Chromatographic SAR (Synthetic Aperture Radar) super-resolution imaging method based on structured sparse network

Abstract

The invention is suitable for the technical field of radar signal processing, and provides a tomographic SAR super-resolution imaging method based on a structured sparse network, and the method comprises the steps: firstly obtaining multi-channel SAR observation data, constructing multi-channel observation vector MMV data in a data domain, and constructing a multi-pixel signal model corresponding to the MMV data based on a neighborhood pixel elevation consistency hypothesis. The method comprises the following steps: designing a kernel principal component analysis KPCA expansion network model, carrying out dimension reduction and enhancement on MMV data, introducing a norm compressed sensing model on the basis of the MMV data after dimension reduction and enhancement, solving the compressed sensing model by using an ADMM iterative algorithm, expanding the ADMM algorithm into a deep network, reconstructing an elevation spectrum, and obtaining an SAR image super-resolution three-dimensional reconstruction result. According to the method, the super-resolution performance and the solving efficiency of three-dimensional reconstruction can be effectively improved, and high-resolution three-dimensional reconstruction of a large-scale scene can be efficiently realized.

Description

Technical Field

[0001] This application belongs to the field of radar signal processing technology, and in particular relates to a tomographic SAR super-resolution imaging method based on structured sparse networks. Background Technology

[0002] Synthetic Aperture Radar (SAR) is an active microwave remote sensing system with all-weather, all-day imaging capabilities, widely used in topographic mapping, environmental monitoring, and military reconnaissance. SAR systems acquire high-resolution two-dimensional images by creating a virtual aperture through the relative motion between the platform and the target. However, traditional SAR imaging only provides two-dimensional projection information of the target scene and cannot reflect the three-dimensional structure, easily leading to problems such as overlay and geometric distortion. To address these issues, TomoSAR technology was developed, which reconstructs the three-dimensional structure of the target scene by acquiring multiple two-dimensional SAR images at different incident angles.

[0003] In related technologies, compressed sensing methods are often used to mine sparse features in the elevation direction to improve reconstruction accuracy. However, they fail to effectively utilize the structural consistency between neighboring pixels, resulting in limited improvement in elevation resolution, large noise in reconstruction results, and low algorithm efficiency. Summary of the Invention

[0004] This application provides a tomographic SAR super-resolution imaging method based on structured sparse networks, which can solve the problems of limited elevation resolution improvement, large noise in reconstruction results, and low algorithm efficiency caused by the failure to effectively utilize the structural consistency between neighboring pixels, which is usually achieved by using compressed sensing methods to mine sparsity features in the elevation direction to improve reconstruction accuracy.

[0005] This application provides a tomographic SAR super-resolution imaging method based on structured sparse networks, including: Step 1, acquiring multi-channel SAR observation data and constructing multi-channel observation vector MMV data in the data domain; Step 2, based on the assumption of neighboring pixel elevation consistency, constructing a multi-pixel signal model corresponding to the MMV data, and designing a kernel principal component analysis (KPCA) expansion network model to reduce the dimensionality and enhance the MMV data; Step 3, based on the dimensionality-reduced and enhanced MMV data, introducing... Norm-compressed sensing model; Step 4: Solve using the ADMM iterative algorithm A norm-compressed sensing model is used, and the ADMM iterative algorithm is expanded into a deep unfolded network to reconstruct the elevation spectrum and obtain the super-resolution 3D reconstruction results of SAR images.

[0006] In one possible implementation of the first aspect, step 1 above, acquiring multi-channel SAR observation data and constructing multi-channel observation vector MMV data in the data domain, includes: Based on the tomographic SAR elevation inversion model, the observation vectors of the center pixel in M ​​observation channels are obtained. ,in, They represent the first to the last. M Echo signals from each channel; Select T neighboring pixels around the center pixel, and extract the observation vector of each neighboring pixel in the M observation channels. ,in, They represent the first to the last. T The observation vectors of each pixel are used to construct a multi-channel data matrix: ;

[0007] The multi-channel data matrix Y is used as MMV data.

