A sea surface sparse target super-resolution imaging method based on radar echo multi-feature divide-and-conquer

Abstract

The application discloses a radar echo multi-feature divide-and-conquer sea surface sparse target super-resolution imaging method, and belongs to the field of radar detection and imaging. The application firstly converts the echo to four types of feature spaces of amplitude, phase, frequency and residence time by using a multi-feature complex network (MF-CNET), and processes by an attention UNet structure to effectively distinguish sea clutter and target echo; then, the separated clutter and target components are subjected to sparse Bayesian learning based on data division to perform Bayesian parameter estimation, so that the estimation accuracy is improved; finally, a parameter pruning solver is introduced to eliminate invalid parameters in the iterative super-resolution process, so that the calculation cost is reduced. Compared with the existing method, the method has superior anti-sea clutter capability and target resolution capability, and can obtain clearer and more reliable sea surface target imaging results.

Description

Technical Field

[0001] This invention belongs to the field of radar detection and imaging, and is particularly suitable for super-resolution imaging of sparse sea surface targets by real aperture radar. Specifically, it relates to a super-resolution imaging method for sparse sea surface targets based on the division and conquer of multiple features of radar echo. Background Technology

[0002] Real aperture radar uses a scanning antenna for wide-area detection and is widely used in military and civilian fields, but its angular resolution is limited by the antenna size and is usually low.

[0003] To improve the angular resolution of real aperture radar, M. Bao et al. proposed a super-resolution method based on deconvolution, which overcomes the limitations of physical antenna aperture by inverting the convolution model of antenna pattern and target response. However, deconvolution is an ill-posed problem, highly sensitive to clutter and noise, and its imaging performance is more easily affected and significantly degraded in sea clutter environments. Subsequently, H. Yang et al. proposed a super-resolution method based on a Bayesian framework, which enhances clutter suppression by explicitly modeling clutter in the likelihood function, thus achieving a significant improvement in sea surface super-resolution imaging. However, when directly applied to mixed echo data with aliased clutter and target signals, it severely impairs the accurate estimation of Bayesian model parameters, ultimately limiting the overall imaging performance. Furthermore, X. Tuo et al. used truncated singular value decomposition to suppress noise components, and then improved resolution under low signal-to-noise ratio conditions through L1-based sparse recovery. However, since it mainly relies on a single explicit eigenrank, it is difficult to distinguish sea clutter and targets in low signal-to-noise ratio environments. Summary of the Invention

[0004] To address the problems of existing methods in the aforementioned technical background, such as clutter sensitivity, insufficient resolution, and reliance on a single explicit feature leading to difficulty in distinguishing sea clutter from targets in low signal-to-clutter ratio environments, this invention proposes a super-resolution imaging method for sparse targets on the sea surface based on the division and conquer of multiple features of radar echoes.

[0005] The solution of this invention is as follows: First, a Multi-Feature Complex Network (MF-CNET) is used to transform complex echoes into four feature spaces: amplitude, phase, frequency, and residence time. These are then processed using an attention-based UNet structure to distinguish between sea clutter and target echoes. Next, sparse Bayesian learning based on data divide-and-conquer is applied to the separated clutter and target components for Bayesian parameter estimation, improving estimation accuracy. Finally, a parameter pruning solver is introduced to remove invalid parameters during the iterative super-resolution process, reducing computational overhead. Compared with existing methods, this invention exhibits superior resistance to sea clutter and target resolution capabilities, resulting in clearer and more reliable sea surface target imaging.

[0006] The specific technical solution provided by this invention is as follows:

[0007] A super-resolution imaging method for sparse targets on the sea surface based on the multi-feature division and control of radar echoes, characterized by the following steps:

[0008] Step 1: The radar transmits a linear frequency modulated signal toward the target area, acquires the echo signal after pulse compression and range migration correction, and then obtains the azimuth echo signal model based on the convolution of the antenna pattern and the scattering coefficient.

[0009] Step 2: Based on the target-clutter divide-and-conquer complex multi-feature enhancement network, target echo-clutter separation is performed; specifically, features in four spaces—amplitude space, phase space, frequency space, and dwell time space—are extracted through a multi-layer convolutional network, and then enhanced and fused through the U-net network to obtain the target echo;

[0010] Step 3: Sparse Bayesian learning super-resolution imaging based on separated data;

[0011] Construct the probability density function of noise clutter, assume that the accuracy of noise clutter follows a gamma distribution, obtain the prior information of target echo based on complex Gaussian distribution, and introduce the prior information of target scattering coefficient to describe the forward-looking scene.

