A tomographic SAR super-resolution imaging method based on structured sparse network

Abstract

The application 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, which comprises the following steps: 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 the assumption of the consistency of the elevations of adjacent pixels. A kernel principal component analysis (KPCA) expansion network model is designed to reduce the dimension and enhance the MMV data. On the basis of the reduced and enhanced MMV data, a norm compressed sensing model is introduced, the ADMM iterative algorithm is used to solve the compressed sensing model, the ADMM algorithm is expanded into a deep network, the elevation spectrum is reconstructed, and the super-resolution three-dimensional reconstruction result of the SAR image is obtained. The application can effectively improve the super-resolution performance and solving efficiency of three-dimensional reconstruction, and is helpful for efficiently realizing high-resolution three-dimensional reconstruction of a large-scale scene.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal processing, and particularly relates to a tomographic SAR super-resolution imaging method based on a structured sparse network. BACKGROUND

[0002] Synthetic Aperture Radar (SAR) is an active microwave remote sensing system with all-weather and all-day imaging capability, which is widely used in topographic mapping, environmental monitoring, military reconnaissance and other fields. SAR system forms a virtual aperture through the relative motion between the platform and the target, thereby realizing high-resolution two-dimensional image acquisition. However, the traditional SAR imaging can only provide two-dimensional projection information of the target scene, and cannot reflect the three-dimensional structure, which is prone to problems such as overlap and geometric distortion. To solve such problems, TomoSAR technology emerges as the times require, which realizes three-dimensional structure reconstruction of the target scene by acquiring multiple two-dimensional SAR images at different incident angles.

[0003] In related technologies, the compressive sensing method is usually used to mine the sparsity characteristics in the elevation direction to improve the reconstruction accuracy, but the structural consistency between neighboring pixels cannot be effectively utilized, thereby causing the problems of limited elevation resolution improvement, large noise of reconstruction results and low algorithm efficiency. SUMMARY

[0004] The embodiment of the application provides a tomographic SAR super-resolution imaging method based on a structured sparse network, which can solve the problems that the compressive sensing method is usually used to mine the sparsity characteristics in the elevation direction to improve the reconstruction accuracy, but the structural consistency between neighboring pixels cannot be effectively utilized, thereby causing the problems of limited elevation resolution improvement, large noise of reconstruction results and low algorithm efficiency.

[0005] The embodiment of the application provides a tomographic SAR super-resolution imaging method based on a structured sparse network, which comprises the following steps: step 1, acquiring multi-channel SAR observation data, and constructing a multi-channel observation vector MMV data in a data domain; step 2, based on the elevation consistency assumption of neighboring pixels, constructing a multi-pixel signal model corresponding to the MMV data, and designing a kernel principal component analysis KPCA expansion network model to reduce and enhance the MMV data; step 3, introducing a norm compressive sensing model on the basis of the MMV data after reduction and enhancement; step 4, solving the norm compressive sensing model by using an ADMM iterative algorithm, and expanding the ADMM iterative algorithm into a deep expansion network to reconstruct an elevation spectrum and obtain a SAR image super-resolution three-dimensional reconstruction result.

[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:

[0007] 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;

[0008] 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:

[0009] ;

[0010] The multi-channel data matrix Y is used as MMV data.

[0011] 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:

[0012] A single-pixel signal model is established, represented as:

[0013] ;

[0014] 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 Backscattering coefficient of each scatterer It is additive white Gaussian noise;

[0015] Based on the single-pixel signal model, a multi-pixel signal model corresponding to the MMV data is constructed, represented as follows:

[0016] ;

[0017] in, Multi-channel data matrix Mathematical modeling expression, neighborhood shared guided vector matrix , a backscattering matrix is constructed for the backscattering coefficient vector, wherein, respectively represent the backscattering coefficient vectors of the first to the T th pixels; in the formula, it is assumed that there are pixel units with approximately the same elevation distribution is an assumed additive white Gaussian noise.