[0008] Optionally, in another possible implementation of the first aspect, step 2 above, based on the assumption of consistent elevation of neighboring pixels, constructs a multi-pixel signal model corresponding to the MMV data, including: A single-pixel signal model is established, represented as: ; in, Center pixel M Observation vectors under each observation channel Mathematical modeling expression, For the guiding vector matrix, This is the backscattering coefficient vector. The number of scattering points superimposed on the center pixel. They represent the first to the last. K The backscattering coefficient of a scatterer It is additive white Gaussian noise; Based on the single-pixel signal model, a multi-pixel signal model corresponding to the MMV data is constructed, represented as follows: ;

[0009] in, Multi-channel data matrix Mathematical modeling expression, neighborhood shared guided vector matrix , The backscattering matrix is ​​constructed for the backscattering coefficient vector, where, They represent the 1st to the 1st. T The backscattering coefficient vector of each pixel; where it is assumed that they have approximately the same elevation distribution. The pixel units have indivual, It is assumed to be additive white Gaussian noise.

[0010] Optionally, in another possible implementation of the first aspect, the specific process of designing the KPCA unfolded network model in step 2 above is as follows: Construct a feature extraction module and a two-branch network; The feature extraction module includes multiple convolutional layers, multiple normalization layers, and multiple non-linear activation layers. The dual-branch network includes a first branch module and a second branch module. The first branch module includes a normalization layer, multiple convolutional layers, and a fully connected layer. The output of the first branch module is the singular value matrix corresponding to the input matrix. The second branch module includes a normalization layer, multiple convolutional layers, and a fully connected layer. The output of the second branch module is the left singular vector matrix corresponding to the input matrix.

[0011] Optionally, in another possible implementation of the first aspect, step 2 above involves dimensionality reduction and enhancement of the MMV data, as follows: The constructed neighborhood multi-pixel signal is input into the KPCA unfolded network model. After processing by the feature extraction module and the dual-branch network, the corresponding singular value matrix and left singular vector matrix are output. Multiplying the singular value matrix by the left singular vector matrix yields the dimensionality reduction result, as follows: ;

[0012] In the formula The left singular vector matrix represents the front List, The singular value matrix before Go forward The matrix formed by the intersection of columns; The multi-pixel signal model after dimensionality reduction is as follows: ;

[0013] in, For dimensionality reduction results Mathematical modeling expression, This represents the elevation spectrum to be reconstructed. This represents the residual noise component after dimensionality reduction and enhancement.

[0014] Optionally, in another possible implementation of the first aspect, step 3 above introduces... The norm-compressed sensing model is as follows: ;

[0015] in, express of Norm, express The i OK, k List the elements, The square of the F norm of the matrix. The reconstruction result to be solved. Indicates the penalty coefficient. This is a guide vector matrix shared by the neighborhood.

[0016] Optionally, in another possible implementation of the first aspect, in step 4 above, the ADMM iterative algorithm is used to solve... The norm-compressed sensing model is as follows: based on Constructing an ADMM optimization problem using a norm-compressed sensing model: ;

[0017] in, Indicates the introduced auxiliary variable; Indicates the auxiliary variable number i Okay, number k Column elements;

[0018] According to the ADMM principle, the iterative steps to solve this optimization problem are as follows: ;

[0019] in, t, t+1 For the number of iterations, For the first t+1 The reconstructed spectrum in the next iteration. For the guiding vector matrix A transpose, They represent the first t, t+1 Auxiliary variables in the next iteration Represents the Lagrange multipliers. Indicates the t Lagrange multipliers in the next iteration Indicates the penalty coefficient. Indicates the iteration step size. Represents the identity matrix. This indicates the operation of retrieving the maximum value within the parentheses.