[0012] The accuracy of the target scattering coefficient is modeled separately using a gamma distribution; the posterior distributions of the accuracy of the target scattering coefficient, noise clutter, and target scattering coefficient are derived using Bayes' rule; and then the three hyperparameters are iteratively solved.

[0013] Step 4: Hyperparameter pruning solver; Use a fixed threshold to remove redundant elements from the parameter active set, and then iteratively solve the three hyperparameters.

[0014] Furthermore, the expression for the azimuth echo signal model is as follows:

[0015]

[0016] in, For azimuth echo, This is the antenna pattern matrix. The target scattering coefficient, This represents the variation in sea surface clutter scattering at different times. This indicates the motion phase modulation at the same position during beam scanning. It represents the Hadamah accumulation. This represents the convolution operation. For antenna pattern function, For slow time, It is noise.

[0017] Furthermore, the complex multi-feature enhancement network for target-clutter divide-and-conquer is specifically as follows:

[0018] Each spatial feature channel extracts features at different depths through a multi-layer convolutional structure. Then, the four spatial features are concatenated and processed through the U-net network to complete feature filtering, aggregation, and channel dimension transformation.

[0019] Each convolutional layer consists of two consecutive 3×3 convolutional operations, interspersed with ReLU activation functions;

[0020] Each spatial domain is specified to contain 6 explicit feature channels and 10 implicit feature channels. The explicit feature channels include local entropy, local variance, local rate of change, local contrast, normalization magnitude, and texture features.

[0021] The complex multi-feature enhancement network for target-clutter divide-and-conquer is trained using a composite loss function.

[0022] The composite loss function includes target amplitude loss, target frequency-phase loss, and dwell time loss based on the target echo.

[0023] Furthermore, step 3 is detailed as follows:

[0024] Construct the probability density functions for noise and clutter:

[0025]

[0026] in, express The probability density function, The probability density function representation of the complex Gaussian distribution. Indicates noise and clutter. Indicates a complex Gaussian distribution. The precision used to represent clutter and noise. Represents variance. Represent the identity matrix; assume It follows a gamma distribution, and the accuracy of clutter and noise is obtained based on the gamma distribution. Shape parameters and scale parameters ,set up We obtain a generalized super-prior that does not affect the final estimate;

[0027] Based on the formula for the complex Gaussian distribution, the target echo signal is derived. for:

[0028]

[0029] Introducing a complex Gaussian distribution as the target scattering coefficient Use prior information to describe the forward-looking scene:

[0030]

[0031] in, , The precision of the target scattering coefficient. Indicates the multiplication symbol. It is the component precision vector The The element represents the target at the [number]th [node]. The accuracy of each relevant part For the target scenario Target scattering coefficients at various azimuth angles This indicates that the vector is diagonalized; β is modeled as an independent gamma distribution, yielding the shape parameters of the gamma distribution of β. and scale parameters The accuracy of the target scattering coefficient Marginalize the data, then calculate the overall prior value;

[0032] Using Bayes' theorem, the posterior distributions of the target scattering coefficient, the accuracy of noise clutter, and the accuracy of the target scattering coefficient are derived. The Expectation-Maximization (EM) algorithm is then used to solve for these distributions, yielding the final iterative expression for updating the target scattering coefficient.

[0033]

[0034]

[0035]

[0036] in, Indicates the number of azimuth sampling points. , , The trace operation is indicated by the superscript U, which indicates the Hermitian transpose.

[0037] Furthermore, step 4 is detailed as follows:

[0038] First, we define the active set of three hyperparameters, where the accuracy of the target scattering coefficients is... active The set is represented as follows:

[0039]

[0040] Remove redundant elements from the active set of parameters using a fixed threshold:

[0041]

[0042] in, It is the pruning threshold. express A set of redundant elements;

[0043] The corresponding redundant target scattering elements and antenna pattern redundancy elements will also be eliminated. This process can be formally represented as:

[0044]

[0045]

[0046] in, and Let x and H represent the active sets of parameters, respectively, for the target scattering coefficient x and the antenna pattern matrix H. and These represent the sets of redundant elements for the target scattering coefficient x and the antenna pattern matrix H, respectively. This represents the parameter pruning mapping relationship related to the target scattering coefficient after parameter pruning. This represents the parameter pruning mapping relationship related to antenna pattern elements after parameter pruning. The first element of the antenna pattern matrix represents the first element of the antenna pattern matrix. One element;

[0047] At this point, the iterative solution is updated to:

[0048]

[0049]

[0050]

[0051] in, This represents the set of elements after pruning in each iteration.

