Depth expansion ISAR (Inverse Synthetic Aperture Radar) super-resolution imaging method based on sparse-neighborhood combined constraint

Abstract

The invention is suitable for the technical field of radar signal processing, and provides a sparse-neighborhood joint constraint-based deep expansion ISAR super-resolution imaging method, which comprises the steps of firstly constructing an ISAR image degradation model, constructing an ISAR super-resolution imaging problem based on the ISAR degradation model and a compressed sensing theory, and solving the ISAR super-resolution imaging problem by using an ADMM (Amplitude Division Multiplexing). The process of solving the ISAR super-resolution imaging problem by the ADMM is expanded into a multi-stage neural network, and finally, the low-resolution ISAR echo is input into the trained neural network to obtain an ISAR super-resolution imaging result. According to the method, the sparsity constraint and the neighborhood amplitude constraint are combined, the corresponding signal model and the ADMM solving algorithm are deduced, the reconstruction capability of the algorithm on complex target details and the representation capability on structural information are effectively improved, and effective super-resolution imaging can be realized based on narrow-band short-aperture echoes.

Description

Technical Field

[0001] This application belongs to the field of radar signal processing technology, and in particular relates to a depth unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraints. Background Technology

[0002] Inverse Synthetic Aperture Radar (ISAR), an active microwave remote sensing technology capable of achieving high-resolution two-dimensional imaging of moving targets, has wide applications in various fields such as aerospace detection, battlefield reconnaissance, and remote sensing mapping due to its advantages of all-weather, all-day operation and independence from lighting and weather conditions. Under ideal conditions, ISAR can obtain high-resolution imaging results by transmitting wide-bandwidth signals and extending the coherent accumulation time. However, in practical applications, wide-bandwidth waveforms require higher anti-jamming capabilities, and long-term coherent processing of moving targets is difficult. This limits the two-dimensional imaging resolution to narrow-bandwidth waveforms used for short-aperture observations in most scenarios. Against this backdrop, how to achieve imaging resolution comparable to wide-bandwidth long-aperture echoes through signal processing algorithms based on narrow-band short-aperture echoes has become an important research topic in the field of radar signal processing—i.e., super-resolution imaging.

[0003] However, existing ISAR super-resolution imaging methods suffer from limitations in representing the details and structures of complex targets under L1 constraints, insufficient deep unfolding networks for mining deep features of images, and strong dependence of supervised learning on high-resolution ISAR images. Summary of the Invention

[0004] This application provides a deep unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraints, which can solve the problems in existing ISAR super-resolution imaging methods, such as the limited ability of L1 constraints to represent complex target details and structures, insufficient mining of deep image features by current deep unfolding networks, and strong dependence of supervised learning on high-resolution ISAR images.

[0005] This application provides a depth-expanded ISAR super-resolution imaging method based on sparse-neighborhood joint constraints, comprising: Step 1, constructing an inverse synthetic aperture radar (ISAR) image degradation model; Step 2, constructing an ISAR super-resolution imaging problem based on the ISAR degradation model and compressed sensing theory; Step 3, solving the ISAR super-resolution imaging problem using the alternating direction multiplier method (ADMM); Step 4, expanding the ADMM solution to the ISAR super-resolution imaging problem into a multi-level neural network; Step 5, inputting low-resolution ISAR echoes into the trained neural network to obtain ISAR super-resolution imaging results.

[0006] In one possible implementation of the first aspect, the ISAR image degradation model constructed in step 1 above is specifically as follows:

[0007] in, This indicates the observed low-resolution echo. and These represent the number of sampling points in the fast time dimension and the number of sampling points in the slow time dimension corresponding to the low-resolution echo, respectively. Represents high-resolution ISAR images, and Let represent the number of sampling points in the fast time dimension and the number of sampling points in the slow time dimension corresponding to the high-resolution ISAR image, respectively. , , Indicates noise. Describe the observation function, define The calculation process is as follows:

[0008] in, Represents the two-dimensional discrete Fourier transform. Indicates matrix transpose. and Let represent the downsampling matrices in the fast time dimension and the slow time dimension, respectively, and define them as follows:

[0009]

[0010] in, Represents the first in the matrix Line number Column elements, For row index, For column indexes, This indicates rounding down to the nearest integer.