[0018] Optionally, in another possible implementation of the first aspect, the specific process of designing the KPCA expansion network model in step 2 is as follows:

[0019] a feature extraction module and a double-branch network are constructed;

[0020] The feature extraction module includes multiple convolution layers, multiple normalization layers, and multiple nonlinear activation layers.

[0021] The double-branch network includes a first branch module and a second branch module. The first branch module includes a normalization layer, multiple convolution layers, and a full connection layer, and the output of the first branch module is a singular value matrix corresponding to the input matrix. The second branch module includes a normalization layer, multiple convolution layers, and a full connection layer, and the output of the second branch module is a left singular vector matrix corresponding to the input matrix.

[0022] Optionally, in another possible implementation of the first aspect, the dimensionality reduction and enhancement of the MMV data in step 2 are as follows:

[0023] The constructed neighborhood multi-pixel signal is input into the KPCA expansion network model, and after being processed by the feature extraction module and the double-branch network, the corresponding singular value matrix and left singular vector matrix are output.

[0024] The singular value matrix and the left singular vector matrix are multiplied to obtain the dimensionality reduction result, which is as follows:

[0025]

[0026] In the formula, the first column of the left singular vector matrix is represented by The intersection matrix formed by the first row of the singular value matrix and the first column is represented by

[0027] The multi-pixel signal model after dimensionality reduction is as follows:

[0028]

[0029] In the formula, the dimensionality reduction result is represented by ​​​​​​​​ mathematical modeling expression of, denotes the elevation spectrum to be reconstructed, denotes the residual noise component after dimension reduction and enhancement.

[0030] Optionally, in another possible implementation of the first aspect, in the step 3 above, the introduced norm compressive sensing model is specifically as follows:

[0031] ;

[0032] wherein, denotes the norm of, denotes the row of, denotes the i row, k column element of, is the square of the norm of the matrix F, is the reconstruction result to be solved, denotes a penalty coefficient, is a steering vector matrix shared by the neighborhood.

[0033] Optionally, in another possible implementation of the first aspect, in the step 4 above, the norm compressive sensing model is solved by using an ADMM iterative algorithm, and the algorithm is specifically as follows:

[0034] Based on the norm compressive sensing model, an ADMM optimization problem is constructed as follows:

[0035] ;

[0036] wherein, denotes an introduced auxiliary variable; denotes the i row, k column element of the auxiliary variable;

[0037] According to the ADMM principle, the iterative step for solving the optimization problem is as follows:

[0038] ;

[0039] wherein, t, t+1 is the iteration number, is the reconstruction spectrum in the t+1 th iteration, is the transpose of the steering vector matrix A , and denotes the auxiliary variable in the t, t+1 th iteration, denotes the Lagrange multiplier, denotes the Lagrange multiplier in the t th iteration, denotes the penalty coefficient, denotes the iteration step size, denotes the identity matrix, denotes the operation of taking the maximum value in the brackets.

[0040] Optionally, in a further possible implementation manner of the first aspect, the deep unfolding network obtained by expanding the ADMM iterative algorithm in the step 4 comprises four reconstruction modules, three regularization modules and three multiplier updating modules; the arrangement order of the four reconstruction modules, the three regularization modules and the three multiplier updating modules is: reconstruction module, regularization module, multiplier updating module, reconstruction module, regularization module, multiplier updating module, reconstruction module, regularization module, multiplier updating module, reconstruction module; wherein, according to the arrangement order, the first reconstruction module is specifically as follows:

[0041] ;

[0042] In the formula, denotes the reconstruction result output by the first reconstruction module;

[0043] In addition to the first reconstruction module, any reconstruction module is specifically as follows:

[0044] ;

[0045] In the formula, denotes the reconstruction result output by the l th reconstruction module, denotes the learnable penalty coefficient, denotes the output result of the l-1 th regularization module, denotes the output result of the l-1 th multiplier updating module;

[0046] Any regularization module is specifically as follows:

[0047] ;

[0048] In the formula, is a sparse transform operation composed of a multi-channel convolution, is a learnable nonlinear function layer used for nonlinear transformation on the matrix after sparse transformation, instead of a threshold operation, is an inverse sparse transform operation composed of a multi-channel convolution, and denote learnable coefficients;

[0049] Any one of the multiplier updating modules is specifically as follows:

[0050]

[0051] In the formula, represents the reconstruction result output by the i-th multiplier updating module, when i is 0, 0 is taken, l l represents the learnable coefficient.

