and improves image focus. Attached Figure Description
[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0019] Figure 1 This is a flowchart of a fast ISAR small-sample imaging method based on stacked complex neural networks; Figure 2 It is based on a stacked complex neural network structure diagram; Figure 3 It is a geometric diagram of a bullet target; Figure 4 It is a BP imaging reconstruction and comparison based on dynamic ensemble machine learning; Figure 5 It is a BP imaging reconstruction and comparison based on stacked complex neural networks. Detailed Implementation
[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0021] Example 1 like Figure 1 As shown, the ISAR small-sample fast imaging method based on stacked complex neural networks includes the following steps: S1. Obtain raw ISAR radar echo data, construct a sample set and divide it into a training set and a test set; perform multi-dimensional feature extraction on the sample set, and construct an enhanced feature vector containing physical coordinate features and local spatial statistical features; The process of extracting multidimensional features from a sample set includes: (1) Constructing and normalizing the basic coordinate grid. Construct a two-dimensional grid based on the input frequency array and azimuth array. Use the meshgrid function to generate a frequency grid matrix and an azimuth grid matrix covering all sampling points. Perform Min-Max normalization on the frequency and azimuth coordinates, mapping them to the [0, 1] interval to eliminate dimensional differences and obtain normalized frequency and normalized azimuth.
[0022] (2) Extract physical coordinate features. For each sampling point, calculate the following 5-dimensional basic features: Frequency coordinates: Original frequency grid values.
[0023] Azimuth coordinates: Original azimuth grid values.
[0024] Frequency squared: The squared value of the frequency coordinate, used to capture second-order nonlinear relationships.
[0025] Azimuth square: The square value of the azimuth coordinate.
[0026] Interaction term: The product of frequency and azimuth angle, used to characterize the coupling effect between two physical dimensions.
[0027] (3) Extract local spatial statistical features. Local spatial statistical features are centered on the current sampling point and within a preset size (e.g., Within a sliding window, the local mean and local variance of the echo amplitude are calculated. Frequency gradient: the forward difference gradient along the frequency axis. Azimuth gradient: the forward difference gradient along the azimuth axis. Global mean: the arithmetic mean of the amplitudes across the entire sample set. Phase variance: the variance of the phase across the entire sample set.
[0028] Enhanced feature vectors specifically include: Physical coordinate characteristics include: frequency, azimuth, the square of the frequency, the square of the azimuth, and the cross product of frequency and azimuth. Local spatial statistical features include: local mean, local variance, gradient along the frequency direction, gradient along the azimuth direction, global mean, and phase variance; Among them, the local spatial statistical features are centered on the current sampling point, within a preset size (e.g., Within a sliding window, the local mean and local variance of the echo amplitude are calculated. To prevent data leakage in the test set, the statistical features extracted from the test set data are forcibly filled with the statistical mean of the corresponding position in the training set. The values of the local spatial statistical features in the feature vector are calculated values of the actual sampling points for the training set samples, and are statistically expected values of similar features in the training set for the test set samples. Furthermore, the feature vector does not contain any original sampling values directly derived from the echo amplitude or phase.
[0029] S2 employs a stacked ensemble strategy to construct a base model library containing multiple heterogeneous machine learning algorithms; it uses K-fold cross-validation to divide the training set, and performs K-fold cross-validation to train the base model for the real and imaginary parts of the echo, generating out-of-bag prediction values, which are then used as meta-features. The training set is divided into K subsets using K-fold cross-validation, with each subset maintaining as much data distribution consistency as possible. One subset is selected as the validation set. The model is trained on the K-1 subsets and validated on the remaining subset. The performance metric for each validation is calculated, and this process is repeated K times to obtain K models and corresponding K performance evaluation metrics. Finally, a comprehensive evaluation of the model performance is obtained, avoiding dependence on specific data partitions and improving the stability and reliability of model evaluation.
[0030] The specific steps of building a base model library containing multiple heterogeneous machine learning algorithms using a stacked integration strategy include: (1) Selection and definition of heterogeneous base models: In order to make full use of the inductive bias of different algorithms to improve the generalization ability of the model, the base models are selected according to the principle of "heterogeneity". The constructed base model library contains the following three categories of significantly different machine learning regression algorithms: Linear regression model: As a baseline model, it is used to capture the global linear trend in radar echo data. Its advantages are high computational efficiency and low risk of overfitting, and it can provide stable low-frequency component predictions for ensemble models.