[0011] Optionally, in another possible implementation of the first aspect, the ISAR super-resolution imaging problem constructed in step 2 above is:

[0012]

[0013] in, For the desired ISAR super-resolution results, Denotes the Frobenius norm of a matrix. Represents the squaring operation. Denotes the L1 norm of a matrix. and They represent Item and The regularization coefficient of the term, This indicates a neighborhood magnitude calculation operation; for The specific method for performing neighborhood magnitude calculation is as follows:

[0014]

[0015] in, This indicates the modulo operation.

[0016] Optionally, in another possible implementation of the first aspect, step 3 above uses ADMM to solve the ISAR super-resolution imaging problem, as follows:

[0017] Step 3.1, Introduction If is an auxiliary variable in ADMM, then the ISAR super-resolution imaging problem constructed in step 2 is rewritten as:

[0018]

[0019] Step 3.2: Based on the rewritten ISAR super-resolution imaging problem in Step 3.1, construct the augmented Lagrangian function. And as follows:

[0020] in, The penalty coefficient is... The dual variable is in scaled form;

[0021] Step 3.3: Decompose the augmented Lagrangian function from Step 3.2 into three subproblems, which are expressed as follows:

[0022] Sub-problems:

[0023] Sub-problems:

[0024] Sub-problems:

[0025] in, Represents the trace operation of a matrix. This represents the conjugate transpose operation;

[0026] Step 3.4: Iteratively solve the three subproblems in Step 3.3 until the preset number of iterations is reached. The solution result is obtained; let the current position be the i-th If we perform multiple iterations, the specific steps for solving the problem iteratively are as follows:

[0027] Step 3.4.1, Solve Subproblems, obtained Update formula:

[0028] in, Indicates the first Variables in round iteration, Indicates step size, This represents the gradient operator. Represents the soft threshold function; defined when the input is The soft threshold is When the soft threshold function is used, it is calculated as follows:

[0029] in, This indicates taking the maximum value of the two numbers;

[0030] Step 3.4.2, Solve Subproblems, obtained Update formula:

[0031] Step 3.4.3, Solve Subproblems, obtained Update formula:

[0032] in, Scale factor;

[0033] Step 3.4.4, Compare and The size, if Less than ,but Increment by 1, repeat steps 3.4.1 to 3.4.4, if... equal ,but The result is the super-resolution imaging.

[0034] Optionally, in another possible implementation of the first aspect, step 4 above expands the process of solving the ISAR super-resolution imaging problem using ADMM into a multi-level neural network, as follows:

[0035] Constructing a multi-level neural network by The network is composed of several cascaded stages, each with the same network structure and a two-stream structure. The two-stream structure includes an unfolded network branch, a convolutional network branch, and a cross-attention module. The unfolded network branch corresponds to one iteration of the ADMM iterative solution process in step 3, the convolutional network branch is a pixel attention module, and the cross-attention module optimizes the output of the unfolded network branch and the convolutional network branch.

[0036] set up This is the stage number. ,stage Receive low-resolution echo and stages Output As input, and output the calculation result. To stage ,in Indicates the stage The output of the convolutional network branch;

[0037] Input for Phase 1 , ,in This represents the two-dimensional discrete inverse Fourier transform. Represents a zero matrix;

[0038] Phase Output and After a Convolutional layers are used for feature extraction to obtain the final super-resolution imaging results. .

[0039] Optionally, in another possible implementation of the first aspect, the expanded network branch in step 4 above is used to perform the following calculations in sequence:

[0040]

[0041]

[0042]

[0043]

[0044] in, Representation phase The part not processed by the cross attention module The update results All of these are network-learnable parameters. Representation phase Cross-attention module;

[0045] Convolutional network branches are used to perform the following computations:

[0046]

[0047]

[0048] in, Representation phase The part not processed by the cross attention module The update results Represents the Hadamard product. This represents the sigmoid activation function. All represent stages The kernel size in the convolutional network branch is Two-dimensional convolutional layers;

[0049] Cross-attention modules are used to receive simultaneously and As input, through feature extraction and cross-attention mechanism... and Achieve attention weighting and output and The specific calculation process is as follows:

[0050]

[0051]

[0052]

[0053] in, All represent stages Two-dimensional convolutional layers in the cross-attention module, Representation phase Regarding the attention score for expanding network branches, Representation phase Attention scores for branches of convolutional networks, Representation phase Cross-attention calculation operation; when the input is and The output attention score is hour, The calculation process is as follows:

[0054]

[0055]

[0056] in, All represent stages Two-dimensional convolutional layers in cross-attention computation operations and These represent the query vector, key vector, and value vector, respectively. This represents the vector normalization operation. This represents the softmax activation function. It is a weight that a network can learn.

