A sparse aperture ISAR imaging method combining laplace, low rank and sparse regularization

Abstract

The application belongs to the field of ISAR imaging, and discloses a sparse aperture ISAR imaging method combining Joint Laplacian, Low-Rank and Sparse Regularization (JLLRSR), which realizes high-resolution ISAR imaging under sparse aperture. The method fully utilizes the low-rank characteristics and local similarity of ISAR echo range images, and combines the sparsity of ISAR images to build an optimization model which comprehensively considers these characteristics. The optimization model is solved by using the Alternating Direction Method of Multipliers (ADMM), and high-resolution reconstruction of ISAR images under sparse aperture is realized. The experimental results show that, compared with the traditional range-Doppler (RD) algorithm and the method based on the Compressed sensing (CS) theory, the JLLRSR method proposed by the application can significantly improve the quality of ISAR images under sparse aperture, and solves the problem of the decline of ISAR imaging quality under sparse aperture.

Description

Technical Field

[0001] This invention belongs to the field of ISAR imaging, specifically relating to a sparse aperture ISAR imaging method that combines Laplacian, low-rank, and sparse regularization. Technical Background

[0002] With the increasing application of radar technology in civilian and military fields, Inverse Synthetic Aperture Radar (ISAR) imaging technology has gradually become a research hotspot. ISAR imaging utilizes the motion synthetic aperture of the target to achieve high-resolution imaging. Traditional ISAR imaging algorithms mainly rely on the range-Doppler (RD) method, which can obtain high-resolution ISAR images under ideal conditions. However, in practical applications, due to the non-cooperative nature of the target and the real-time switching of radar functions, it is often difficult to guarantee a sufficiently long coherent processing interval (CPI), resulting in sparse apertures. In this case, the RD algorithm will be severely affected by the lack of data, impacting the imaging effect. To address the ISAR imaging problem under sparse apertures, methods based on Compressed Sensing (CS) theory have been widely used in recent years. CS-based methods utilize the sparsity of the target as prior information, enabling relatively ideal imaging results under sparse apertures. However, when echo signal data is severely lacking, CS methods relying solely on sparse prior information still struggle to obtain high-quality ISAR images. Summary of the Invention

[0003] To overcome the shortcomings of existing sparse aperture ISAR imaging technology, this invention proposes a sparse aperture ISAR imaging method based on Laplacian, Low-Rank and Sparse Regularization (JLLRSR), which combines the low-rank features and local similarity of ISAR echo range profiles with the sparsity of ISAR images.

[0004] To achieve the above objectives, the present invention employs the following technical methods.

[0005] 1. After preprocessing the ISAR echo (delinear frequency modulation, motion compensation, range compression), the sparse aperture ISAR echo range image H is obtained.

[0006] 2. Utilizing the low-rank characteristics and local similarity properties of ISAR echo range profiles, as well as the sparsity of ISAR images as prior information, a sparse aperture ISAR imaging model jointly employing Laplacian, low-rank, and sparsity regularization is established.

[0007]

[0008] Where Y is the range image that is being recovered during the optimization process, P is a partial Fourier matrix, S is the ISAR high-resolution image to be reconstructed, and Z is an auxiliary variable introduced to facilitate the solution of S. This is a low-rank regularization term that constrains the low-rank characteristics of the ISAR echo range profile using a non-convex singular value logarithm and function, where r represents the number of singular values ​​and σ... i Let δ represent the i-th singular value of Y, where δ is an extremely small positive constant. βTr(YBY) H ) is the Laplacian regularization term, which constrains the local similarity of the ISAR echo range image, where B is the graph Laplacian matrix and β is the penalty parameter. λ||S||1 is the sparsity regularization term, which constrains the sparsity of the ISAR image, where λ is the penalty parameter.

[0009] 3. The Alternating Direction Method of Multipliers (ADMM) is used to solve the above optimization problem to obtain high-resolution ISAR images under sparse apertures. The solution steps are as follows:

[0010] (1) Construct the augmented Lagrange function as follows:

[0011]

[0012] Where R1, R2, and R3 represent Lagrange multiplier matrices, and μ1, μ2, and μ3 represent penalty parameters.

