A near-field SAR image domain interference suppression method based on target and interference decomposition

Abstract

The present invention discloses a method for suppressing interference in the near-field SAR image domain by decomposing targets and interference. It suppresses interference in the image domain, specifically by performing target and interference decomposition on the original near-field SAR image containing interference through iterative solution, to obtain a target image without interference. In each iteration, the target image is updated first; then the interference image is updated; based on the relative change between the target image updated in this iteration and the target image updated in the previous iteration, it is determined whether to stop the iteration, and the latest updated target image is output as the near-field SAR interference suppression result. The method of the present invention can effectively suppress interference and extract the target image; compared with the traditional background cancellation interference suppression method, the method of the present invention has the characteristics of not requiring two consecutive imaging of the system and significantly improving efficiency; the target image has high quality after interference suppression; and is also suitable for interference suppression of near-field SAR two-dimensional and three-dimensional images.

Description

Technical Field

[0001] The present invention belongs to the field of synthetic aperture radar technology, and particularly relates to the field of synthetic aperture radar (SAR) near-field imaging technology. Background Art

[0002] Synthetic Aperture Radar (SAR) is a radar system with all-day, all-weather imaging capabilities. It can image at any time, day or night, in clear skies or rain or snow, overcoming the limitations of optical and infrared systems, which cannot image at night or in complex weather conditions. However, traditional SAR has long observation ranges, a small change in viewing angle relative to the observed target, and a small synthetic aperture angle, resulting in limited azimuth resolution.

[0003] Unlike traditional SAR, near-field SAR operates in the near-field area of ​​the target. At this time, the change in the relative viewing angle to the observed target increases significantly, and the synthetic aperture angle is therefore large, which significantly improves the azimuth resolution of the image, reaching a resolution of the order of centimeters. In addition, near-field SAR systems can usually use stepped frequency signals as transmission signals, so that the image range resolution can reach the same order of magnitude as the azimuth resolution. In addition, near-field SAR, combined with a vertical plane mechanical scanning structure, can stably synthesize one-dimensional or two-dimensional apertures, corresponding to two-dimensional and three-dimensional imaging results. Near-field SAR can achieve refined imaging of targets and has broad application value in many fields such as human body security imaging, hidden object detection, building deformation detection, autonomous driving, and scattering characteristic measurement.

[0004] Because radar systems are located in the near-field, various interference signals, including leakage signals between the transmitting and receiving systems, clutter from the system's mechanical structure, and clutter from the ground environment, will overlap with the return signal from the target. After processing by the imaging algorithm, the target image in the resulting image will be obscured or even buried by the image formed by the interference signals, hindering subsequent radar image applications, including target scattering characteristics interpretation and target identification. Therefore, to address this issue, it is necessary to propose an effective near-field SAR interference suppression method.

[0005] Existing near-field SAR interference suppression methods are mainly background cancellation methods. This method relies on the relative stability of the interference signal within a certain period of time. The system performs two consecutive imaging operations on the scene containing the target and the scene excluding the target, and the obtained imaging results are coherently cancelled to achieve interference suppression. Obviously, in order to obtain effective imaging results without interference, the time consumed will be doubled. In addition, due to the reliance on the relative stability of the interference signal, this requires the radar system's transmitted signal to have a high stability and the imaging background environment state to remain relatively unchanged; when the transmitted signal or the environmental state changes, the interference suppression effect will be affected and reduced. Therefore, in order to improve efficiency and reduce dependence on the stability of the transmitted signal and the imaging environment, the present invention proposes a near-field SAR image domain interference suppression method that decomposes the target and interference. Summary of the Invention

[0006] This paper proposes a near-field SAR image domain interference suppression method using target and interference decomposition. This method suppresses interference in the image domain by iteratively decomposing the target and interference of the original near-field SAR image containing interference, obtaining an interference-free target image. In each iteration, an L1-norm regularized denoising equation based on the target image is first established and solved to update the target image. Then, a nuclear-norm regularized denoising equation based on the interference image is established and solved to update the interference image. The iteration is terminated based on the relative change between the target image updated in the current iteration and the target image updated in the previous iteration. When the relative change exceeds a threshold, the iteration continues; when it is less than the threshold, the iteration stops and the latest updated target image is output as the near-field SAR interference suppression result. This method effectively suppresses interference and extracts the target image. Compared with background cancellation interference suppression methods, this method does not require the system to undergo two consecutive imaging cycles, significantly improving efficiency. After interference suppression, the target image has less residual clutter and noise, resulting in higher image quality. The method is also applicable to interference suppression for both two-dimensional and three-dimensional near-field SAR images.

[0007] In order to facilitate the description of the present invention, the following terms are first defined:

[0008] Definition 1. Synthetic Aperture Radar

[0009] Synthetic Aperture Radar (SAR) is a high-resolution microwave imaging radar that obtains high-resolution and high-precision microwave images through signal processing. It has the advantages of all-day and all-weather operation and has been widely used in various fields such as terrain mapping, guidance, environmental remote sensing, and resource exploration. For details, see "Pi Yiming, Yang Jianyu, Fu Yusheng, Yang Xiaobo. Principles of Synthetic Aperture Radar Imaging [M]. University of Electronic Science and Technology of China Press. 2007."