[0057] Optionally, in another possible implementation of the first aspect, the process of obtaining the trained neural network in step 5 above is as follows:

[0058] Step 5.1: Collect low-resolution ISAR echoes as a training set and normalize the amplitude of the training set.

[0059] Step 5.2: Define the loss function for training the neural network as follows:

[0060] in, for The regularization coefficient of the term;

[0061] Step 5.3: With the goal of minimizing the loss function, train the neural network in an unsupervised manner on the amplitude-normalized training set, and save the trained neural network.

[0062] Beneficial Effects: First, an ISAR image degradation model is constructed. Based on the ISAR degradation model and compressed sensing theory, an ISAR super-resolution imaging problem is established. The ADMM algorithm is used to solve the ISAR super-resolution imaging problem. The process of solving the ISAR super-resolution imaging problem using ADMM is expanded into a multi-level neural network. Finally, low-resolution ISAR echoes are input into the trained neural network to obtain the ISAR super-resolution imaging results. This application combines sparsity constraints and neighborhood amplitude constraints, derives the corresponding signal model and ADMM solution algorithm, effectively improving the algorithm's ability to reconstruct complex target details and represent structural information, and enabling effective super-resolution imaging based on narrowband short-aperture echoes. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a flowchart illustrating a depth unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraints provided in an embodiment of this application.

[0065] Figure 2 This is an overall structural diagram of a multi-level neural network provided in an embodiment of this application;

[0066] Figure 3 This application provides a multi-level neural network in one embodiment at a certain stage. Structural diagram;

[0067] Figure 4 This application provides a multi-level neural network in one of its embodiments at the stage of... The structure diagram of the cross-attention module;

[0068] Figure 5 This is a schematic diagram of ISAR imaging results based on simulated satellite data and measured data from a Yak-42 aircraft, provided in an embodiment of this application.

[0069] Figure 6 This is a comparison diagram of the 4×4x super-resolution imaging results of simulated satellite targets provided by an embodiment of this application and the RD, L1-ADMM, and ATS-ADMM algorithms under different signal-to-noise ratios;

[0070] Figure 7 This is a comparison chart of PSNR, CC, and SSIM of the present application and L1-ADMM and ATS-ADMM algorithms when performing 4×4x super-resolution imaging of simulated satellite targets under different signal-to-noise ratios, provided by an embodiment of the present application.

[0071] Figure 8 This is a comparison diagram of the results of 4×4x super-resolution imaging of measured Yak-42 aircraft data provided by an embodiment of this application and the RD, L1-ADMM, and ATS-ADMM algorithms. Detailed Implementation

[0072] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0073] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0074] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0075] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0076] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0077] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0078] The following is a detailed description of a tomographic SAR super-resolution imaging method based on structured sparse networks provided in this application, with reference to the accompanying drawings.

[0079] Figure 1 The illustration shows a flowchart of a depth unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraints provided in an embodiment of this application.

[0080] like Figure 1 As shown, this depth unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraints includes the following steps:

[0081] Step 1: Construct an inverse synthetic aperture radar (ISAR) image degradation model;

[0082] Furthermore, in this embodiment of the application, the ISAR image degradation model constructed in step 1 above is specifically as follows:

[0083] in, This indicates the observed low-resolution echo. and These represent the number of sampling points in the fast time dimension and the number of sampling points in the slow time dimension corresponding to the low-resolution echo, respectively. Represents high-resolution ISAR images, and Let represent the number of sampling points in the fast time dimension and the number of sampling points in the slow time dimension corresponding to the high-resolution ISAR image, respectively. , , Indicates noise. Describe the observation function, define The calculation process is as follows:

[0084] in, Represents the two-dimensional discrete Fourier transform. Indicates matrix transpose. and Let represent the downsampling matrices in the fast time dimension and the slow time dimension, respectively, and define them as follows:

[0085]

[0086] in, Represents the first in the matrix Line number Column elements, For row index, For column indexes, This indicates rounding down to the nearest integer.