[0052] The beneficial effects of this invention are as follows:

[0053] First, the complex echo is transformed into four feature spaces—amplitude, phase, frequency, and dwell time—using MF-CNET to enhance the distinguishability between the target and sea clutter. Then, an attention-enhanced UNet architecture is used to process the multi-space representation, achieving effective separation of the target and clutter. Sparse Bayesian learning (SBL) is then combined to estimate Bayesian parameters for the separated clutter and target components, improving estimation accuracy. Finally, a parameter pruning solver is introduced to remove redundant parameters during the super-resolution iteration process, significantly reducing computational cost. Compared to existing methods, this invention demonstrates superior performance in clutter suppression and resolution enhancement, providing clearer and more reliable sea surface target imaging. It also addresses the problems of poor imaging performance and high computational cost associated with traditional methods under strong sea clutter. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the geometric model of a real aperture radar scanning the sea surface.

[0055] Figure 2 This is a schematic diagram of the framework of the method of the present invention.

[0056] Figure 3 This is a schematic diagram of the feature space expansion block.

[0057] Figure 4 This is a schematic diagram of the results of a super-resolution imaging simulation experiment.

[0058] Figure 5 This is a schematic diagram of imaging time for different data dimensions. Detailed Implementation

[0059] This invention is primarily verified using simulation experiments; all steps and conclusions are presented in [the relevant documentation / documentation]. The above verification is correct. The method of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0060] A super-resolution imaging method for sparse targets on the sea surface based on the multi-feature division and control of radar echoes includes the following steps:

[0061] Step 1: Establishing the sea surface target echo model;

[0062] The forward-looking scanning process of the radar and the geometric relationship between the radar and the target, as follows: Figure 1 As shown. The airborne platform travels at a constant speed. The radar moves while simultaneously transmitting a fixed-frequency linear frequency modulated signal to sequentially scan the area ahead. The radar elevation angle is... azimuth angle is After pulse compression and range migration correction, a high-resolution range echo can be obtained:

[0063]

[0064] in, At the speed of light, It is the imaginary unit. For noise, To save time, For slow time, The target scattering amplitude, For antenna pattern function, For signal bandwidth, Let be the distance pulse compression response function. The initial distance, For wavelength, This is the distance history. After range pulse compression, the range resolution becomes... .

[0065] However, in a sea surface scenario, the received echo consists of both the target response and sea clutter scattering. After converting the received echo signal to the range-angle domain, the azimuth echo within each range cell can be modeled as the convolution of the antenna pattern and the scattering coefficients, as expressed below:

[0066]

[0067] in, For azimuth echo, This is the antenna pattern matrix. The target scattering coefficient, This represents the variation in sea surface clutter scattering at different times. This indicates the motion phase modulation at the same position during beam scanning. It represents the Hadamah accumulation. This represents the convolution operation.

[0068] Step 2: Target echo-clutter separation;

[0069] To address the challenges posed by complex and difficult-to-suppress sea clutter, a super-resolution imaging method for sparse targets on the sea surface based on multi-feature divide-and-conquer of radar echoes is proposed. This method consists of three key components: a Complex Multi-Feature Enhancement Network (CMFE-NET) for target-clutter divide-and-conquer, a data-based divide-and-conquer sparse Bayesian learning (DD&C-based SBL) super-resolution imaging algorithm, and an efficient parameter pruning solver. A schematic diagram of the entire framework is shown below. Figure 2 As shown. MF-CNET is designed to effectively distinguish between targets and clutter. The core module of this network is the Feature Space Extension Block. Its main structural design is as follows. Figure 3 As shown.

[0070] In traditional image processing, super-resolution tasks typically rely on three RGB channels in the real domain. However, radar echo data is inherently different; it contains complex-valued information and lacks RGB features. Directly inputting this single-channel complex data into the network limits its receptive field and may hinder effective feature extraction.

[0071] In amplitude space, target echoes are often masked by strong clutter. However, unlike the randomness of sea clutter, targets possess structured statistical characteristics. Therefore, features such as local amplitude variance and entropy are effective distinguishing factors. In phase space, ships exhibit stable scattering characteristics due to their rigid structure, while sea clutter consists of randomly distributed dynamic scatterers, whose phase characteristics are affected by wave height, ocean currents, and wind, resulting in violent fluctuations. Therefore, phase-based features can enhance the separability of targets from clutter. In frequency space, moving targets such as ships, due to their near-uniform motion during rapid beam scanning, produce a stable Doppler shift and a concentrated spectrum; conversely, sea clutter, due to its random low-speed motion, exhibits a lower or near-zero Doppler shift and a more pronounced spectrum broadening, thus enabling effective spectral differentiation.