[0010] Definition 2. Traditional Backprojection Algorithm

[0011] The back-projection algorithm (BP) uses the radar platform's trajectory information to calculate the distance history between the radar platform and scene pixels. It then traverses this distance history to find matching echo data within the echo data, performs phase compensation and coherent accumulation, and then back-projects the complex-valued result into the image space to complete the imaging process. For details on the traditional back-projection algorithm, see "Shi Jun. Research on the Principles and Imaging Technology of Bistatic SAR and Linear Array SAR [D]. Doctoral Dissertation, University of Electronic Science and Technology of China, 2009."

[0012] Definition 3. Traditional Matrix Vectorization Operator Method

[0013] The matrix vectorization operator vec(A) is an operation that arranges the input matrix A into columns to form a column vector. Specifically, the matrix vectorization operator arranges the columns of an m×n matrix A from left to right, forming a column vector vec(A):

[0014] vec(A)=[a 1,1 ,…,a m,1 ,a 1,2 ,…,a m,2 ,…a 1,n ,…,a m,n ] T

[0015] where a i,j A(i,j) represents the element in the i-th row and j-th column of matrix A; the superscript T denotes the matrix transpose operation. For details on traditional matrix vectorization operators, see Zhang Xianda. Matrix Analysis and Applications [M]. Tsinghua University Press, 2004.

[0016] Definition 4. Traditional vector matrix diagonal operator method

[0017] The traditional vector matrix diagonal operator diag(a) method is a calculation method that generates a matrix A from an input vector a, where the diagonal elements of A are composed of vector a. Specifically, the vector matrix diagonal operator constructs the diagonal elements of matrix A from top to bottom by taking the elements of a column vector a with dimension n×1, and the other elements of the matrix are 0. diag(a) is expressed as:

[0018]

[0019] where a i , i = 1, 2, 3, ... N represents the i-th element of a. For details on the traditional vector matrix diagonal operator method, see "Zhang Xianda. Matrix Analysis and Applications [M]. Tsinghua University Press, 2004".

[0020] Definition 5. Traditional element-wise signed operator method

[0021] sign(·) represents the element-wise sign operator, which calculates the sign of each element of a matrix or vector. The calculation formula is as follows:

[0022] For matrices: For vectors:

[0023] where x ij is the element in the i-th row and j-th column of the matrix, |x| ij Indicates the amplitude value of the element; x i is the i-th element of the vector, |x| i Represents the amplitude value of the element. For details on the traditional element-by-element sign operator method, see "Wang Y, He Z, Yang F, et al. 3D Sparse SAR Image Reconstruction Based on Cauchy Penalty and ConvexOptimization[J]. Remote Sensing, 2022, 14(10): 2308".

[0024] Definition 6. Traditional element-wise hard threshold operator method

[0025] thr(·) represents an element-wise hard thresholding operator for a matrix or vector. This operator applies a hard threshold to each element of the matrix or vector. If the magnitude of the element is less than 0, the element is set to 0; otherwise, it remains unchanged. For details on traditional element-wise hard thresholding operators, see "Wang Y, He Z, Yang F, et al. 3D Sparse SAR Image Reconstruction Based on Cauchy Penalty and Convex Optimization [J]. Remote Sensing, 2022, 14(10): 2308."

[0026] Definition 7. Traditional Singular Value Decomposition Method

[0027] The traditional singular value decomposition method is an important matrix decomposition method in linear algebra. Performing singular value decomposition on a matrix A can obtain the equation A=Udiag(σ(A))V H , where U and V HFor the left and right singular matrices of a matrix, σ(A) is the vector of the matrix's singular values, and diag(σ(A)) is the singular value matrix formed by applying the vector matrix diagonal operator in Definition 4 to the singular value vector σ(A). For details on traditional singular value decomposition methods, see Zhang Xianda. Matrix Analysis and Applications [M]. Tsinghua University Press, 2004.

[0028] Definition 8. Traditional Background Cancellation Interference Suppression Method

[0029] Traditional background cancellation interference suppression methods achieve interference suppression by imaging a scene containing a target and a pure background without a target separately, then canceling the two obtained imaging results. For details on traditional background cancellation interference suppression methods, see "Sensani S, Sarri A, Fiori L, et al. Radar Image Based Near-Field to Far-Field Conversion Algorithmin RCS Measurements[C] / / 2019 IEEE International Symposium on Measurements&Networking(M&N).IEEE, 2019" and "Xu XA background and target signal separation technique for exact RCS measurement[C] / / International Conference on Electromagnetics in Advanced Applications.IEEE, 2012."

[0030] The present invention provides a method for suppressing interference in near-field SAR image domain by decomposing target and interference, which is characterized by comprising the following steps:

[0031] Step 1. Initialize relevant parameters

[0032] The number of pixels in the image direction, denoted as N a ; The number of pixels in the image distance direction, recorded as N r , the image height is the number of pixels, recorded as N h , for a two-dimensional image, its N h =1; the original near-field SAR image containing interference is obtained by processing the traditional back-projection algorithm described in Definition 2, and is denoted as Initialize the target image component, denoted as S(0); initialize the interference image component, denoted as J(0); initialize the Lagrange multiplier matrix, denoted as Y(0); the interference image decomposition weight coefficient, denoted as ξ; and the iterative convergence threshold, denoted as ε.