[0052] Optionally, in another possible implementation manner of the first aspect, the step of reconstructing the height spectrum to obtain the super-resolution three-dimensional reconstruction result of the SAR image comprises the following steps:

[0053] obtaining the height normalized frequency based on the spatial spectrum output by the deep unfolding network;

[0054] inverting the height normalized frequency to obtain the height information;

[0055] combining the height information with the range-azimuth two-dimensional information of the target scene to obtain the super-resolution three-dimensional reconstruction result of the SAR image.

[0056] Beneficial effects: first, multi-channel SAR observation data is obtained, a multi-channel observation vector MMV data is constructed in a data domain, then a multi-pixel signal model corresponding to the MMV data is constructed based on the assumption of neighborhood pixel height consistency, a kernel principal component analysis KPCA unfolding network model is designed to reduce the dimension and enhance the MMV data, then a norm compressed sensing model is introduced based on the MMV data after the dimension reduction and enhancement, finally, the norm compressed sensing model is solved by using an ADMM iterative algorithm, and the ADMM iterative algorithm is unfolded into a deep unfolding network to reconstruct the height spectrum and obtain the super-resolution three-dimensional reconstruction result of the SAR image. The application can effectively improve the super-resolution performance of three-dimensional reconstruction, and the solving efficiency is improved by using the deep network, which is helpful for efficiently realizing high-resolution reconstruction of a large-scale TomoSAR imaging scene. BRIEF DESCRIPTION OF DRAWINGS

[0057] 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.

[0058] Figure 1 is a flowchart of a tomographic SAR super-resolution imaging method based on a structured sparse network provided by an embodiment of the present application;

[0059] Figure 2 ​​​is a Z-shaped simulation building tomography SAR imaging experiment provided by an embodiment of the present application. The application method and the atomic norm, M-SL1MMER algorithm processing result comparison chart are respectively applied to the Z-shaped simulation building tomography SAR imaging experiment;

[0060] Figure 3 is a measured airborne data provided by an embodiment of the present application. The application method and the atomic norm, M-SL1MMER algorithm processing result comparison chart are respectively applied to the measured airborne data;

[0061] Figure 4 is a land exploration-1 satellite urban data imaging result chart provided by an embodiment of the present application. DETAILED DESCRIPTION

[0062] In the following description, specific details are set forth, such as particular system configurations, techniques, etc., in order to provide a thorough understanding of the embodiments of the present application. However, persons skilled in the art will understand that the present application can be practiced without these specific details. In other instances, well-known systems, structures, circuits, and techniques have not been shown in detail in order not to obscure the understanding of this description.

[0063] It should be understood that the term "comprises" as used in the specification and the appended claims indicates the presence of the described 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.

[0064] It should also be understood that the term "and / or" as used herein refers to any combination of associated listed items, and all possible combinations thereof, and includes these combinations.

[0065] As used in the specification and the appended claims, the term "if' can be interpreted as meaning "when" or "once" or "in response to a determination" or "in response to a detection" depending on the context. Similarly, the phrase "if determined" or "if detected [the described condition or event]" can be interpreted as meaning "once determined" or "in response to a determination" or "once detected [the described condition or event]" or "in response to a detection [the described condition or event]" depending on the context.

[0066] In addition, in the description of the present application and the appended claims, the terms "first", "second", "third", etc. are only used for differentiation of description, and cannot be understood as indicating or implying relative importance.

[0067] Reference within the specification of this application to "one embodiment" or "some embodiments" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the application. The appearances of the phrase "in one embodiment" or "in some embodiments" in various places within specified

[0068] A structured sparse network based tomographic SAR super-resolution imaging method provided by the application is described in detail below with reference to the accompanying drawings.