[0072] To further utilize radar scanning characteristics, a dwell time space is introduced, which represents the duration for which the beam illuminates the scattering object. Dwell time The calculation formula is as follows:

[0073]

[0074] in, Indicates the main lobe width of the beam. Indicates the actual scanning speed. Indicates the mechanical scanning speed. Indicates pitch angle, This represents the distance between the target and the radar. Due to the non-stationary nature of the sea surface, beam modulation may become discontinuous if clutter changes more rapidly than the scan duration. Therefore, the variance of the dwell time can be used as a distinguishing feature, and the antenna pattern is incorporated into the network to construct this spatial distribution.

[0075] according to Figure 3 The network structure shown extracts features from four spaces: amplitude space, phase space, frequency space, and dwell time space. Specifically, the feature channels in each space are expanded through two consecutive 3×3 convolution operations, interspersed with ReLU activation functions. Furthermore, this method employs a multi-level convolutional structure to extract features at different depths, thereby preserving both deep and shallow features and ensuring that the target echo is not lost. This embodiment uses a 3-layer convolutional structure. To optimize computational efficiency and reduce feature redundancy, each spatial domain is designated to contain 6 explicit feature channels, including local entropy, local variance, local rate of change, local contrast, normalized amplitude, and texture features. In addition, each spatial domain is allocated 10 additional implicit feature channels. Therefore, each spatial region contains a total of 16 channels, resulting in a total of 64 feature channels.

[0076]

[0077]

[0078] in, Indicates the first The first space Layer feature information ( , ), Represents 64-channel multi-feature data, the first The input data for each space is , Indicates the first The output of the layer, This means that the number of channels in the input feature is expanded from 1 channel to 16 channels through a convolution operation. This means merging the feature tensors along the channel direction to form a new feature tensor with more channels. , Indicates the first Feature information of each space.

[0079] Finally, multifaceted features from the four spatial domains are integrated and transmitted to the feature enhancement and fusion part of the network. This part adopts the U-net architecture, which incorporates a spatial attention mechanism to prioritize and enhance feature information related to the target echo. This design improves the efficiency of target feature extraction and sets skip connections at the corresponding matching upsampling and downsampling levels to mitigate the loss of key features during sampling. Finally, feature filtering, aggregation, and channel dimension transformation are completed through a channel attention mechanism and a two-layer convolutional structure.

[0080] In the process of separating clutter from the target, it is necessary to evaluate the feature representation capabilities of multiple spatial spaces. To effectively train MF-CNET, a composite loss function is designed to evaluate and balance the accuracy of the four feature space representations.

[0081] To ensure the accuracy of amplitude feature extraction, the target amplitude loss is defined in terms of modulus:

[0082]

[0083] in, It involves calculating the expectation of the loss function. This represents the L2 norm, which is used here to calculate vectors. 2-norm, It is the target echo output by the network. It is the target echo information marked.

[0084] To ensure the accuracy of frequency and phase space feature extraction, the target frequency-phase loss is defined in complex form:

[0085]

[0086] in, and These represent the operations of extracting the real part and the imaginary part, respectively.

[0087] To ensure the accuracy of dwell time feature extraction, a dwell time loss is defined based on the dwell time length:

[0088]

[0089] in, It is the beam dwell time of the stable scattering target in the marker. It is the dwell time of the target echo output by the network.

[0090] Therefore, the composite loss function is expressed as follows:

[0091]

[0092] in, , and Represents the normalized loss weights, and .

[0093] Step 3: Sparse Bayesian learning super-resolution imaging based on separated data;

[0094] To achieve enhanced resolution, the deconvolution problem related to the target scattering coefficient must be addressed. The aforementioned network has effectively separated clutter from target echoes, providing a solid data foundation for parameter estimation within the Bayesian model. This model inherently requires careful parameter selection, and the separated echoes mitigate the effects of echo aliasing, thereby improving the accuracy of the parameter estimation process. Therefore, this step introduces a data-divide-and-conquer sparse Bayesian learning method with adaptively learned parameters, aiming to improve the imaging performance of sea surface targets.