[0020] Optionally, in another possible implementation of the first aspect, in step 4 above, the deep unfolded network obtained by the ADMM iterative algorithm includes four reconstruction modules, three regularization modules, and three multiplier update modules; the order of the four reconstruction modules, three regularization modules, and three multiplier update modules is: reconstruction module, regularization module, multiplier update module, reconstruction module, regularization module, multiplier update module, reconstruction module, regularization module, multiplier update module, reconstruction module; wherein, according to the order, the first reconstruction module is as follows: ;

[0021] In the formula, This indicates the reconstruction result output by the first reconstruction module;

[0022] Except for the first reconstruction module, any of the reconstruction modules are as follows: ;

[0023] In the formula, Indicates the l The reconstruction results output by each reconstruction module. This represents the learnable penalty coefficient. Indicates the l-1 The output of the regularization module Indicates the l-1 The output of the multiplier update module; Any regularization module, specifically as follows: ;

[0024] In the formula, It is a sparse transformation operation consisting of a multi-channel convolution. It is a learnable nonlinear function layer used to perform nonlinear transformations on sparsely transformed matrices, replacing thresholding operations. It is an inverse sparse transformation operation consisting of a multi-channel convolution. and Represents the learnable coefficients; Any multiplier update module is as follows: ;

[0025] In the formula, Indicates the l The reconstruction result output by the multiplier update module, when l When the value is 0, take 0. This represents the learnable coefficient.

[0026] Optionally, in another possible implementation of the first aspect, reconstructing the elevation spectrum in step 4 above to obtain the SAR image super-resolution 3D reconstruction result includes: Based on the spatial spectrum output by the deep unfolded network, the elevation-normalized frequency is obtained. The elevation information is obtained by inverting the normalized frequency of the elevation. By combining elevation information with the range-azimuth two-dimensional information of the target scene, super-resolution three-dimensional reconstruction results of SAR images are obtained.

[0027] Beneficial Effects: First, multi-channel SAR observation data is acquired, and multi-channel observation vector MMV data is constructed in the data domain. Then, based on the assumption of neighboring pixel elevation consistency, a multi-pixel signal model corresponding to the MMV data is constructed, and a kernel principal component analysis (KPCA) unfolded network model is designed to reduce the dimensionality and enhance the MMV data. Next, based on the dimensionality-reduced and enhanced MMV data, a norm compressed sensing model is introduced. Finally, the ADMM iterative algorithm is used to solve the norm compressed sensing model, and the ADMM iterative algorithm is unfolded into a deep unfolded network to reconstruct the elevation spectrum and obtain the super-resolution 3D reconstruction results of the SAR image. This application can effectively improve the super-resolution performance of 3D reconstruction and improve the solution efficiency by utilizing a deep network, which helps to efficiently realize high-resolution reconstruction of large-scale TomoSAR imaging scenes. Attached Figure Description

[0028] 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.

[0029] Figure 1 This is a flowchart illustrating a tomographic SAR super-resolution imaging method based on structured sparse networks provided in an embodiment of this application. Figure 2 This is a comparison of the results of a Z-shaped simulated building tomography SAR imaging experiment provided in an embodiment of this application, processed by the method of this application and the atomic norm, M-SL1MMER algorithm respectively; Figure 3 This is a comparison chart showing the results of processing measured airborne data provided in an embodiment of this application using the method of this application and the atomic norm, and the M-SL1MMER algorithm. Figure 4 This is an image showing the imaging result of the urban area data carried by the LuTan-1 satellite according to an embodiment of this application. Detailed Implementation

[0030] 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.

[0031] 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.

[0032] 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.

[0033] 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]."

[0034] 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.

[0035] 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.

[0036] 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.

[0037] Figure 1 The illustration shows a flowchart of a tomographic SAR super-resolution imaging method based on structured sparse networks provided in an embodiment of this application.

[0038] like Figure 1 As shown, this tomographic SAR super-resolution imaging method based on structured sparse networks includes the following steps: Step 1: Acquire multi-channel SAR observation data and construct multi-channel observation vector MMV data in the data domain; Furthermore, in this embodiment of the application, step 1 above includes: Based on the tomographic SAR elevation inversion model, the observation vectors of the center pixel in M ​​observation channels are obtained. ,in, They represent the first to the last. M Echo signals from each channel; Select T neighboring pixels around the center pixel, and extract the observation vector of each neighboring pixel in the M observation channels. ,in, They represent the first to the last. T The observation vectors of each pixel are used to construct a multi-channel data matrix: ;

[0039] The multi-channel data matrix Y is used as MMV data.