[0031] Support Vector Regression (SVR) model: This model uses radial basis functions as kernel functions to map low-dimensional inputs to a high-dimensional space. It focuses on capturing nonlinear relationships in small sample data and exhibits good robustness to noise, making it suitable for handling nonlinear distortions in radar signals.
[0032] Random Forest Regression Model: This model integrates multiple decision trees based on a Bagging strategy. It excels at handling high-dimensional features and complex interactions between features (such as the coupling term between frequency and azimuth) and can effectively extract local abrupt changes in echoes.
[0033] (2) Initialization of the Dual-Channel Independent Model Library: Considering the characteristics of complex radar echo data, instead of directly processing complex numbers, a "real-imaginary decoupling" strategy is adopted to construct two independent base model libraries. Real Part Model Library: Instantiates the three algorithms mentioned above, specifically for fitting the real part of the echo signal. Imaginary Part Model Library: Similarly, instantiates the three algorithms mentioned above, specifically for fitting the imaginary part of the echo signal. The two sets of model libraries do not interfere with each other, and the parameters are updated independently, thus avoiding mutual interference caused by differences in the distribution of real and imaginary part data.
[0034] (3) Data partitioning and training for K-fold cross-validation: The training set is partitioned using K-fold cross-validation (e.g., K=5). The training data is randomly shuffled and then divided into K non-overlapping subsets.
[0035] Validation by partitioning: In each iteration, one subset is selected as the validation set, and the remaining K-1 subsets are selected as the training set. This process ensures that each subset has a chance to become the validation set, and that the data distribution of the training set and the validation set is kept as consistent as possible.
[0036] Generate out-of-bag (OOF) predictions: Train each base model in the real and imaginary part model libraries on K-1 training subsets. Use the trained base models to make predictions on the reserved validation subset and record the prediction results.
[0037] Looping and concatenation: Repeat the above process K times until all subsets have been predicted once. Concatenate the validation set predictions generated from the K iterations in the original index order to form the complete out-of-bag predictions.
[0038] (4) Construction of Meta-Features: The out-of-bag predictions are used as meta-features. For each sample, the base model library generates a total of 6 predictions (real part predictions of 3 models + imaginary part predictions of 3 models), which constitute the input of the Level-1 meta-model.
[0039] The base models in the base model library include at least: Linear Regression, Support Vector Regression (SVR), and Random Forest Regression; the base models are trained under a K-fold cross-validation framework (e.g., K=5), and the generated preliminary predictions are out-of-fold (OOF) predictions.
[0040] Independent prediction channels are established for the real and imaginary parts of the echo data. In each fold, a base model is trained using K-1 data points, and validated on the remaining data point to generate OOF (Out-of-Flight) prediction values. All OOF prediction values are then concatenated to form meta-features.
[0041] Specifically, the process of dividing the training set using K-fold cross-validation and training base models in the base model library for the real and imaginary parts of the echo separately, and generating OOF predictions, includes: Data partitioning: Randomly divide the training set samples into K non-overlapping subsets (e.g., K=5).
[0042] Cyclic prediction: Independent prediction channels are established for the real and imaginary parts of the echo data. For each base model, K iterations are performed: each iteration selects one subset as the validation set and the remaining K-1 subsets as the training set. The model is trained using the training set, and predictions are made on the validation set, with the prediction results filled into the corresponding positions of the subsets.
[0043] Feature concatenation: After all subsets have been predicted, the predicted values generated by base models such as linear regression, SVR, and random forest in the real and imaginary channels are concatenated along the feature dimensions to form the final meta-features. This process ensures that each value in the meta-features comes from validation data that the model has not seen, effectively preventing data leakage.
[0044] S3 constructs a fully complex neural network (CVNN) as a meta-model, which integrates a Fourier feature mapping module. The physical coordinate features in the enhanced feature vector are mapped to high-frequency phase features through the Fourier feature mapping module, and then concatenated with the meta-features produced by S2 as the complex domain input of the meta-model. To enable the meta-model to fit the high-frequency oscillation components of the radar echo, a Fourier feature mapping module is introduced to map the low-frequency physical coordinate features to high-frequency phase features. The calculation formula is as follows: in, For normalized frequency and azimuth coordinate vectors, For a random projection matrix that follows a Gaussian distribution and is not trainable, This is the high-frequency phase eigenvector output; this mapping enables the meta-model to fit the high-frequency oscillation components of the radar echo.