[0069] Figure 1 A flowchart of the structured sparse network based tomographic SAR super-resolution imaging method provided by the embodiments of the application is shown.

[0070] As Figure 1 shown, the structured sparse network based tomographic SAR super-resolution imaging method includes the following steps:

[0071] Step 1, acquiring multi-channel SAR observation data, and constructing a multi-channel observation vector MMV data in a data domain;

[0072] Further, in the embodiments of the application, the above step 1 includes:

[0073] Based on a tomographic SAR height inversion model, an observation vector of a center pixel point under M observation channels is acquired , wherein, represents echo signals of the 1st to M Mth channels, respectively;

[0074] T adjacent pixel points are selected around the center pixel point, and an observation vector of each adjacent pixel point under the M observation channels is extracted , wherein, represents observation vectors of the 1st to T Mth pixel points, respectively, and a multi-channel data matrix Y is constructed:

[0075]

[0076] The multi-channel data matrix Y is taken as MMV data.

[0077] ​Step 2, based on the assumption of the consistency of the elevation of the neighborhood pixels, a multi-pixel signal model corresponding to the MMV data is constructed, and a kernel principal component analysis (KPCA) expansion network model is designed to reduce the dimension and enhance the MMV data;

[0078] Further, in the embodiment of the present application, the multi-pixel signal model corresponding to the MMV data is constructed based on the assumption of the consistency of the elevation of the neighborhood pixels in step 2, comprising:

[0079] The single-pixel signal model is established and expressed as:

[0080] ;

[0081] Wherein, is the mathematical modeling expression of the observation vector M of the central pixel point in the observation channel, is the steering vector matrix, is the backscattering coefficient vector, is the number of scattering points overlapped by the central pixel, respectively represent the backscattering coefficients of the first to K scattering bodies, is the additive white Gaussian noise;

[0082] According to the single-pixel signal model, the multi-pixel signal model corresponding to the MMV data is constructed and expressed as:

[0083] ;

[0084] Wherein, is the mathematical modeling expression of the multi-channel data matrix , and the neighborhood shared steering vector matrix , is the backscattering matrix constructed by the backscattering coefficient vector, wherein, respectively represent the backscattering coefficient vectors of the first to the T pixels; in the formula, it is assumed that the pixel units with approximately the same elevation distribution have , is the assumed additive white Gaussian noise.

[0085] Further, in the embodiment of the present application, the specific process of designing the KPCA expansion network model in step 2 is as follows:

[0086] A feature extraction module and a double-branch network are constructed;

[0087] Wherein, the feature extraction module includes multiple convolution layers, multiple normalization layers, and multiple nonlinear activation layers.

[0088] 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.

[0089] Furthermore, in this embodiment of the application, the dimensionality reduction and enhancement of the MMV data in step 2 above are performed as follows:

[0090] 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.

[0091] Multiplying the singular value matrix by the left singular vector matrix yields the dimensionality reduction result, as follows:

[0092] ;

[0093] 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;

[0094] The multi-pixel signal model after dimensionality reduction is as follows:

[0095] ;

[0096] 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.

[0097] Step 3: Based on the dimensionality-reduced and enhanced MMV data, introduce... Norm-compressed sensing model;

[0098] Furthermore, in the embodiments of this application, step 3 above introduces... The norm-compressed sensing model is as follows:

[0099] ;

[0100] 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.

[0101] 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.

[0102] 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:

[0103] based on Constructing an ADMM optimization problem using a norm-compressed sensing model:

[0104] ;

[0105] in, Indicates the introduced auxiliary variable; Indicates the auxiliary variable number i Okay, number k The elements of the column.

[0106] According to the ADMM principle, the iterative steps to solve this optimization problem are as follows:

[0107] ;

[0108] 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 first 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.