[0087] Step 2: Based on the ISAR degradation model and compressed sensing theory, construct the ISAR super-resolution imaging problem;

[0088] Furthermore, in this embodiment, the ISAR super-resolution imaging problem constructed in step 2 above is:

[0089]

[0090] in, For the desired ISAR super-resolution results, Denotes the Frobenius norm of a matrix. Represents the squaring operation. Denotes the L1 norm of a matrix. and They represent Item and The regularization coefficient of the term, This indicates a neighborhood magnitude calculation operation; for The specific method for performing neighborhood magnitude calculation is as follows:

[0091]

[0092] in, This indicates the modulo operation.

[0093] Step 3: Solve the ISAR super-resolution imaging problem using the Alternating Direction Multiplier Method (ADMM);

[0094] Furthermore, in this embodiment, step 3 above uses ADMM to solve the ISAR super-resolution imaging problem, as detailed below:

[0095] Step 3.1, Introduction If is an auxiliary variable in ADMM, then the ISAR super-resolution imaging problem constructed in step 2 is rewritten as:

[0096]

[0097] Step 3.2: Based on the rewritten ISAR super-resolution imaging problem in Step 3.1, construct the augmented Lagrangian function. And as follows:

[0098] in, The penalty coefficient is... The dual variable is in scaled form;

[0099] Step 3.3: Decompose the augmented Lagrangian function from Step 3.2 into three subproblems, which are expressed as follows:

[0100] Sub-problems:

[0101] Sub-problems:

[0102] Sub-problems:

[0103] in, Represents the trace operation of a matrix. This represents the conjugate transpose operation;

[0104] Step 3.4: Iteratively solve the three subproblems in Step 3.3 until the preset number of iterations is reached. The solution result is obtained; let the current position be the i-th If we perform multiple iterations, the specific steps for solving the problem iteratively are as follows:

[0105] Step 3.4.1, Solve Subproblems, obtained Update formula:

[0106] in, Indicates the first Variables in round iteration, Indicates step size, This represents the gradient operator. Represents the soft threshold function; defined when the input is The soft threshold is When the soft threshold function is used, it is calculated as follows:

[0107] in, This indicates taking the maximum value of the two numbers;

[0108] Step 3.4.2, Solve Subproblems, obtained Update formula:

[0109] Step 3.4.3, Solve Subproblems, obtained Update formula:

[0110] in, Scale factor;

[0111] Step 3.4.4, Compare and The size, if Less than ,but Increment by 1, repeat steps 3.4.1 to 3.4.4, if... equal ,but The result is the super-resolution imaging.

[0112] Step 4: Expand the process of solving the ISAR super-resolution imaging problem using ADMM into a multi-level neural network;

[0113] Furthermore, in this embodiment, step 4 above, which involves solving the ISAR super-resolution imaging problem using ADMM, is expanded into a multi-level neural network, as follows:

[0114] like Figure 2 As shown, the construction of a multi-level neural network is achieved by... It is composed of cascaded stages, where each stage uses the same network structure, such as... Figure 3 The dual-stream structure shown includes an unfolded network branch, a convolutional network branch, and a cross-attention module. The unfolded network branch corresponds to one iteration of the ADMM iterative solution process in step 3, the convolutional network branch is a pixel attention module, and the cross-attention module optimizes the outputs of the unfolded network branch and the convolutional network branch.

[0115] set up This is the stage number. ,stage Receive low-resolution echo and stages Output As input, and output the calculation result. To stage ,in Indicates the stage The output of the convolutional network branch;

[0116] Input for Phase 1 , ,in This represents the two-dimensional discrete inverse Fourier transform. Represents a zero matrix;

[0117] Phase Output and After a Convolutional layers are used for feature extraction to obtain the final super-resolution imaging results. .

[0118] Furthermore, in this embodiment, the expanded network branch in step 4 above is used to perform the following calculations sequentially:

[0119]

[0120]

[0121]

[0122]

[0123] in, Representation phase The part not processed by the cross attention module The update results All of these are network-learnable parameters. Representation phase Cross-attention module;

[0124] Convolutional network branches are used to perform the following computations:

[0125]

[0126]

[0127] in, Representation phase The part not processed by the cross attention module The update results Represents the Hadamard product. This represents the sigmoid activation function. All represent stages The kernel size in the convolutional network branch is Two-dimensional convolutional layers;

[0128] Reference Figure 4 , Figure 4 These are schematic diagrams of the cross-attention module and the cross-attention calculation operation within it, respectively. The cross-attention module is used to simultaneously receive... and As input, through feature extraction and cross-attention mechanism... and Achieve attention weighting and output and The specific calculation process is as follows:

[0129]

[0130]

[0131]

[0132] in, All represent stages Two-dimensional convolutional layers in the cross-attention module, Representation phase Regarding the attention score for expanding network branches, Representation phase Attention scores for branches of convolutional networks, Representation phase Cross-attention calculation operation; when the input is and The output attention score is hour, The calculation process is as follows:

[0133]

[0134]

[0135] in, All represent stages Two-dimensional convolutional layers in cross-attention computation operations and These represent the query vector, key vector, and value vector, respectively. This represents the vector normalization operation. This represents the softmax activation function. It is a weight that a network can learn.

[0136] Step 5: Input the low-resolution ISAR echo into the trained neural network to obtain the ISAR super-resolution imaging results.

[0137] Furthermore, in this embodiment, the process of obtaining the trained neural network in step 5 above is as follows:

[0138] Step 5.1: Collect low-resolution ISAR echoes as a training set and normalize the amplitude of the training set.

[0139] Step 5.2: Define the loss function for training the neural network as follows:

[0140] in, for The regularization coefficient of the term;

[0141] Step 5.3: With the goal of minimizing the loss function, train the neural network in an unsupervised manner on the amplitude-normalized training set, and save the trained neural network.

[0142] For example, in an X-band ISAR experiment, the system parameters are as follows: Radar operating bandwidth: 500 MHz; target coherence accumulation angle: 3°.

[0143] Based on the imaging principle, the two-dimensional resolution at this time is: distance resolution approximately 0.3 m; azimuth resolution approximately 0.3 m.

[0144] This resolution level can only roughly distinguish the outline of the target, with imaging accuracy at the decimeter level, and can be considered low resolution. For example, the general shape of the target (such as the fuselage and tail fins) can be seen, but the detailed structures (such as the radome, winglets, and antennas) are still blurry.

[0145] Next, the bandwidth was extended to 2GHz and the coherence accumulation angle was increased to 12°. At this point, the distance resolution was approximately 0.075 m and the azimuth resolution was approximately 0.075 m. The imaging accuracy was improved to the centimeter level, which can be considered as high resolution. It can clearly distinguish small parts and deformation features on the target surface.

[0146] In radar imaging, especially ISAR, image resolution is primarily determined by two factors: range resolution and azimuth resolution. Therefore, under different system parameters, images of the same target may be considered "high-resolution" or "low-resolution": for a system with a bandwidth of 500MHz and an accumulation angle of 3°, a resolution of 0.3m is already the system limit, termed low-resolution imaging; if the bandwidth is extended to 2GHz and the accumulation angle increased to 12°, the resolution can reach 0.075m, which is considered high-resolution imaging. However, there is no fixed "threshold" to distinguish between the two. The terms "low-resolution" and "high-resolution" are relative to specific system parameters and mission requirements. For example, for ship identification, 0.3m may be sufficient (to identify the ship's outline), constituting "high-resolution"; for aircraft structural feature identification, 0.3m is too coarse and still falls under "low-resolution."

[0147] This application provides a depth-unfolded ISAR super-resolution imaging method based on sparse-neighborhood joint constraints. First, an ISAR image degradation model is constructed. Based on the ISAR degradation model and compressed sensing theory, an ISAR super-resolution imaging problem is constructed. The Advanced Dynamic Model (ADMM) is used to solve the ISAR super-resolution imaging problem. The ADMM solution process is unfolded into a multi-level neural network. Finally, low-resolution ISAR echoes are input into the trained neural network to obtain the ISAR super-resolution imaging results. This application combines sparsity constraints and neighborhood amplitude constraints, deriving the corresponding signal model and ADMM solution algorithm, effectively improving the algorithm's ability to reconstruct complex target details and represent structural information. It can achieve effective super-resolution imaging based on narrowband short-aperture echoes.

