Depth unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraint

Abstract

The application is suitable for the technical field of radar signal processing, and provides a deep unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraint, comprising: firstly, constructing an ISAR image degradation model, constructing an ISAR super-resolution imaging problem based on the ISAR degradation model and the compressed sensing theory, using ADMM to solve the ISAR super-resolution imaging problem, unfolding the process of solving the ISAR super-resolution imaging problem by ADMM into a multi-level neural network, and finally inputting low-resolution ISAR echoes into the trained neural network to obtain an ISAR super-resolution imaging result. The application combines sparse constraint and neighborhood amplitude constraint, deduces a corresponding signal model and an ADMM solving algorithm, effectively improves the reconstruction ability of the algorithm to complex target details and the representation ability of the algorithm to structural information, and can realize effective super-resolution imaging based on narrowband short-aperture echoes.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal processing, and particularly relates to a deep unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraint. BACKGROUND

[0002] Inverse Synthetic Aperture Radar (ISAR) is a kind of active microwave remote sensing technology that can realize two-dimensional high-resolution imaging of moving targets. It has a wide range of applications in space exploration, battlefield reconnaissance, remote sensing mapping and other fields due to its advantages of all-weather and all-day operation, and not being limited by light and weather conditions. Under ideal conditions, ISAR can obtain high-resolution imaging results by transmitting a wide-band signal and prolonging the coherent accumulation time. However, in practical applications, the requirement for anti-interference ability of wide-band waveform is higher, and it is difficult to implement long-time coherent processing on a mobile target, which limits the two-dimensional imaging resolution under most circumstances. Under this background, how to achieve imaging resolution comparable to that of wide-band long-aperture echo based on narrow-band short-aperture echo through signal processing algorithm has become an important research topic in the field of radar signal processing, namely super-resolution imaging.

[0003] However, the existing ISAR super-resolution imaging method has the problems of limited representation ability of complex target details and structure for L1 constraint, insufficient deep feature mining of current deep unfolding network, and strong dependence of supervised learning on high-resolution ISAR images. SUMMARY

[0004] The embodiment of the application provides a deep unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraint, which can solve the problems of limited representation ability of complex target details and structure for L1 constraint, insufficient deep feature mining of current deep unfolding network, and strong dependence of supervised learning on high-resolution ISAR images in the existing ISAR super-resolution imaging method.

[0005] The embodiment of the application provides a deep unfolding ISAR super-resolution imaging method based on sparse-neighborhood joint constraint, which comprises the following steps: step 1, constructing an inverse synthetic aperture radar (ISAR) image degradation model; step 2, based on the ISAR degradation model and the compressed sensing theory, constructing an ISAR super-resolution imaging problem; step 3, using an alternating direction multiplier method (ADMM) to solve the ISAR super-resolution imaging problem; step 4, unfolding the process of solving the ISAR super-resolution imaging problem by ADMM into a multi-level neural network; and step 5, inputting low-resolution ISAR echo into the trained neural network to obtain an ISAR super-resolution imaging result.

[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 1 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 the 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 result of the first network, denotes a Hadamard product, denotes a sigmoid activation function, each denotes a stage the size of a convolution kernel in the convolution network branch is a two-dimensional convolution layer of the first network;

[0049] The cross-attention module is used to simultaneously receive and as inputs, and realizes attention weighting on and through feature extraction and cross-attention mechanisms, and outputs and The specific calculation process is as follows:

[0050]

[0051]

[0052]

[0053] wherein, each denotes a stage a two-dimensional convolution layer in the cross-attention module, denotes a stage the attention score of the unrolled network branch, denotes a stage the attention score of the convolution network branch, denotes a stage a cross-attention calculation operation; when the inputs are and , the output attention score is , the calculation process of is as follows:

[0054]

[0055]

[0056] wherein, each denotes a stage a two-dimensional convolution layer in the cross-attention calculation operation, and denote a query vector, a key vector and a value vector respectively, denotes a vector normalization operation, denotes a softmax activation function, is a network learnable weight.