[0045] like Figure 2 As shown, a fully complex neural network (CVNN) specifically includes: a multi-source input fusion layer, a complex feature extraction hidden layer, and a physically consistent output layer; wherein: Multi-source input fusion layer: This layer serves as the network's input interface and is configured to receive three data streams. The first data stream comes from the feature vectors generated by the feature extraction module; the second data stream comes from the set of out-of-bag predictions generated by all base models in the base model library for the real part of the echo; and the third data stream comes from the set of out-of-bag predictions generated by all base models in the base model library for the imaginary part of the echo.
[0046] Complex Feature Extraction Hidden Layer: This module contains several cascaded complex linear processing units that perform complex network operations. This layer uses feature vectors to rotate and scale the real and imaginary part predictions provided by the base model. The complex operation structure ensures that the real and imaginary parts remain coupled throughout the propagation process, thereby repairing the phase consistency lost by the base model due to independent training.
[0047] Physically Consistent Output Layer: The network terminates at a complex output node, which outputs the final corrected complex echo prediction value. This layer not only outputs numerical results but also establishes a constraint relationship with the true label through a physics-driven loss function.
[0048] Complex network operations: In the fully complex neural network described above, the weights, biases, and activation functions of the network layers are all defined in the complex domain. Complex linear layers define weights... and input Its forward propagation operation follows the rules of complex multiplication: Among them, subscript and Let represent the real and imaginary parts, respectively; W be the weight matrix; and x be the input feature vector. The bias is Output, which is the result of the linear transformation.
[0049] S4, construct a hybrid loss function, which includes a data-driven term for constraining the numerical errors of the real and imaginary parts of the complex echo, and a physical-driven term for constraining the consistency of the echo amplitude energy distribution; use the hybrid loss function to train the meta-model on the training set, and update the meta-model parameters through backpropagation; The hybrid loss function is defined as follows: in, This represents the total mixed loss function value. This is a balancing coefficient used to adjust the weighting of the physics-driven terms in the total loss. This is a data-driven term used to constrain the numerical errors (such as mean square error, MSE) of the real and imaginary parts of the complex echo. This is a physics-driven term used to constrain the envelope distribution of echo amplitude (such as amplitude L1 norm error), forcing the network to learn the correct energy distribution and eliminate image smudges.
[0050] S5 retrains the base model using the training set data, inputs the data to be predicted (i.e., the test set) into the trained base model and meta-model, outputs the final complex echo prediction value, and performs ISAR imaging.
[0051] In this step, the test set is defined as the data to be predicted that the radar system failed to acquire in real-world application scenarios and needs to be recovered by the algorithm. Its purpose is twofold: first, as independent samples not involved in training, it verifies the model's generalization prediction accuracy for new data; second, it receives the prediction outputs of the trained base model and complex model, filling in the sparse gaps in the echo data matrix, thus providing complete full-aperture complex data support for subsequent ISAR high-resolution imaging, ensuring that the final image eliminates sidelobe interference and blurring caused by missing data.
[0052] After the meta-model training is completed, all base models in S2 are retrained using the full training data to obtain the best generalization performance. The data to be predicted is input into the trained base models to obtain preliminary predictions, and then input into the trained meta-model to output the final complex echo prediction values. Finally, the back projection (BP) algorithm is used to perform inverse synthetic aperture radar (ISAR) imaging on the predicted complex echo data to obtain high-resolution target scattering images.
[0053] Based on a similar inventive concept, embodiments of the present invention also provide a computer storage medium storing a readable program that, when run by a processor, can execute the above-described ISAR small-sample fast imaging method based on stacked complex neural networks.
[0054] Based on a similar inventive concept, this invention provides an electronic device, including: a processor, a memory, a communication interface, and a communication bus, wherein the processor, the memory, and the communication interface communicate with each other through the communication bus; The memory is used to store at least one executable instruction, which causes the processor to perform the operation corresponding to the above-described ISAR small sample fast imaging method based on stacked complex neural networks.
[0055] Based on a similar inventive concept, embodiments of the present invention also provide a computer program product, including computer instructions, which instruct a computing device to perform the operations corresponding to the above-described ISAR small sample fast imaging method based on stacked complex neural networks.
[0056] Example 2 In this embodiment, the method described in this invention is used to analyze an ISAR image of a bullet head model.
[0057] In this embodiment, the algorithm model and feature parameters used are fixed as follows: Feature extraction: For each sampling point, a fixed 10-dimensional enhanced feature vector is constructed, including frequency, azimuth, the square of the frequency, the square of the azimuth, and the cross product of frequency and azimuth. For the training set, local mean, local variance, frequency gradient, azimuth gradient, global mean, and phase variance are calculated; for the test set, the statistical mean of the training set is forcibly used to fill the gaps to prevent information leakage.