[0148] To verify the beneficial effects of this application, simulation and experimental data of ISAR imaging were conducted. Comparative algorithms included the Range-Doppler (RD) algorithm, the ADMM algorithm with L1 constraints (L1-ADMM), and the ADMM algorithm with dynamic thresholding (ATS-ADMM). Quantitative analysis was performed using three indicators: Peak Signal-to-Noise Ratio (PSNR), Correlation Coefficient (CC), and Structural Similarity (SSIM). Considering the combined range-azimuth super-resolution case, given the original echo, the echo at one-quarter bandwidth and one-quarter aperture of the original echo was extracted and denoted as... Super-resolution; specific experimental details are as follows:

[0149] 1. Input simulated satellite data, and successively set the echo signal-to-noise ratio to 5 dB, 10 dB, and 20 dB. Use different algorithms to process the simulated satellite data. The ISAR super-resolution imaging processing was performed, and the visual effects of each algorithm under different echo SNR were compared.

[0150] 2. Input simulated satellite data, and use different algorithms to process the simulated satellite data. The ISAR super-resolution imaging processing was performed, and the PSNR, CC, and SSIM of each algorithm were compared under different echo SNR.

[0151] 3. Input the measured data of the Yak-42 aircraft and truncate the measured data to simulate... In cases of super-resolution, different algorithms are used to process the truncated data. The imaging performance of each algorithm was evaluated by performing ISAR super-resolution imaging processing.

[0152] The experimental results are as follows:

[0153] Reference Figure 5 , Figure 5 The images are ISAR imaging results from the simulated satellite and the Yak-42 aircraft used in the experiment, respectively. Figure 5 High-resolution image used as a reference.

[0154] Reference Figure 6 , Figure 6 This invention, along with RD, L1-ADMM, and ATS-ADMM algorithms, performs simulations on satellite targets under different echo signal-to-noise ratios. A comparison of super-resolution imaging results. As can be seen from the figure, the imaging results of this invention are closer to the reference high-resolution image at different signal-to-noise ratios. Moreover, while improving the resolution, it can well preserve the target details and structural information, and also has a good suppression effect on clutter interference.

[0155] Reference Figure 7 , Figure 7 This is a comparison of PSNR, CC, and SSIM of the present invention with those of the L1-ADMM and ATS-ADMM algorithms when performing 4×4x super-resolution imaging of simulated satellite targets under different signal-to-noise ratios. The figures show that the imaging results of the present invention perform well across all imaging metrics and have significant advantages over the compared algorithms.

[0156] Reference Figure 8 , Figure 8 This image shows a comparison of the 4×4x super-resolution imaging results of the present invention with the RD, L1-ADMM, and ATS-ADMM algorithms on measured Yak-42 aircraft data. As can be seen from the image, the present invention can achieve two-dimensional super-resolution imaging of measured data, and the imaging results are close to the reference image. This indicates that the present invention also has good super-resolution performance and generalization ability under actual measurement conditions, and can be applied to different types of targets.

[0157] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0158] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A depth unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraints, characterized in that, The specific steps are as follows: Step 1: Construct an inverse synthetic aperture radar (ISAR) image degradation model; Step 2: Based on the ISAR degradation model and compressed sensing theory, construct the ISAR super-resolution imaging problem; Step 3: Solve the ISAR super-resolution imaging problem using the Alternating Direction Multiplier Method (ADMM). Step 4: Expand the process of ADMM in solving the ISAR super-resolution imaging problem into a multi-level neural network; Step 5: Input the low-resolution ISAR echo into the trained neural network to obtain the ISAR super-resolution imaging results.

2. The method according to claim 1, characterized in that, The ISAR image degradation model constructed in step 1 is specifically as follows: ; in, This indicates the observed low-resolution echo. and These represent the number of sampling points in the fast time dimension and the number of sampling points in the slow time dimension corresponding to the low-resolution echo, respectively. Represents high-resolution ISAR images, and Let represent the number of sampling points in the fast time dimension and the number of sampling points in the slow time dimension corresponding to the high-resolution ISAR image, respectively. , , Indicates noise. Describe the observation function, define The calculation process is as follows: ; in, Represents the two-dimensional discrete Fourier transform. Indicates matrix transpose. and Let represent the downsampling matrices in the fast time dimension and the slow time dimension, respectively, and define them as follows: ; in, Represents the first in the matrix Line number Column elements, For row index, For column indexes, This indicates rounding down to the nearest integer.

3. The method according to claim 2, characterized in that, The ISAR super-resolution imaging problem constructed in step 2 is as follows: ； in, For the desired ISAR super-resolution results, Denotes the Frobenius norm of a matrix. Represents the squaring operation. Denotes the L1 norm of a matrix. and They represent Item and The regularization coefficient of the term, This indicates a neighborhood magnitude calculation operation; for The specific method for performing the neighborhood magnitude calculation operation is as follows: ； in, This indicates the modulo operation.