[0013] (2) Algorithm initialization: k represents the number of updates, and the initial value of k is 1; Z 1 =P H H; λ>0, β=0.01λ, μ1=μ2=μ3>0, δ=10 -16 ,

[0014] (3) Update Y

[0015]

[0016] Where U and V are auxiliary matrices The unitary matrix obtained after singular value decomposition. This is a diagonal matrix, and its diagonal elements are the updated singular values ​​σ. i

[0017]

[0018] in, Let X be the i-th singular value. It is ζ(Y) with respect to Y in Y=Y k gradient at

[0019]

[0020] Here, ζ(Y) is the linearized result of all terms in the Lag function related to Y except φ(Y).

[0021]

[0022] (4) Update Z

[0023]

[0024] (5) Update S

[0025]

[0026] (6) Update the Lagrange multiplier matrices R1, R2, R3 and the penalty parameters μ1, μ2, μ3.

[0027]

[0028] Where ρ > 1 is the increase factor;

[0029] (7) Determine whether the updated S satisfies the convergence condition.

[0030]

[0031] If satisfied, output S; otherwise, return to step (3), k = k + 1. Attached Figure Description

[0032] Figure 1 This is a flowchart of the JLLRSR method proposed in the patent.

[0033] Figure 2 These are ISAR images obtained using the RD algorithm at full aperture.

[0034] Figure 3 These are ISAR images obtained using the RD algorithm under sparse aperture conditions.

[0035] Figure 4 These are ISAR images obtained using the OMP method based on CS theory under sparse aperture conditions.

[0036] Figure 5 These are ISAR images obtained using the JLLRSR method under sparse aperture conditions. Detailed Implementation

[0037] The present invention will now be further described with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0038] Figure 1 This is a flowchart of the sparse aperture ISAR high-resolution imaging method proposed in the patent, which includes the following steps:

[0039] Step 1: Perform delinear frequency modulation and motion compensation preprocessing on the ISAR echo to obtain the sparse aperture ISAR echo range profile H.

[0040] Step 2: Construct a sparse aperture ISAR imaging model based on Laplacian, low-rank, and sparse regularization.

[0041]

[0042] Where Y is the range image that is being recovered during the optimization process, P is a partial Fourier matrix, S is the ISAR high-resolution image to be reconstructed, and Z is an auxiliary variable introduced to facilitate the solution of S. It is a low-rank regularization term, representing the low-rank characteristics of the ISAR echo range profile, where r represents the number of singular values, and σ i Let δ represent the i-th singular value of matrix Y, where δ is a very small positive constant to avoid generating singular points. βTr(YBY) H ) is the Laplacian regularization term, representing the local similarity of the ISAR echo range profile, where B is the graph Laplacian matrix and β is the penalty parameter. λ||S||1 is the sparsity regularization term, representing the sparsity of the ISAR image, where λ is the penalty parameter.

[0043] Step 3: Solve the optimization problem obtained in Step 2 using the ADMM method to finally obtain the sparse aperture high-resolution ISAR imaging result S. The solution steps are as follows:

[0044] (1) Constructing the augmented Lagrange function

[0045]

[0046] Where R1, R2, and R3 represent Lagrange multiplier matrices, and μ1, μ2, and μ3 represent penalty parameters.

[0047] (2) Algorithm initialization: k represents the number of updates, and the initial value of k is 1; Z 1 =P H H; λ>0, β=0.01λ, μ1=μ2=μ3>0, δ=10 -16 ,

[0048] (3) Update Y

[0049]

[0050] Where U and V are auxiliary matrices The unitary matrix obtained after singular value decomposition. It is a diagonal matrix, and the diagonal elements are the updated singular values ​​σ. i

[0051]

[0052] in, Let be the i-th singular value of X. It is ζ(Y) with respect to Y in Y=Y k gradient at

[0053]

[0054] Here, ζ(Y) is the linearized result of all terms in the Lag function related to Y except φ(Y).