[0058] Base model library: Linear regression uses default parameters and no regularization. Support vector regression uses radial basis function as the kernel function and penalty coefficient C=1.0. Random forest: The number of decision trees is set to 100, the maximum depth is set to automatic expansion, and the random seed is fixed at 42.
[0059] Complex Neural Network: Contains two complex fully connected layers, with 64 neurons in each layer, and uses complex ReLU as the activation function.
[0060] Training hyperparameters: The optimizer uses the Adam algorithm, the learning rate is set to 0.002, and the weight coefficient of the physics term in the mixed loss function is set to 1.0.
[0061] like Figure 3 As shown, a 1m high bullet model was simulated using FEKO software. 20% of the input data was selected as the training set to train the model, and its performance was evaluated on the remaining 80% of the test set. ISAR echo data of a set of bullet targets were tested, with a center frequency of 3GHz and a resolution of 0.075m × 0.032m. ISAR images obtained from the original simulation data and ensemble machine learning prediction data are shown below. Figure 4 As shown, the ISAR image obtained from the original simulation data and the predicted data from the stacked ensemble network is as follows: Figure 5 As shown. From Figure 4 and Figure 5 As can be seen from the data, while the image predicted by the ensemble machine learning model restores the main bright structures in the center of the image, the image appears very blurry. The clear radial stripes (detailed textures) in the original image are lost here, turning into smooth color blocks. This indicates that the model failed to capture high-frequency details or phase information well. The present invention, by stacking complex neural networks, effectively preserves the radial stripes and edge sharpness of the original image.
[0062] Example 3 In this embodiment, a fast ISAR small-sample imaging system based on stacked complex neural networks is proposed, specifically including: Data acquisition and feature extraction module: acquire raw ISAR radar echo data, construct a sample set and divide it into training and test sets; perform multi-dimensional feature extraction on the sample set, and construct an enhanced feature vector containing physical coordinate features and local spatial statistical features; Meta-feature generation module: It adopts a stacked ensemble strategy to build a base model library containing multiple heterogeneous machine learning algorithms; it uses K-fold cross-validation to divide the training set, and performs K-fold cross-validation to train the base model for the real and imaginary parts of the echo respectively, generating out-of-bag prediction values, which are used as meta-features; Feature fusion module: Construct a fully complex neural network including a Fourier feature mapping module as a meta-model; map the physical coordinate features into high-frequency phase features through the Fourier feature mapping module, and concatenate them with the meta-features, then input them into the meta-model; Meta-model training module: Constructs a hybrid loss function, which includes a data-driven term for constraining the numerical errors of the real and imaginary parts of the complex echo, and a physical-driven term for constraining the consistency of the echo amplitude energy distribution; The meta-model is trained on the training set using the hybrid loss function, and the meta-model parameters are updated through backpropagation; Prediction module: Retrains the base model using training set data, inputs the data to be predicted (i.e., the data in the test set) into the trained base model and meta-model, outputs the final complex echo prediction value, and performs ISAR imaging.
[0063] The methods of the present invention can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD-ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code originally stored on a remote recording medium or a non-transitory machine-readable medium and subsequently stored on a local recording medium, downloaded via a network. Thus, the methods described herein can be processed by software stored on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that the computer, processor, microprocessor controller, or programmable hardware includes storage components (e.g., RAM, ROM, flash memory, etc.) capable of storing or receiving software or computer code that, when accessed and executed by the computer, processor, or hardware, implements the methods described herein. Furthermore, when a general-purpose computer accesses the code used to implement the methods shown herein, the execution of the code transforms the general-purpose computer into a dedicated computer for performing the methods shown herein.
[0064] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.
Claims
1. A fast ISAR imaging method for small samples based on stacked complex neural networks, characterized in that, Includes the following steps: Obtain raw ISAR radar echo data, construct a sample set and divide it into a training set and a test set; perform multi-dimensional feature extraction on the sample set, and construct an enhanced feature vector containing physical coordinate features and local spatial statistical features; A stacked ensemble strategy is adopted to build a base model library containing multiple heterogeneous machine learning algorithms; the training set is divided using K-fold cross-validation, and the base model is trained by K-fold cross-validation on the real and imaginary parts of the echo, generating out-of-bag prediction values, which are used as meta-features. A fully complex neural network including a Fourier feature mapping module is constructed as a meta-model; the physical coordinate features are mapped to high-frequency phase features through the Fourier feature mapping module, and then concatenated with the meta-features and input into the meta-model; A hybrid loss function is constructed, which includes a data-driven term for constraining the numerical errors of the real and imaginary parts of the complex echo, and a physical-driven term for constraining the consistency of the echo amplitude energy distribution. The meta-model is trained on the training set using the hybrid loss function, and the meta-model parameters are updated through backpropagation. The base model is retrained using the training set data, and the test set data is input into the trained base model and meta-model to output the final complex echo prediction value and perform ISAR imaging.