[0095]

[0096] in, Represents random variables The probability density function, The probability density function representation of the complex Gaussian distribution. Indicates noise and clutter. Indicates a complex Gaussian distribution. The precision used to represent clutter and noise. Represents variance. Let represent the identity matrix. Since the precision of noise and clutter is unknown, it is assumed to follow a gamma distribution:

[0097]

[0098] in, Represents the gamma distribution. Represents the gamma function. and These are the shape and scale parameters of parameter a. Let... We obtain a generalized prior that does not affect the final estimate. Combining this with the above equation, we can give an initial value for the clutter variance based on the clutter data. The specific process is as follows:

[0099] Based on the formula for the complex Gaussian distribution, the echo signal can be derived. for:

[0100]

[0101] Simultaneously, a complex Gaussian distribution is introduced as the target scattering coefficient. Use prior information to describe the forward-looking scene:

[0102]

[0103] in, , Indicates the precision of the target. Indicates the multiplication symbol. It is the component precision vector The The element represents the target at the [number]th [node]. The accuracy of each relevant part For observation data, This indicates that the vector is diagonalized. Given that most regions in a sparse scene lack targets, it is advantageous to employ a two-level hierarchical prior that is biased towards zero in most regions. To achieve this, [the following is implied:] Modeled as an independent gamma distribution:

[0104]

[0105] in, and These represent the shape and scale parameters of the β-gamma distribution, respectively. The separated clutter and target components can then be used to accurately estimate the parameters, thereby improving subsequent super-resolution imaging performance.

[0106] By adjusting parameters Marginalize the data, then calculate the overall prior value as follows:

[0107]

[0108] Wherein, probability density function yes The conjugate priors, To represent the target scene Target scattering coefficients at various azimuth angles Let be the likelihood function. Therefore, This can be derived analytically, and the result corresponds to the Student-t distribution. By appropriately selecting... and (For example, , The Student-t distribution will be... A distinct peak will form nearby, which gives the prior a strong zero bias, reflecting the sparsity characteristic.

[0109] Based on the established model structure, the posterior distribution of all unknown variables can be derived using Bayes' rule. Combining prior knowledge and observational data, the target scattering coefficient is estimated, and its expression is:

[0110]

[0111] The above equation is derived through Bayesian inference and solved using the Expectation-Maximization (EM) algorithm to obtain the final iterative expression for updating the target scattering coefficients:

[0112]

[0113]

[0114]

[0115] in, Indicates the number of azimuth sampling points. , , This indicates the trace operation, with the superscript U indicating the Hermitian transpose. When ( When the parameter update process converges (to a small positive value), the parameter update process converges.

[0116] Step 4: Hyperparameter pruning solver;

[0117] This step aims to improve the solution efficiency of DD&C-based SBL by introducing a parameter pruning strategy. Although MF-CNET can effectively separate clutter and highlight the target region, it may still leave noise and clutter components with minimal amplitude. These components, though weak, introduce redundant parameters, increase computational overhead, and have limited value to the super-resolution process. Furthermore, the posterior estimates of parameters related to clutter and noise tend to decay to zero throughout the iterative inference process, indicating their low correlation. To address this issue, this application implements a pruning mechanism for iteratively removing redundant parameters. In each iteration, redundant parameters in the antenna pattern measurement matrix and parameter vector are pruned. This adaptive reduction of model dimensionality not only reduces the computational burden but also accelerates convergence. By continuously optimizing the active parameter set, this method achieves a more efficient and focused super-resolution imaging process.

[0118] Define the active set of parameters as:

[0119]

[0120] Among them, each hyperparameter Prior information on the target scattering coefficient at each azimuth angle in the target scene. Indicates the target scenario The target scattering coefficients at various azimuth angles. Therefore, pruning redundant parameters is also pruning for azimuth angles without targets. The simplest pruning method is to remove redundant elements from the active parameter set using a fixed threshold:

[0121]

[0122] in, It is the pruning threshold. express A set of redundant elements;

[0123] During the parametric pruning solver process, redundant parameter elements corresponding to the azimuth angle information are removed, and corresponding redundant target scattering elements and antenna pattern redundant elements are also removed. This process can be formally represented as:

[0124]

[0125]

[0126] in, and Let x and H represent the active sets of parameters, respectively, for the target scattering coefficient x and the antenna pattern matrix H. and These represent the sets of redundant elements for the target scattering coefficient x and the antenna pattern matrix H, respectively. This represents the parameter pruning mapping relationship related to the target scattering coefficient after parameter pruning. This represents the parameter pruning mapping relationship related to antenna pattern elements after parameter pruning. The first element of the antenna pattern matrix represents the first element of the antenna pattern matrix. There are 10 elements. At this point, the iterative solution is updated to:

[0127]

[0128]

[0129]

[0130] in, This represents the set of elements pruned in each iteration. Through this iterative operation, the computational complexity of the super-resolution imaging process is gradually reduced. This gradual reduction not only accelerates the convergence of the iterative algorithm but also improves its overall computational efficiency. To ensure effective parameter pruning while avoiding over-elimination, the Bayesian Information Criterion (BIC) is introduced as a regularization constraint. BIC imposes a strict penalty on model complexity, thereby inherently promoting sparsity. This property is particularly suitable for the sparsity of sea surface targets. The formula for BIC is as follows:

[0131]

[0132] in, It is the likelihood function of the model. It is the number of parameters in the model (i.e., non-zero). (quantity) It represents the number of echo samples.