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

[0058] Step 5.1, collect low-resolution ISAR echoes as a training set, and perform amplitude normalization on the training set;

[0059] Step 5.2, define the loss function of neural network training as:

[0060] wherein, is a regularization coefficient of the term;

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

[0062] Beneficial effects: first, an ISAR image degradation model is constructed, and then based on the ISAR degradation model and the compressed sensing theory, an ISAR super-resolution imaging problem is constructed, the ADMM is used to solve the ISAR super-resolution imaging problem, the process of solving the ISAR super-resolution imaging problem by the ADMM is expanded into a multi-stage neural network, finally, the low-resolution ISAR echoes are input into the trained neural network to obtain the ISAR super-resolution imaging result. The sparsity constraint and the neighborhood amplitude constraint are combined in the present application, the corresponding signal model and the ADMM solving algorithm are derived, the reconstruction ability of the algorithm to the details of a complex target and the representation ability of the algorithm to structural information are effectively improved, and effective super-resolution imaging can be realized based on narrowband short-aperture echoes. BRIEF DESCRIPTION OF DRAWINGS

[0063] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0064] Figure 1 is a flowchart of a deep expansion ISAR super-resolution imaging method based on sparse-neighborhood joint constraint provided by an embodiment of the present application;

[0065] Figure 2 is a whole structure diagram of a multi-stage neural network provided by an embodiment of the present application;

[0066] Figure 3 is a structure diagram of a multi-stage neural network provided by an embodiment of the present application in stage ; and ​

[0067] Figure 4 is a structure diagram of a cross attention module in a stage of a multi-level neural network provided by an embodiment of the present application.

[0068] Figure 5 is an ISAR imaging result schematic diagram of simulation satellite data and Yak-42 aircraft measured data provided by an embodiment of the present application.

[0069] Figure 6 is a comparison diagram of 4x4 super-resolution imaging results of simulation satellite targets by the present application and RD, L1-ADMM, ATS-ADMM algorithms under different signal-to-noise ratios.

[0070] Figure 7 is a comparison diagram of PSNR, CC and SSIM when 4x4 super-resolution imaging is performed on simulation satellite targets by the present application and L1-ADMM, ATS-ADMM algorithms under different signal-to-noise ratios.

[0071] Figure 8 is a comparison diagram of 4x4 super-resolution imaging results of measured Yak-42 aircraft data by the present application and RD, L1-ADMM, ATS-ADMM algorithms. DETAILED DESCRIPTION

[0072] In the following description, specific details are set forth in order to provide a thorough understanding of embodiments of the application. However, persons having ordinary skill in the art will readily recognize that embodiments of the application can be practiced without some or all of the specific details set forth herein. In other instances, well known structures have not been described in detail in order to avoid obscuring the application.

[0073] It should be understood that the term "comprises / comprising" when used in this specification and the appended claims indicates the presence of stated features, integers, steps, operations, elements, and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0074] It should also be understood that the term "and / or" when used in this specification and the appended claims indicates that one or more of the associated listed items can be present.

[0075] ​As used in the specification and the appended claims herein, the term “if’ can be interpreted as meaning “when” or “upon” or “in response to a determination” or “in response to a detection” depending on the context. Similarly, the phrase “if it is determined” or “if [the described condition or event] is detected” can be interpreted as meaning “upon a determination” or “in response to a determination” or “upon a detection” or “in response to a detection” of [the described condition or event], depending on the context.

[0076] In addition, in the description of the present application and the appended claims, the terms “first”, “second”, “third”, etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0077] In the present application, the reference “one embodiment” or “some embodiments” and the like means that the specific features, structures or characteristics described in connection with the embodiment are included in one or more embodiments of the present application. Therefore, the statements “in one embodiment”, “in some embodiments”, “in other some embodiments”, “in further some embodiments” and the like appearing in different places in the specification are not necessarily all referring to the same embodiment, but mean “one or more but not all embodiments”, unless otherwise specifically emphasized. The terms “include”, “contain”, “have” and their variants mean “include but not limited to”, unless otherwise specifically emphasized.

[0078] A structured sparse network-based tomographic SAR super-resolution imaging method provided by the present application is described in detail below with reference to the accompanying drawings.

[0079] Figure 1 A flowchart of a sparse-neighborhood joint constraint-based deep unfolding ISAR super-resolution imaging method provided by an embodiment of the present application is shown.

[0080] As Figure 1 shown, the sparse-neighborhood joint constraint-based deep unfolding ISAR super-resolution imaging method includes the following steps:

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

[0082] Further, in the present application, the ISAR image degradation model constructed in step 1 is specifically:

[0083] wherein, represents the observed low-resolution echo, and respectively 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, represents a high-resolution ISAR image, and respectively 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, and , , represents noise, represents an observation function, defined as The calculation process of

[0084] wherein, represents a two-dimensional discrete Fourier transform, represents matrix transposition, and respectively represent down-sampling matrices in the fast time dimension and the slow time dimension, and are defined as

[0085]

[0086] wherein, represents an element in the row and the column of the matrix, is a row index, is a column index, represents rounding down.