2. The ISAR small-sample fast imaging method based on stacked complex neural networks according to claim 1, characterized in that, The enhanced feature vector includes: Physical coordinate characteristics include: frequency, azimuth, the square of the frequency, the square of the azimuth, and the cross product of frequency and azimuth. Local spatial statistical features include: local mean, local variance, gradient along the frequency direction, gradient along the azimuth direction, global mean, and phase variance.
3. The ISAR small-sample fast imaging method based on stacked complex neural networks according to claim 1, characterized in that, The base models in the base model library include at least: linear regression model, support vector regression model, and random forest regression model.
4. The ISAR small-sample fast imaging method based on stacked complex neural networks according to claim 1, characterized in that, The formula by which the Fourier feature mapping module maps physical coordinate features to high-frequency phase features is: in, For normalized frequency and azimuth coordinate vectors, For a random projection matrix that follows a Gaussian distribution and is not trainable, This is the high-frequency phase eigenvector of the output.
5. The ISAR small-sample fast imaging method based on stacked complex neural networks according to claim 1, characterized in that, The weights, biases, and activation functions of the network layers in the fully complex neural network are all defined in the complex domain; among them, the weights of the complex linear layers are defined. and input Its forward propagation operation follows the rules of complex multiplication: Among them, subscript and Let represent the real and imaginary parts, respectively; W be the weight matrix; and x be the input feature vector. The bias is Output, which is the result of the linear transformation.
6. The ISAR small-sample fast imaging method based on stacked complex neural networks according to claim 1, characterized in that, The hybrid loss function is: in, This represents the total mixed loss function value; This is a balancing coefficient used to adjust the weighting of the physics-driven terms in the total loss. This is a data-driven term used to constrain the numerical error of the real and imaginary parts of the complex echo; This is a physical driving term used to constrain the envelope distribution of the echo amplitude.
7. A rapid ISAR imaging system for small samples based on stacked complex neural networks, comprising the method described in any one of claims 1-6, characterized in that, include: Data acquisition and feature extraction module: acquire raw ISAR radar echo data, construct a sample set and divide it into training and test sets; perform multi-dimensional feature extraction on the sample set, and construct an enhanced feature vector containing physical coordinate features and local spatial statistical features; Meta-feature generation module: It adopts a stacked ensemble strategy to build a base model library containing multiple heterogeneous machine learning algorithms; it uses K-fold cross-validation to divide the training set, and performs K-fold cross-validation to train the base model for the real and imaginary parts of the echo respectively, generating out-of-bag prediction values, which are used as meta-features; Feature fusion module: Construct a fully complex neural network including a Fourier feature mapping module as a meta-model; map the physical coordinate features into high-frequency phase features through the Fourier feature mapping module, and concatenate them with the meta-features, then input them into the meta-model; Meta-model training module: Constructs a hybrid loss function, which includes a data-driven term for constraining the numerical errors of the real and imaginary parts of the complex echo, and a physical-driven term for constraining the consistency of the echo amplitude energy distribution; The meta-model is trained on the training set using the hybrid loss function, and the meta-model parameters are updated through backpropagation; Prediction module: Retrains the base model using training set data, inputs the data from the test set into the trained base model and meta-model, outputs the final complex echo prediction value, and performs ISAR imaging.
8. A computer storage medium storing a readable program, characterized in that, When the program runs, it can instruct the computing device to perform the ISAR small sample fast imaging method based on stacked complex neural networks as described in any one of claims 1-6.
9. An electronic device, characterized in that, include: The processor, memory, communication interface, and communication bus are provided, wherein the processor, memory, and communication interface communicate with each other via the communication bus. The memory is used to store at least one executable instruction, which causes the processor to perform the operation corresponding to the ISAR small sample fast imaging method based on stacked complex neural networks as described in any one of claims 1-6.
10. A computer program product comprising computer instructions, characterized in that, The computer instructions instruct the computing device to perform the operations corresponding to the ISAR small sample fast imaging method based on stacked complex neural networks as described in any one of claims 1-6.