[0133] To achieve adaptive pruning, parameters close to zero are... Set the threshold to zero and recalculate the marginal log-likelihood of the model. If the BIC value decreases, prune relevant parameters to reduce model complexity; otherwise, retain these parameters to prevent over-pruning. This BIC-guided strategy effectively solves the threshold selection problem and promotes data-driven adaptive parameter pruning.

[0134] To verify the effectiveness of the method of this invention, five ship point targets were set in a sea surface scene, and sea clutter was modeled using a K-distribution to reflect the actual sea surface scattering. The forward scan parameters used in the simulation are summarized in Table 1.

[0135] Table 1: Simulation Forward Scanning Parameters

[0136] parameter numerical values carrier frequency 10GHz Pulse interval <![CDATA[2*10 -6 s <!-- 9 -->]]> bandwidth 30MHz Antenna scanning speed 60° / s Main lobe beamwidth 3° Pulse repetition frequency 1000Hz Platform speed 50m / s Scanning area ±10° Target distance 10km

[0137] Figure 4(a) shows the spatial location and intensity level of five sparse ship targets on the sea surface. Figure 4 (b) shows the sea scene we constructed. Figure 4 (c) shows the target echo received at a signal-to-clutter ratio of 5 dB. Due to limited resolution, two adjacent targets cannot be distinguished, and the presence of a large amount of sea clutter further obscures the target information. Figure 4 Figure (d) shows the imaging results obtained using the Bayesian super-resolution method with maximum a posteriori constraint (MAP-GG), where the target amplitude is significantly reduced and almost submerged in clutter, and there are also a large number of false targets in the scene. Figure 4 (e) in the figure shows the results of the L1 method based on rank decomposition (Rank-L1). Strong sea clutter and peak effects hinder the separation of the target from the background, resulting in the persistence of strong clutter points and the inability to distinguish the target. Figure 4 (f) shows the imaging results of the two-step regularization strategy L1 method (TSVD-L1). Although singular value truncation reduces the amplification effect of clutter, the target amplitude is still low and false alarms are still prominent. Figure 4 (g) in the figure shows the imaging results of the super-resolution method (DBR) based on the online detection and reconstruction framework. This method can effectively distinguish target points, but due to the influence of clutter intensity, a large number of false alarm areas appear, and there are also many false targets in the imaging results. Figure 4 (h) in the figure shows the imaging results of the sparse Bayesian learning method (SBL). Although the target is clearly distinguished, many high-intensity false targets appear in the image. Figure 4 Image (i) shows the imaging results of the Probabilistic Sparse Bayesian Learning (PSBL) method. Compared with the Sparse Bayesian Learning method, the Probabilistic Sparse Bayesian Learning method effectively suppresses background clutter, enhances the amplitude of the real target, and improves the overall scene clarity by adaptively eliminating redundant parameters. Figure 4 (j) in the figure demonstrates the results of multi-feature divide-and-conquer imaging without pruning (MF-CNET-SBL), which generates clutter-free images and fully resolves all five ship targets. Finally, Figure 4 Figure (k) shows the imaging results of this method, which combines a multi-feature complex network method and a pruning-based sparse Bayesian imaging method. Its imaging performance is comparable to that of the multi-feature complex network-sparse Bayesian learning method, while further enhancing clutter suppression capabilities and maintaining robust super-resolution capabilities for maritime targets.

[0138] Then, the imaging performance of the proposed method is quantitatively evaluated using the signal-to-noise ratio improvement, beam sharpening capability, mean square error, and imaging efficiency metrics. Beam sharpness ratio and mean square error are defined as follows:

[0139]

[0140]

[0141] in, and These represent the target half-power beamwidth before and after super-resolution, respectively. and These represent the original angle of the target and the angle of the target after imaging, respectively. Indicates the number of samples.

[0142] To more intuitively compare metrics such as signal-to-noise ratio, beam sharpness ratio, and mean square error, we conducted 50 Monte Carlo simulations, and the results are summarized in Table 2.