[0040] Step 2: Based on the assumption of consistent elevation of neighboring pixels, construct a multi-pixel signal model corresponding to MMV data, and design a kernel principal component analysis (KPCA) expansion network model to reduce the dimensionality and enhance the MMV data. Furthermore, in this embodiment, step 2 above, based on the assumption of consistent elevation of neighboring pixels, constructs a multi-pixel signal model corresponding to the MMV data, including: A single-pixel signal model is established, represented as: ; in, Center pixel M Observation vectors under each observation channel Mathematical modeling expression, For the guiding vector matrix, This is the backscattering coefficient vector. The number of scattering points superimposed on the center pixel. They represent the first to the last. K The backscattering coefficient of a scatterer It is additive white Gaussian noise; Based on the single-pixel signal model, a multi-pixel signal model corresponding to the MMV data is constructed, represented as follows: ;

[0041] in, Multi-channel data matrix Mathematical modeling expression, neighborhood shared guided vector matrix , The backscattering matrix is ​​constructed for the backscattering coefficient vector, where, They represent the 1st to the 1st. T The backscattering coefficient vector of each pixel; where it is assumed that they have approximately the same elevation distribution. The pixel units have indivual, It is assumed to be additive white Gaussian noise.

[0042] Furthermore, in this embodiment, the specific process of designing the KPCA unfolded network model in step 2 above is as follows: Construct a feature extraction module and a two-branch network; The feature extraction module includes multiple convolutional layers, multiple normalization layers, and multiple non-linear activation layers. The dual-branch network includes a first branch module and a second branch module. The first branch module includes a normalization layer, multiple convolutional layers, and a fully connected layer. The output of the first branch module is the singular value matrix corresponding to the input matrix. The second branch module includes a normalization layer, multiple convolutional layers, and a fully connected layer. The output of the second branch module is the left singular vector matrix corresponding to the input matrix.

[0043] Furthermore, in this embodiment of the application, the dimensionality reduction and enhancement of the MMV data in step 2 above are performed as follows: The constructed neighborhood multi-pixel signal is input into the KPCA unfolded network model. After processing by the feature extraction module and the dual-branch network, the corresponding singular value matrix and left singular vector matrix are output. Multiplying the singular value matrix by the left singular vector matrix yields the dimensionality reduction result, as follows: ;

[0044] In the formula The left singular vector matrix represents the front List, The singular value matrix before Go forward The matrix formed by the intersection of columns; The multi-pixel signal model after dimensionality reduction is as follows: ;

[0045] in, For dimensionality reduction results Mathematical modeling expression, This represents the elevation spectrum to be reconstructed. This represents the residual noise component after dimensionality reduction and enhancement.

[0046] Step 3: Based on the dimensionality-reduced and enhanced MMV data, introduce... Norm-compressed sensing model; Furthermore, in the embodiments of this application, step 3 above introduces... The norm-compressed sensing model is as follows: ;

[0047] in, express of Norm, express The i OK, k List the elements, The square of the F norm of the matrix. The reconstruction result to be solved. Indicates the penalty coefficient. This is a guide vector matrix shared by the neighborhood.

[0048] Step 4: Solve using the ADMM iterative algorithm A norm-compressed sensing model is used, and the ADMM iterative algorithm is expanded into a deep unfolded network to reconstruct the elevation spectrum and obtain the super-resolution 3D reconstruction results of SAR images.

[0049] Furthermore, in the embodiments of this application, in step 4 above, the ADMM iterative algorithm is used to solve... The norm-compressed sensing model is as follows: based on Constructing an ADMM optimization problem using a norm-compressed sensing model: ;

[0050] in, Indicates the introduced auxiliary variable; Indicates the auxiliary variable number i Okay, number k The elements of the column.