[0087] Step 2, based on the ISAR degradation model and the compressed sensing theory, an ISAR super-resolution imaging problem is constructed;

[0088] Further, in the embodiments of the present application, the ISAR super-resolution imaging problem constructed in step 2 above is:

[0089]

[0090] wherein, is an ISAR super-resolution result to be solved, represents the Frobenius norm of a matrix, represents squaring operation, represents the L1 element norm of a matrix, and respectively represent regularization coefficients of terms and terms, represents a neighborhood amplitude calculation operation; the specific way of taking the neighborhood amplitude calculation operation on is:

[0091]

[0092] wherein, 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 the variable in the iteration, denotes the step size, denotes the gradient operator, denotes the soft threshold function; when the input is , the soft threshold is , the calculation method of the soft threshold function is:

[0107] wherein, denotes taking the maximum value of two numbers;

[0108] Step 3.4.2, solving the sub-problem , the update formula of is obtained:

[0109] Step 3.4.3, solving the sub-problem , the update formula of is obtained:

[0110] wherein, is a scale factor;

[0111] Step 3.4.4, comparing and , if is less than , then is increased by 1, and steps 3.4.1 to 3.4.4 are repeated, if is equal to , then is the obtained super-resolution imaging result.

[0112] Step 4, the process of solving the ISAR super-resolution imaging problem by ADMM is expanded into a multi-stage neural network;

[0113] Further, in the embodiments of the present application, the process of solving the ISAR super-resolution imaging problem by ADMM in step 4 is expanded into a multi-stage neural network, which is specifically as follows:

[0114] As shown in Figure 2 , the multi-stage neural network is constructed by cascading stages, wherein each stage adopts the same network form, that is, a double-flow structure as shown in Figure 3 ; the double-flow structure includes an expansion network branch, a convolution network branch and a cross-attention module; the expansion network branch corresponds to one iteration of the ADMM iteration solving process in step 3, the convolution network branch is a pixel attention module, and the cross-attention module optimizes the results output by the expansion network branch and the convolution network branch;

[0115] Let Phase number, , phase receiving low-resolution echo and phase output as input, and output the calculation result to phase , wherein represents the output result of the convolutional network branch at phase ;

[0116] define the input of phase 1 , , wherein represents the two-dimensional inverse discrete Fourier transform, represents a zero matrix;

[0117] The output of phase and and are extracted by a convolutional layer to obtain the final super-resolution imaging result .

[0118] Further, in the embodiments of the present application, the unfolding network branch in step 4 is used to sequentially perform the following calculations:

[0119]

[0120]

[0121]

[0122]

[0123] wherein, represents the update result of in phase without being processed by the cross-attention module, all are network learnable parameters, represents the cross-attention module of phase ;

[0124] The convolutional network branch is used to perform the following calculations:

[0125]

[0126]

[0127] wherein, represents the update result of in phase without being processed by the cross-attention module, denotes a Hadamard product, denotes a sigmoid activation function, each denotes a stage the size of the convolution kernel in the convolution network branch is a two-dimensional convolution layer;

[0128] Referring to Figure 4 , Figure 4 are respectively a cross-attention module and a structure diagram of a cross-attention calculation operation in the module, wherein the cross-attention module is used to simultaneously receive and as inputs, and implements attention weighting on and through feature extraction and cross-attention mechanism, and outputs and , and the specific calculation process is as follows:

[0129]

[0130]

[0131]

[0132] wherein, each denotes a stage a two-dimensional convolution layer in the cross-attention module, denotes a stage an attention score for the unfolded network branch, denotes a stage an attention score for the convolution network branch, denotes a stage a cross-attention calculation operation; when the inputs are and , the output attention score is , the calculation process is as follows:

[0133]

[0134]

[0135] wherein, each denotes a stage a two-dimensional convolution layer in the cross-attention calculation operation, and denote respectively a query vector, a key vector and a value vector, denotes a vector normalization operation, denotes a softmax activation function, is a network learnable weight.

[0136] Step 5, input the low-resolution ISAR echo to the trained neural network to obtain an ISAR super-resolution imaging result.