[0143] Table 2: Comparison of Monte Carlo Simulation Results

[0144] method SCR(dB) BSR(dB) MSE (dB) Bayesian Super-Resolution Method Based on Maximum A posteriori Generalized Gaussian Constraints -0.2037 18.2517 -13.5469 <![CDATA[L1 Method Based on Rank Decomposition]]> 2.8937 9.6914 -2.1494 <![CDATA[Truncated Singular Value Decomposition - L1 Method]]> 2.5645 14.8945 -24.4283 Super-resolution methods based on online detection and reconstruction framework 5.4445 12.5910 -18.4077 Sparse Bayesian learning method 5.1130 25.8583 -23.0856 Probabilistic Sparse Bayesian Learning Method 13.2936 25.1609 -23.2104 Multi-feature complex networks - sparse Bayesian learning method 38.0724 25.5692 -51.1758 The method proposed in this invention 38.7499 25.0019 -15.4782

[0145] Table 2 shows that, due to effective clutter filtering during detection, the super-resolution method based on the online detection and reconstruction framework slightly improves the signal-to-clutter ratio (SCR) to 5.4445 dB. The sparse Bayesian learning method exhibits strong target resolution capabilities, resulting in a significant reduction in both clutter and target energy, with minimal impact on the SCR. The probabilistic sparse Bayesian learning method effectively eliminates a large amount of redundant clutter information, thereby improving the SCR. The multi-feature complex network-sparse Bayesian learning method achieves a significant SCR improvement of 38.0724 dB due to its network-based divide-and-conquer approach. Notably, the proposed method achieves the highest SCR improvement, reaching 38.7499 dB.

[0146] Bayesian super-resolution method based on maximum a posteriori generalized Gaussian constraints, truncated singular value decomposition - The beam sharpening ratios of the proposed method and the super-resolution method based on the online detection and reconstruction framework are both between 10 dB and 20 dB. Methods related to sparse Bayesian learning methods all achieve beam sharpening ratios above 25 dB, with the sparse Bayesian learning method showing the highest beam sharpening ratio at 25.8583 dB. Although the proposed method has a slightly lower beam sharpening ratio of 25.0019 dB, it has the smallest mean square error (MSE) of -51.4782 dB. Among other methods, only the multi-feature complex network-sparse Bayesian learning method achieves an MSE below -50 dB, while the largest is based on rank decomposition. The method yielded a noise level of -2.1494 dB. Overall, these metrics demonstrate that the proposed method performs excellently in terms of signal-to-noise ratio improvement, super-resolution accuracy, and beam sharpening.

[0147] To illustrate the impact of the proposed network and pruning solver on improving imaging efficiency, we present the processing time for different matrix dimensions. Figure 5 Figure (a) shows the processing time of each method under different orientation dimensions when the distance dimension is fixed at 200. Clearly, the sparse Bayesian learning method has the lowest processing efficiency, while the proposed method has the highest. Notably, when the orientation dimension reaches 2000, the efficiency of the proposed method is 80 times that of the traditional sparse Bayesian learning method. As the orientation dimension increases, the processing efficiency of all methods gradually decreases, while the processing time of high-complexity methods increases explosively. Figure 5 Figure (b) shows the processing time of each method under different distance dimensions when the orientation dimension is fixed at 200. The sparse Bayesian learning method again exhibits the lowest processing efficiency, while the proposed method continues to maintain the highest efficiency. Specifically, at a distance dimension of 2000, the efficiency of the proposed method is 21 times that of the traditional sparse Bayesian learning method. With increasing distance dimension, the processing efficiency of all methods decreases linearly.

[0148] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A super-resolution imaging method for sparse targets on the sea surface based on the multi-feature divide-and-conquer approach of radar echoes, characterized in that, Includes the following steps: Step 1: The radar transmits a linear frequency modulated signal toward the target area, acquires the echo signal after pulse compression and range migration correction, and then obtains the azimuth echo signal model based on the convolution of the antenna pattern and the scattering coefficient. Step 2: Based on the target-clutter divide-and-conquer complex multi-feature enhancement network, target echo-clutter separation is performed; specifically, features in four spaces—amplitude space, phase space, frequency space, and dwell time space—are extracted through a multi-layer convolutional network, and then enhanced and fused through the U-net network to obtain the target echo; Step 3: Sparse Bayesian learning super-resolution imaging based on separated data; Construct the probability density function of noise clutter, assume that the accuracy of noise clutter follows a gamma distribution, obtain the prior information of target echo based on complex Gaussian distribution, and introduce the prior information of target scattering coefficient to describe the forward-looking scene. The accuracy of the target scattering coefficient is modeled separately using a gamma distribution; the posterior distributions of the accuracy of the target scattering coefficient, noise clutter, and target scattering coefficient are derived using Bayes' rule; and then the three hyperparameters are iteratively solved. Step 4: Hyperparameter pruning solver; Use a fixed threshold to remove redundant elements from the parameter active set, and then iteratively solve the three hyperparameters.