[0051] According to the ADMM principle, the iterative steps to solve this optimization problem are as follows: ;

[0052] in, t, t+1 For the number of iterations, For the first t+1 The reconstructed spectrum in the next iteration. For the guiding vector matrix A transpose, They represent the first t, t+1 Auxiliary variables in the next iteration Represents the Lagrange multipliers. Indicates the t Lagrange multipliers in the next iteration Indicates the penalty coefficient. Indicates the iteration step size. Represents the identity matrix. This indicates the operation of retrieving the maximum value within the parentheses.

[0053] Furthermore, in this embodiment, in step 4 above, the deep unfolded network obtained by the ADMM iterative algorithm includes four reconstruction modules, three regularization modules, and three multiplier update modules; the order of the four reconstruction modules, three regularization modules, and three multiplier update modules is: reconstruction module, regularization module, multiplier update module, reconstruction module, regularization module, multiplier update module, reconstruction module, regularization module, multiplier update module, reconstruction module; wherein, according to the order, the first reconstruction module is as follows: ;

[0054] In the formula, This indicates the reconstruction result output by the first reconstruction module;

[0055] Except for the first reconstruction module, any of the reconstruction modules are as follows: ;

[0056] In the formula, Indicates the l The reconstruction results output by each reconstruction module. This represents the learnable penalty coefficient. Indicates the l-1 The output of the regularization module Indicates the l-1 The output of the multiplier update module; Any regularization module, specifically as follows: ;

[0057] In the formula, It is a sparse transformation operation consisting of a multi-channel convolution. It is a learnable nonlinear function layer used to perform nonlinear transformations on sparsely transformed matrices, replacing thresholding operations. It is an inverse sparse transformation operation consisting of a multi-channel convolution. and Represents the learnable coefficients; Any multiplier update module is as follows: ;

[0058] In the formula, Indicates the l The reconstruction result output by the multiplier update module, when l When the value is 0, take 0. This represents the learnable coefficient.

[0059] Furthermore, in this embodiment of the application, step 4 above, reconstructing the elevation spectrum and obtaining the SAR image super-resolution 3D reconstruction result, includes: Based on the spatial spectrum output by the deep unfolded network, the elevation-normalized frequency is obtained. The elevation information is obtained by inverting the normalized frequency of the elevation. By combining elevation information with the range-azimuth two-dimensional information of the target scene, super-resolution three-dimensional reconstruction results of SAR images are obtained.

[0060] This application provides a tomographic SAR super-resolution imaging method based on structured sparse networks. First, multi-channel SAR observation data is acquired, and multi-channel observation vector MMV data is constructed in the data domain. Then, based on the assumption of neighboring pixel elevation consistency, a multi-pixel signal model corresponding to the MMV data is constructed, and a kernel principal component analysis (KPCA) unfolded network model is designed to reduce the dimensionality and enhance the MMV data. Next, based on the dimensionality-reduced and enhanced MMV data, a norm compressed sensing model is introduced. Finally, the ADMM iterative algorithm is used to solve the norm compressed sensing model, and the ADMM iterative algorithm is unfolded into a deep unfolded network to reconstruct the elevation spectrum, obtaining the SAR image super-resolution 3D reconstruction result. This application can effectively improve the super-resolution performance of 3D reconstruction and improves the solution efficiency by utilizing deep networks, which helps to efficiently achieve high-resolution reconstruction of large-scale TomoSAR imaging scenes.

[0061] To verify the beneficial effects of this application, the following experiments were conducted: 1. Under the same data conditions, a simulated experimental dataset for L-band SAR tomography of a single building was constructed, and different algorithms were used to perform 3D imaging processing on the dataset. 2. The SARMV3D-1.0 Yuncheng airborne dataset, publicly available from the Aerospace Information Research Institute of the Chinese Academy of Sciences, was selected, and different algorithms were applied for 3D imaging. The 3D reconstruction results generated by each algorithm were compared. After obtaining the 3D reconstruction results, the image quality reconstructed by different algorithms was compared based on structure, sharpness, and clutter. 3. A 3D imaging experiment was conducted using spaceborne LuTan-1 data to verify the high-resolution 3D imaging performance of the algorithm.