[0109] Further, in the embodiment of the present application, the deep unfolding network obtained by expanding the ADMM iterative algorithm in step 4 above comprises four reconstruction modules, three regularization modules and three multiplier update modules; the arrangement order of the four reconstruction modules, the three regularization modules and the 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 arrangement order, the first reconstruction module is specifically as follows:

[0110] ;

[0111] In the formula, denotes the reconstruction result output by the first reconstruction module;

[0112] In addition to the first reconstruction module, any reconstruction module is specifically as follows:

[0113] ;

[0114] In the formula, denotes the reconstruction result output by the first reconstruction module, l denotes a learnable penalty coefficient, denotes the output result of the first regularization module, denotes the output result of the first multiplier update module; l-1 Any regularization module is specifically as follows: l-1

[0115] ;

[0116] ;

[0117] In the formula, is a sparse transformation operation composed of a multi-channel convolution, is a learnable nonlinear function layer for performing nonlinear transformation on the matrix after sparse transformation instead of threshold operation, is an inverse sparse transformation operation composed of a multi-channel convolution, and denote learnable coefficients;

[0118] Any multiplier update module is specifically as follows:

[0119] ;

[0120] In the formula, denotes the reconstruction result output by the first multiplier update module, and when l is 0, 0 is taken, l ​​​denotes a learnable coefficient.

[0121] Further, in the embodiments of the present application, the step 4 of reconstructing the height spectrum to obtain the SAR image super-resolution three-dimensional reconstruction result comprises:

[0122] Based on the spatial spectrum output by the deep unfolding network, the height normalized frequency is obtained;

[0123] The height normalized frequency is inverted to obtain the height information;

[0124] The height information is combined with the range-azimuth two-dimensional information of the target scene to obtain the SAR image super-resolution three-dimensional reconstruction result.

[0125] The present application provides a tomographic SAR super-resolution imaging method based on a structured sparse network, which first obtains multi-channel SAR observation data, constructs a multi-channel observation vector MMV data in the data domain, then constructs a multi-pixel signal model corresponding to the MMV data based on the assumption of neighborhood pixel height consistency, and designs a kernel principal component analysis KPCA unfolding network model to reduce and enhance the MMV data, then introduces a norm compressed sensing model based on the reduced and enhanced MMV data, and finally solves the norm compressed sensing model by using an ADMM iterative algorithm, and expands the ADMM iterative algorithm into a deep unfolding network to reconstruct the height spectrum and obtain the SAR image super-resolution three-dimensional reconstruction result. The present application can effectively improve the super-resolution performance of three-dimensional reconstruction, and improve the solving efficiency by using a deep network, which is helpful for efficiently realizing high-resolution reconstruction of large-scale TomoSAR imaging scenes.

[0126] In order to verify the beneficial effects of the present application, the following experiments are carried out:

[0127] 1. Under the same data conditions, a simulation experiment data set of L-band single building SAR tomographic imaging is built, and different algorithms are used to implement three-dimensional imaging processing on the data set respectively. 2. The SARMV3D-1.0 Yun Cheng airborne data set publicly disclosed by the Chinese Academy of Space Information Innovation is selected, and different algorithms are applied to three-dimensional imaging respectively, and the three-dimensional reconstruction results generated by each algorithm are compared. After obtaining the three-dimensional reconstruction results, the image quality of the reconstruction images of different algorithms is compared through structure, definition and stray point conditions. 3. The spaceborne land exploration-1 data is selected for three-dimensional imaging experiment to verify the high-resolution three-dimensional imaging performance of the algorithm.

[0128] The experimental results are as follows: refer to the schematic Figure 2 In the simulation experiment results, it can be seen that the reconstruction result of the present application presents the most complete building structure and the least number of stray points, and the imaging quality is the highest. Refer to Figure 3The algorithm of the application realizes clear reconstruction of a building structure, especially presents a better visual effect at detail positions such as a roof and a window, and significantly reduces interference of stray points. Figure 4 The high-resolution three-dimensional SAR imaging verification is realized by using the land satellite LOP-1 data, Figure 4 to obtain the three-dimensional high-resolution imaging result.

[0129] It should be understood that the size of the serial number of each step in the above embodiment 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 application.