4. The method according to claim 3, characterized in that, Step 3 uses ADMM to solve the ISAR super-resolution imaging problem, as detailed below: Step 3.1, Introduction If is an auxiliary variable in ADMM, then the ISAR super-resolution imaging problem constructed in step 2 is rewritten as: ； Step 3.2: Based on the rewritten ISAR super-resolution imaging problem in Step 3.1, construct the augmented Lagrangian function. And as follows: ； in, The penalty coefficient is... The dual variable is in scaled form; Step 3.3: Decompose the augmented Lagrangian function described in Step 3.2 into three subproblems, which are expressed as follows: Sub-problems: ; Sub-problems: ; Sub-problems: ; in, Represents the trace operation of a matrix. This represents the conjugate transpose operation; Step 3.4: Iteratively solve the three sub-problems described in Step 3.3 until the preset number of iterations is reached. The solution result is obtained; let the current position be the i-th If we perform multiple iterations, the specific steps for solving the problem iteratively are as follows: Step 3.4.1, Solve Subproblems, obtained Update formula: ; in, Indicates the first Variables in round iteration, Indicates step size, This represents the gradient operator. Represents the soft threshold function; defined when the input is The soft threshold is When the soft threshold function is used, it is calculated as follows: ; in, This indicates taking the maximum value of the two numbers; Step 3.4.2, Solve Subproblems, obtained Update formula: ; Step 3.4.3, Solve Subproblems, obtained Update formula: ; in, Scale factor; Step 3.4.4, Compare and The size, if Less than ,but Increment by 1, repeat steps 3.4.1 to 3.4.4, if... equal ,but The result is the super-resolution imaging.

5. The method according to claim 4, characterized in that, In step 4, the process of solving the ISAR super-resolution imaging problem using ADMM is expanded into a multi-level neural network, as follows: The multi-level neural network is constructed by The network is composed of cascaded stages, each stage having the same network structure and being a two-stream structure. The two-stream structure includes an unfolded network branch, a convolutional network branch, and a cross-attention module. The unfolded network branch corresponds to one iteration of the ADMM iterative solution process in step 3, the convolutional network branch is a pixel attention module, and the cross-attention module optimizes the outputs of the unfolded network branch and the convolutional network branch. set up This is the stage number. ,stage Receive low-resolution echo and stages Output As input, and output the calculation result. To stage ,in Indicates the stage The output of the convolutional network branch; Input for Phase 1 , ,in This represents the two-dimensional discrete inverse Fourier transform. Represents a zero matrix; Phase Output and After a Convolutional layers are used for feature extraction to obtain the final super-resolution imaging results. .

6. The method according to claim 5, characterized in that, The expanded network branch in step 4 is used to perform the following calculations sequentially: ； ； ； in, Representation phase The part not processed by the cross attention module The update results All of these are network-learnable parameters. Representation phase Cross-attention module; The convolutional network branch is used to perform the following calculations: ； ； in, Representation phase The part not processed by the cross attention module The update results Represents the Hadamard product. This represents the sigmoid activation function. All represent stages The kernel size in the convolutional network branch is Two-dimensional convolutional layers; The cross-attention module is used to receive simultaneously and As input, through feature extraction and cross-attention mechanism... and Achieve attention weighting and output and The specific calculation process is as follows: ； in, All represent stages Two-dimensional convolutional layers in the cross-attention module, Representation phase Regarding the attention score for expanding network branches, Representation phase Attention scores for branches of convolutional networks, Representation phase Cross-attention calculation operation; when the input is and The output attention score is hour, The calculation process is as follows: ； ； ； in, All represent stages Two-dimensional convolutional layers in cross-attention computation operations and These represent the query vector, key vector, and value vector, respectively. This represents the vector normalization operation. This represents the softmax activation function. It is a weight that a network can learn.

7. The method according to claim 6, characterized in that, The process of obtaining the trained neural network in step 5 is as follows: Step 5.1: Collect low-resolution ISAR echoes as a training set and normalize the amplitude of the training set. Step 5.2: Define the loss function for training the neural network as follows: ； in, for The regularization coefficient of the term; Step 5.3: With the goal of minimizing the loss function, train the neural network in an unsupervised manner on the amplitude-normalized training set, and save the trained neural network.

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