[0137] Further, in the embodiments of the present application, the obtaining process of the trained neural network in step 5 is as follows:

[0138] Step 5.1, collect low-resolution ISAR echoes as a training set, and perform amplitude normalization on the training set;

[0139] Step 5.2, define the loss function for neural network training as:

[0140] wherein, is a regularization coefficient of the term;

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

[0142] For example, in an X-band ISAR experiment, the system parameters are as follows:

[0143] Radar operating bandwidth: 500 MHz; target coherent accumulation angle: 3°.

[0144] According to the imaging principle, the two-dimensional resolution at this time is: distance resolution is about 0.3 m; azimuth resolution is about 0.3 m.

[0145] This resolution level can only roughly distinguish the target outline, and the imaging accuracy is in the decimeter level, which can be regarded as low resolution. For example, the general shape of the target (such as the fuselage, tail wing) can be seen, but the detailed structure (such as the radome, winglet, antenna) is still unclear.

[0146] Then the bandwidth is expanded to 2 GHz, and the coherent accumulation angle is increased to 12°, at this time the distance resolution is about 0.075 m, and the azimuth resolution is about 0.075 m, at this time the imaging accuracy is improved to the centimeter level, which can be regarded as high resolution, and the small parts and deformation characteristics of the target surface can be clearly distinguished.

[0147] ​In radar imaging, especially in ISAR, the resolution of the image is mainly determined by two factors: range resolution and azimuth resolution. Therefore, the images of the same target under different system parameters can be considered as "high resolution" or "low resolution": for a system with a bandwidth of 500 MHz and an accumulation angle of 3°, the resolution of 0.3 m is the limit of the system, which is called low resolution imaging; if the bandwidth is expanded to 2 GHz and the accumulation angle is increased to 12°, the resolution can reach 0.075 m, which is high resolution imaging. However, there is no fixed "threshold" to divide them. Low resolution and high resolution are relative to specific system parameters and task requirements, for example: for ship identification tasks, 0.3 m may be sufficient (to identify the hull profile), which is "high resolution"; for aircraft structure feature identification, 0.3 m is too rough, which is still "low resolution".

[0148] The application provides a deep unfolding ISAR super-resolution imaging method based on sparse-neighbor joint constraint. First, an ISAR image degradation model is constructed. Based on the ISAR degradation model and the compressed sensing theory, an ISAR super-resolution imaging problem is constructed. The ADMM is used to solve the ISAR super-resolution imaging problem. The process of solving the ISAR super-resolution imaging problem by the ADMM is unfolded into a multi-level neural network. Finally, the low-resolution ISAR echo is input into the trained neural network to obtain the ISAR super-resolution imaging result. The application combines sparse constraint and neighborhood amplitude constraint, derives the corresponding signal model and ADMM solving algorithm, effectively improves the reconstruction ability of the algorithm to complex target details and the representation ability of structural information, and can realize effective super-resolution imaging based on narrowband short-aperture echo.

[0149] In order to verify the beneficial effects of the application, simulation and real data experiments of ISAR imaging are carried out. The comparison algorithms include range Doppler algorithm (RD), ADMM algorithm with L1 constraint (L1-ADMM) and ADMM algorithm with dynamic threshold (ATS-ADMM). Peak signal-to-noise ratio (PSNR), correlation coefficient (CC) and structural similarity (SSIM) are used for quantitative analysis. Considering the joint range-azimuth super-resolution, the original echo is intercepted under the condition of one quarter of the bandwidth and one quarter of the aperture, which is denoted as times super-resolution. The specific experimental content is as follows:

[0150] 1. Input the simulation satellite data. The echo signal-to-noise ratio is set to 5 dB, 10 dB and 20 dB in sequence. Different algorithms are used to perform times ISAR super-resolution imaging processing on the simulation satellite data, and the visual effects of imaging of each algorithm under different echo SNRs are compared.

[0151] 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.

[0152] 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.

[0153] The experimental results are as follows:

[0154] 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.

[0155] 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.

[0156] 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.

[0157] 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.

[0158] It should be understood that the size of the serial number of each step in the above-mentioned embodiments does not mean the order of execution, and the execution order of each process should be determined according to its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0159] The above-described embodiments are only used to illustrate the technical solutions of the present application, but not limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present 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; 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 1 Column elements, For row index, For column indexes, Indicates rounding down; 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 represents the modulo operation; 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 the 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 obtained super-resolution imaging results; 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. .

2. The method according to claim 1, characterized in that, The expanded network branch in step 4 is used to perform the following calculations in sequence: ； ； ； 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.

3. The method according to claim 2, 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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