[0130] The above-described embodiments are only used to illustrate the technical solutions of the present application, but not to 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 some 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 method of tomographic SAR super-resolution imaging based on structured sparse networks, characterized in that, The method comprises the following steps, Step 1, obtaining multi-channel SAR observation data, and constructing multi-channel observation vector MMV data in a data domain; Step 2, constructing a multi-pixel signal model corresponding to the MMV data based on a neighborhood pixel elevation consistency assumption, and designing a KPCA expansion network model to reduce and enhance the MMV data; Step 3, on the basis of the MMV data after dimension reduction and enhancement, the l 2,1 norm compressive sensing model; Step 4, solve l by ADMM iterative algorithm 2,1 The norm compressive sensing model is used, and the ADMM iterative algorithm is expanded into a deep expansion network to reconstruct the height spectrum and obtain the super-resolution three-dimensional reconstruction result of the SAR image. In the step 4, the deep expansion network expanded by the ADMM iterative algorithm comprises four reconstruction modules, three regularization modules and three multiplier updating modules; the arrangement order of the four reconstruction modules, the three regularization modules and the three multiplier updating modules is: a reconstruction module, a regularization module, a multiplier updating module, a reconstruction module, a regularization module, a multiplier updating module, a reconstruction module, a regularization module, a multiplier updating module, and a reconstruction module; wherein, according to the arrangement order, the first reconstruction module is specifically as follows: In the formula, denotes the reconstruction result output by the first reconstruction module; In addition to the first reconstruction module, any reconstruction module is specifically as follows: wherein denotes the reconstruction result output by the l-th reconstruction module, denotes a learnable penalty coefficient, Z (l-1) denotes the output result of the l-1-th regularization module, μ (l-1) denotes the output result of the l-1-th multiplier update module; Any regularization module is specifically as follows: wherein is a sparse transform operation consisting of a multi-channel convolution, is a learnable non-linear function layer for non-linear transformation of the matrix after sparse transformation instead of thresholding, is an inverse sparse transform operation consisting of a multi-channel convolution, and denote learnable coefficients; Any multiplier updating module is specifically as follows: In the formula, μ (l) represents the reconstruction result output by the lth multiplier update module, and when l is 0, 0 is taken, represents a learnable coefficient.

2. The structured sparse network based tomographic SAR super-resolution imaging method of claim 1 wherein, In the step 1, the multi-channel SAR observation data is obtained, and the multi-channel observation vector MMV data is constructed in a data domain, which comprises: Based on the tomographic SAR elevation inversion model, the observation vector y = [y1, y2, K, y] of the center pixel in M ​​observation channels is obtained. M ] T Where y1, y2, K, y M These represent the echo signals of channels 1 to M, respectively. T neighboring pixel points are selected around the center pixel point, and an observation vector y1, y2,..., y T where y1,..., y T represent the observation vectors of the 1st to Tth pixel points, respectively, and a multi-channel data matrix is constructed: Y = [yl, y2,..., y T ]; The multi-channel data matrix Y is taken as the MMV data.

3. The structured sparse network based tomographic SAR super-resolution imaging method of claim 2, wherein, In the step 2, the multi-pixel signal model corresponding to the MMV data is constructed based on the neighborhood pixel elevation consistency assumption, which comprises: A single-pixel signal model is established and represented as: y'=Gγ+n; where y' is a mathematical modeling expression of the observation vector y of the center pixel point under M observation channels, G is a steering vector matrix, γ = [γ1, K, γK+1, K, · · ·, γM, K] is a vector of the center pixel point, and K is the number of scattering points of the center pixel overlap. K ] T is a backscattering coefficient vector, K is the number of scattering points of the center pixel overlap, γ1, K, γ K K+1, K, · · ·, γM, K] is a vector of the center pixel point, and K is the number of scattering points of the center pixel overlap, γ1, K, γ K+1, K, · · ·, γM, K] is a vector of the center pixel point, and K is the number of scattering points of the center pixel overlap, γ1, K, γ According to the single-pixel signal model, the multi-pixel signal model corresponding to the MMV data is constructed and represented as: Y'=GΓ+N; where Y' is a mathematical modeling expression of the multi-channel data matrix Y, the neighborhood shares the steering vector matrix G, Γ = [γ1, γ2,..., γ T ] is a backscattering matrix constructed by a backscattering coefficient vector, where γ1,..., γ T respectively represent the backscattering coefficient vectors of the 1st to Tth pixels; in the formula, it is assumed that there are T pixel units with approximately the same elevation distribution γ T , and N is an assumed additive white noise.