[0062] The experimental results are as follows: (Refer to the diagram) Figure 2 The simulation results show that the reconstruction results of this application present the clearest and most complete building structure, with the fewest stray points and the highest imaging quality. (Refer to...) Figure 3 The algorithm in this application achieves clear reconstruction of the building structure, especially in details such as rooftops and windows, presenting a better visual effect while significantly reducing interference from stray points. (See reference...) Figure 4 High-resolution three-dimensional SAR imaging verification was achieved using data from the spaceborne land exploration-1 satellite. Figure 4 This is a three-dimensional high-resolution imaging result.

[0063] 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.

[0064] 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 tomographic SAR super-resolution imaging method based on structured sparse networks, characterized in that, Includes the following steps, Step 1: Acquire multi-channel SAR observation data and construct multi-channel observation vector MMV data in the data domain; Step 2: Based on the assumption of consistent elevation of neighboring pixels, construct the multi-pixel signal model corresponding to the MMV data, and design a kernel principal component analysis (KPCA) expansion network model to reduce the dimensionality and enhance the MMV data. Step 3: Based on the dimensionality-reduced and enhanced MMV data, introduce... Norm-compressed sensing model; Step 4: Solve using the ADMM iterative algorithm A norm-compressed sensing model is used, and the ADMM iterative algorithm is expanded into a deep unfolded network to reconstruct the elevation spectrum and obtain the super-resolution 3D reconstruction results of SAR images.

2. The tomographic SAR super-resolution imaging method based on structured sparse networks as described in claim 1, characterized in that, Step 1, acquiring multi-channel SAR observation data and constructing multi-channel observation vector MMV data in the data domain, includes: Based on the tomographic SAR elevation inversion model, the observation vectors of the center pixel in M ​​observation channels are obtained. ,in, They represent the first to the last. M Echo signals from each channel; Select T neighboring pixels around the center pixel, and extract the observation vector of each neighboring pixel in the M observation channels. ,in, They represent the first to the last. T The observation vectors of each pixel are used to construct a multi-channel data matrix: ； The multi-channel data matrix As MMV data.

3. The tomographic SAR super-resolution imaging method based on structured sparse networks as described in claim 2, characterized in that, Step 2, based on the assumption of consistent elevation of neighboring pixels, constructs a multi-pixel signal model corresponding to the MMV data, including: A single-pixel signal model is established, represented as: ； in, For the center pixel point in M Observation vectors under each observation channel Mathematical modeling expression, For the guiding vector matrix, This is the backscattering coefficient vector. The number of scattering points superimposed on the center pixel. They represent the first to the last. K The backscattering coefficient of a scatterer It is additive white Gaussian noise; Based on the single-pixel signal model, a multi-pixel signal model corresponding to the MMV data is constructed, represented as follows: ； in, For the multi-channel data matrix The mathematical modeling expression, in which the neighborhood shares the guiding vector matrix. , The backscattering matrix is ​​constructed for the backscattering coefficient vector, where, They represent the 1st to the 1st. T The backscattering coefficient vector of each pixel; where it is assumed that they have approximately the same elevation distribution. The pixel units have indivual, It is assumed to be additive white Gaussian noise.

4. The tomographic SAR super-resolution imaging method based on structured sparse networks as described in claim 3, characterized in that, The specific process of designing the KPCA unfolded network model in step 2 is as follows: Construct a feature extraction module and a two-branch network; The feature extraction module includes multiple convolutional layers, multiple normalization layers, and multiple nonlinear activation layers. The dual-branch network includes a first branch module and a second branch module. The first branch module includes a normalization layer, multiple convolutional layers, and a fully connected layer. The output of the first branch module is the singular value matrix corresponding to the input matrix. The second branch module includes a normalization layer, multiple convolutional layers, and a fully connected layer. The output of the second branch module is the left singular vector matrix corresponding to the input matrix.