[0055]

[0056] (4) Update Z

[0057]

[0058] (5) Update S

[0059]

[0060] Where soft(x, v) = sgn(x)·max(|x|-v, 0) is the soft thresholding operator.

[0061] (6) Update the Lagrange multiplier matrices R1, R2, R3 and the penalty parameters μ1, μ2, μ3.

[0062]

[0063] Where ρ > 1 is the increase factor;

[0064] (7) Determine whether the updated S satisfies

[0065]

[0066] If satisfied, output S; otherwise, return to sub-step (3), k = k + 1.

[0067] Figure 2 This is an ISAR image obtained using the RD algorithm at full aperture.

[0068] Figure 3 This is an ISAR image obtained using the RD algorithm under sparse aperture conditions, with 50% of the data randomly missing in the azimuth direction.

[0069] Figure 4 This is an ISAR image obtained using the OMP algorithm based on compressed sensing theory under sparse aperture conditions, with 50% of the data randomly missing in the azimuth direction.

[0070] Figure 5 The ISAR image obtained by the algorithm proposed in the patent has 50% of the data randomly missing in the azimuth direction.

Claims

1. A sparse aperture ISAR imaging method combining Laplacian, low-rank, and sparse regularization, characterized in that, The method includes the following steps: Step 1: Perform delinear frequency modulation, motion compensation, and range compression preprocessing on the ISAR echo to obtain the sparse aperture ISAR echo range profile H; Step 2: Using the low-rank features and local similarity of the ISAR echo range profile, as well as the sparsity of the ISAR image as prior information, establish a sparse aperture ISAR imaging model that combines Laplacian, low-rank, and sparse regularization. Step 3: Solve the above optimization problem using the ADMM method to obtain a high-resolution ISAR image under sparse aperture.

2. The sparse aperture ISAR imaging method combining Laplacian, low-rank, and sparse regularization as described in claim 1, characterized in that, The sparse aperture ISAR imaging model constructed in step 2, which combines Laplacian, low-rank, and sparse regularization, is as follows: Where Y is the range image that is being recovered during the optimization process, P is a partial Fourier matrix, S is the ISAR high-resolution image to be reconstructed, and Z is an auxiliary variable introduced to facilitate the solution of S. It is a low-rank regularization term, representing the low-rank characteristics of the ISAR echo range profile, where r represents the number of singular values, and σ i Let δ represent the i-th singular value of matrix Y, where δ is a very small positive constant to avoid generating singular points. βTr(YBY) H ) is the Laplacian regularization term, representing the local similarity of the ISAR echo range profile, where B is the graph Laplacian matrix and β is the penalty parameter. λ||S||1 is the sparsity regularization term, representing the sparsity of the ISAR image, where λ is the penalty parameter.

3. The sparse aperture ISAR imaging method combining Laplacian, low-rank, and sparse regularization as described in claim 1, characterized in that, Step 3 includes the following sub-steps: (1) Constructing the augmented Lagrange function Where R1, R2, and R3 represent Lagrange multiplier matrices, and μ1, μ2, and μ3 represent penalty parameters. (2) Algorithm initialization: k represents the number of updates, and the initial value of k is 1; Z 1 =P H H; λ>0, β=0.01λ, μ1=μ2=μ3>0, δ=10-16, (3) Update Y Where U and V are auxiliary matrices The unitary matrix obtained after singular value decomposition. It is a diagonal matrix, and the diagonal elements are the updated singular values ​​σ. i in, Let X be the i-th singular value. It is ζ(Y) with respect to Y in Y=Y k gradient at Where ζ(Y) is the linearized result of all terms related to Y in the Lag function of substep (1), except for φ(Y). (4) Update Z (5) Update S Where soft(x, v) = sgn(x)·max(|x|-v, 0) is the soft thresholding operator; (6) Update the Lagrange multiplier matrices R1, R2, R3 and the penalty parameters μ1, μ2, μ3. Where ρ > 1 is the increase factor; (7) Determine whether the updated S satisfies If satisfied, output S; otherwise, return to sub-step (3), k = k + 1.

Images