4. The structured sparse network based tomographic SAR super-resolution imaging method of claim 3, wherein, The specific process of designing the KPCA expansion network model in the step 2 is as follows: A feature extraction module and a double-branch network are constructed; The feature extraction module comprises a plurality of convolution layers, a plurality of normalization layers and a plurality of nonlinear activation layers; The double-branch network comprises a first branch module and a second branch module; the first branch module comprises a normalization layer, a plurality of convolution layers and a full connection layer, and the output of the first branch module is a singular value matrix corresponding to an input matrix; the second branch module comprises a normalization layer, a plurality of convolution layers and a full connection layer, and the output of the second branch module is a left singular vector matrix corresponding to the input matrix.

5. The structured sparse network-based tomographic SAR super-resolution imaging method of claim 4, wherein, In the step 2, the MMV data is reduced and enhanced, and the specific process is as follows: The constructed neighborhood multi-pixel signal is input into the KPCA expansion network model, and after being processed by the feature extraction module and the double-branch network, corresponding singular value matrices and left singular vector matrices are output; The singular value matrix and the left singular vector matrix are multiplied to obtain a dimension reduction result, and the specific process is as follows: Y K = U K ∑ K ; where U K denotes the first K columns of the left-singular vector matrix,∑ K denotes the matrix formed by the intersection of the first K rows and the first K columns of the singular value matrix; The multi-pixel signal model after dimension reduction is as follows: Y K ' = G I K + N K ; where Y K is the dimensionality reduction result Y K is a mathematical modeling expression of the dimensionality reduction result Y K represents the elevation spectrum to be reconstructed, N K represents the residual noise component after dimensionality reduction and enhancement.

6. The structured sparse network-based tomographic SAR super-resolution imaging method of claim 5, wherein, In step 3, the l 2,1 The norm compressive sensing model is as follows: wherein denotes Γ K l 2,1 norm, Γ Ki (k) denotes the i-th row, k-th column element of Γ K is the square of the matrix F norm, is the reconstruction result to be solved, ξ denotes a penalty coefficient, and A is a steering vector matrix shared by the neighborhood.​ 7. The structured sparse network-based tomographic SAR super-resolution imaging method of claim 6, wherein, In step 4, the l 2,1 The norm compressive sensing model is specifically as follows: Based on l 2,1 Norm-compressive sensing model constructs ADMM optimization problem: s.t. Z = Γ K ; where Z represents an introduced auxiliary variable; Z i (k) represents the element in the i-th row and the k-th column of the auxiliary variable According to the ADMM principle, the iterative steps for solving the optimization problem are as follows: where t, t + 1 are iteration numbers, is the reconstructed spectrum in the t + 1th iteration, A T is the transpose of the steering vector matrix A, Z (t) , Z (t+1) denote auxiliary variables in the t, t + 1th iteration, respectively, μ denotes a Lagrange multiplier, μ (t) denotes the Lagrange multiplier in the tth iteration, ρ denotes a penalty coefficient, η denotes an iteration step size, I denotes an identity matrix, and max(*) denotes an operation of taking the maximum value in the parentheses.

8. The structured sparse network-based tomographic SAR super-resolution imaging method of claim 7, wherein, In the step 4, the elevation spectrum is reconstructed to obtain a SAR image super-resolution three-dimensional reconstruction result, which comprises: Based on the spatial spectrum output by the deep expansion network, an elevation normalized frequency is obtained; The elevation normalized frequency is inverted to obtain elevation information; The elevation information is combined with distance-azimuth two-dimensional information of a target scene to obtain a SAR image super-resolution three-dimensional reconstruction result.

Images