2. The super-resolution imaging method for sparse targets on the sea surface based on multi-feature division and control of radar echoes according to claim 1, characterized in that, The expression for the azimuth echo signal model is as follows: ； in, For azimuth echo, This is the antenna pattern matrix. The target scattering coefficient, This represents the variation in sea surface clutter scattering at different times. This indicates the motion phase modulation at the same position during beam scanning. It represents the Hadamah accumulation. This represents the convolution operation. For antenna pattern function, For slow time, It is noise.

3. The super-resolution imaging method for sparse targets on the sea surface based on multi-feature division and control of radar echoes according to claim 2, characterized in that, The complex multi-feature enhancement network for target-clutter divide-and-conquer is as follows: Each spatial feature channel extracts features at different depths through a multi-layer convolutional structure. Then, the four spatial features are concatenated and passed through the U-net network to complete feature filtering, aggregation, and channel dimension transformation. Each convolutional layer in the multi-layer convolutional structure includes two consecutive 3×3 convolutional operations, interspersed with ReLU activation functions; Each spatial domain is specified to contain 6 explicit feature channels and 10 implicit feature channels. The explicit feature channels include local entropy, local variance, local rate of change, local contrast, normalization magnitude, and texture features. The complex multi-feature enhancement network for target-clutter divide-and-conquer is trained using a composite loss function.

4. The super-resolution imaging method for sparse targets on the sea surface based on multi-feature division and control of radar echoes according to claim 3, characterized in that, The composite loss function includes target amplitude loss, target frequency-phase loss, and dwell time loss based on the target echo.

5. The super-resolution imaging method for sparse targets on the sea surface based on multi-feature division and control of radar echoes according to claim 4, characterized in that, Step 3 is as follows: Construct the probability density functions for noise and clutter: ； in, express The probability density function, The probability density function representation of the complex Gaussian distribution. Indicates noise and clutter. Indicates a complex Gaussian distribution. The precision used to represent clutter and noise. Represents variance. Represent the identity matrix; assume It follows a gamma distribution, and the accuracy of clutter and noise is obtained based on the gamma distribution. Shape parameters and scale parameters ,set up We obtain a generalized super-prior that does not affect the final estimate; Based on the formula for the complex Gaussian distribution, the target echo signal is derived. for: ； Introducing a complex Gaussian distribution as the target scattering coefficient Use prior information to describe the forward-looking scene: ； in, , The precision of the target scattering coefficient. Indicates the multiplication symbol. It is the first in terms of the accuracy of the target scattering coefficient. The element represents the target at the [number]th [node]. The accuracy of each relevant part For the target scenario Target scattering coefficients at various azimuth angles This indicates diagonalizing the vector; Modeling it as an independent gamma distribution, we obtain the shape parameters of the gamma distribution of β. and scale parameters The accuracy of the target scattering coefficient Marginalize the data, then calculate the overall prior value; Using Bayes' theorem, the posterior distributions of the target scattering coefficient, the accuracy of noise clutter, and the accuracy of the target scattering coefficient are derived. The Expectation-Maximization (EM) algorithm is then used to solve for these distributions, yielding the final iterative expression for updating the target scattering coefficient. ； ； ； in, Indicates the number of azimuth sampling points. , , The trace operation is indicated by the superscript U, which indicates the Hermitian transpose.

6. The super-resolution imaging method for sparse targets on the sea surface based on multi-feature division and control of radar echoes according to claim 5, characterized in that, Step 4 is as follows: First, we define the active set of three hyperparameters, where the accuracy of the target scattering coefficients is... active The set is represented as follows: ； Remove redundant elements from the active set of parameters using a fixed threshold: ； in, It is the pruning threshold. express A set of redundant elements; The corresponding redundant target scattering elements and antenna pattern redundancy elements will also be eliminated. This process can be formally represented as: ； ； in, and Let x and H represent the active sets of parameters, respectively, for the target scattering coefficient x and the antenna pattern matrix H. and These represent the sets of redundant elements for the target scattering coefficient x and the antenna pattern matrix H, respectively. This represents the parameter pruning mapping relationship related to the target scattering coefficient after parameter pruning. This represents the parameter pruning mapping relationship related to antenna pattern elements after parameter pruning. The first element of the antenna pattern matrix represents the first element of the antenna pattern matrix. One element; At this point, the iterative solution is updated to: ； ； ； in, This represents the set of elements after pruning in each iteration.

7. The super-resolution imaging method for sparse targets on the sea surface based on multi-feature division and control of radar echoes according to claim 6, characterized in that, When performing pruning, the Bayesian Information Criterion (BIC) is used as a regularization constraint.

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