5. The tomographic SAR super-resolution imaging method based on structured sparse networks as described in claim 4, characterized in that, Step 2 involves dimensionality reduction and enhancement of the MMV data, as detailed below: The constructed neighborhood multi-pixel signal is input into the KPCA unfolded network model. After processing by the feature extraction module and the dual-branch network, the corresponding singular value matrix and left singular vector matrix are output. Multiplying the singular value matrix by the left singular vector matrix yields the dimensionality reduction result, as follows: ； In the formula The left singular vector matrix represents the front List, The singular value matrix before Go forward The matrix formed by the intersection of columns; The multi-pixel signal model after dimensionality reduction is as follows: ； in, The dimensionality reduction result Mathematical modeling expression, This represents the elevation spectrum to be reconstructed. This represents the residual noise component after dimensionality reduction and enhancement.

6. The tomographic SAR super-resolution imaging method based on structured sparse networks as described in claim 5, characterized in that, In step 3, the introduced The norm-compressed sensing model is as follows: ； in, express of Norm, express The i OK, k List the elements, The square of the F norm of the matrix. The reconstruction result to be solved. Indicates the penalty coefficient. This is a guide vector matrix shared by the neighborhood.

7. The tomographic SAR super-resolution imaging method based on structured sparse networks as described in claim 6, characterized in that, In step 4, the ADMM iterative algorithm is used to solve the problem. The norm-compressed sensing model is as follows: based on Constructing an ADMM optimization problem using a norm-compressed sensing model: ； in, Indicates the introduced auxiliary variable; Indicates the auxiliary variable number i Okay, number k Column elements; According to the ADMM principle, the iterative steps to solve this optimization problem are as follows: ； in, t, t+1 For the number of iterations, For the first t+1 The reconstructed spectrum in the next iteration. For the guiding vector matrix A transpose, They represent the first t, t+1 Auxiliary variables in the next iteration Represents the Lagrange multipliers. Indicates the t Lagrange multipliers in the next iteration Indicates the penalty coefficient. Indicates the iteration step size. Represents the identity matrix. This indicates the operation of retrieving the maximum value within the parentheses.

8. The tomographic SAR super-resolution imaging method based on structured sparse networks as described in claim 7, characterized in that, In step 4, the deep unfolded network obtained by the ADMM iterative algorithm includes four reconstruction modules, three regularization modules, and three multiplier update modules. The order of the four reconstruction modules, three regularization modules, and three multiplier update modules is: reconstruction module, regularization module, multiplier update module, reconstruction module, regularization module, multiplier update module, reconstruction module, regularization module, multiplier update module, reconstruction module. Specifically, the first reconstruction module, according to this order, is as follows: ； In the formula, This indicates the reconstruction result output by the first reconstruction module; Apart from the first reconstruction module, any other reconstruction module is as follows: ； In the formula, Indicates the l The reconstruction results output by each reconstruction module. This represents the learnable penalty coefficient. Indicates the l-1 The output of the regularization module Indicates the l-1 The output of the multiplier update module; Any regularization module, specifically as follows: ； In the formula, It is a sparse transformation operation consisting of a multi-channel convolution. It is a learnable nonlinear function layer used to perform nonlinear transformations on sparsely transformed matrices, replacing thresholding operations. It is an inverse sparse transformation operation consisting of a multi-channel convolution. and Represents the learnable coefficients; Any multiplier update module is as follows: ； In the formula, Indicates the l The reconstruction result output by the multiplier update module, when l When the value is 0, take 0. This represents the learnable coefficient.

9. The tomographic SAR super-resolution imaging method based on structured sparse networks as described in claim 8, characterized in that, Step 4, reconstructing the elevation spectrum and obtaining the SAR image super-resolution 3D reconstruction results, includes: Based on the spatial spectrum output by the deep unfolded network, the elevation-normalized frequency is obtained. The elevation information is obtained by inverting the normalized elevation frequency. By combining the elevation information with the range-azimuth two-dimensional information of the target scene, the super-resolution three-dimensional reconstruction result of the SAR image is obtained.

Images