[0033] Step 2. Height Rearrangement

[0034] The original near-field SAR image containing interference obtained by initialization in step 1 is Each height slice in is rearranged into a column vector using the traditional matrix vectorization operator method described in Definition 3, denoted as d(i), and the dimension of the vector is (N a ×N r )×1, i=1, 2,…, N h Then the column vectors corresponding to each height slice are arranged from left to right to form the rearranged near-field SAR original image containing interference.

[0035] Step 3. Construct the target and interference image decomposition equations

[0036] According to the rearranged near-field SAR original image containing interference obtained by initialization in step 2 Interference image decomposition weight coefficient ξ, construct the target and interference image decomposition equation.

[0037]

[0038] where argmin J,S,Y Indicates Take the minimum values ​​of J, S and Y, where J, S and Y are the interference image, target image and Lagrange multiplier matrix respectively. I is the rearranged near-field SAR original image containing interference obtained in step 2. ‖·‖1 represents the matrix L1 norm, ‖·‖ * represents the matrix nuclear norm, represents the square of the matrix Fibonacci norm, Tr(·) represents the matrix trace, (·) H represents the matrix transpose conjugate.

[0039] Step 4. Iterative decomposition of target and interference images

[0040] For the interference image decomposition weight coefficient ξ and iterative convergence threshold ε initialized in step 1, the target and interference image decomposition equations constructed in step 3 are solved iteratively to achieve iterative decomposition of the target and interference images. In the kth iteration, the following steps are performed:

[0041] Step 4.1. Establish the denoising equation based on the L1 norm regularization of the target image:

[0042]

[0043] O=IJ(k-1)+Y(k-1)

[0044] where argminS Indicates Take the minimum value of S, where S is the target image and O is the noisy target image; I is the rearranged near-field SAR original image with interference obtained in step 2, and J(k-1) and Y(k-1) are the interference image and Lagrange multiplier matrix obtained in the k-1th iteration, respectively.

[0045] Step 4.2 Target image decomposition:

[0046] According to the target image L1 norm regularization denoising equation established in step 4.1, the target image decomposition is achieved using the following formula.

[0047]

[0048] O=IJ(k-1)+Y(k-1)

[0049] where sign(·) is the element-wise sign operator defined in Definition 5, thr(·) is the element-wise hard threshold operator defined in Definition 6, and ⊙ represents the matrix Hadamard product. Represents the dimension as (N a ×N r )×N h where is a matrix with all 1s, O is the noisy target image, and |·| represents the matrix 1-norm. I is the permuted near-field SAR original image containing interference obtained in step 2. J(k-1) and Y(k-1) are the interference image and Lagrange multiplier matrix obtained in the k-1th iteration, respectively. S(k) is the target image updated in the kth iteration.

[0050] Step 4.3. Establish a regularized denoising equation based on the interference image nuclear norm:

[0051]

[0052] P=IS(k)+Y(k-1)

[0053] where argmin J Indicates Take the minimum value of J, where J is the interference image and P is the interference image containing noise; I is the rearranged interference-containing near-field SAR original image obtained in step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, S(k) is the updated target image obtained in step 4.2, and ξ is the interference image decomposition weight coefficient.

[0054] Step 4.4 Interference image decomposition:

[0055] According to the interference image nuclear norm regularization denoising equation established in step 4.3, the interference image decomposition is achieved using the following formula.

[0056] J(k)=U·M·V H

[0057]

[0058] Σ=diag(σ(P))

[0059] P=IS(k)+Y(k-1)

[0060] Among them, U and V H are the left singular matrix and the right singular matrix obtained by decomposing the matrix P according to Definition 7, P is the interference image containing noise; ∑ is the singular value matrix of P, σ(P) is the singular value vector of P, ξ is the decomposition weight coefficient of the interference image, Represents the dimension as (N a ×N r )×N h where is a matrix with all 1s, sign(·) is the element-wise sign operator defined in Definition 5, diag(·) is the vector matrix diagonal operator defined in Definition 4, and M is the singular value matrix after P denoising. I is the permuted near-field SAR original image containing interference obtained in Step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, and S(k) is the updated target image obtained in Step 4.2. J(k) is the interference image updated in the kth iteration.

[0061] Step 4.5. Use the following formula to update the Lagrange multiplier matrix:

[0062] Y(k)=Y(k-1)+IJ(k)-S(k)

[0063] Y(k) is the Lagrange multiplier matrix updated in the kth iteration. I is the permuted near-field SAR original image containing interference obtained in step 2, S(k) is the updated target image obtained in step 4.2, J(k) is the updated interference image obtained in step 4.4, and Y(k-1) is the Lagrange multiplier matrix updated in the k-1th iteration.

[0064] Step 4.6. Iteration stop judgment:

[0065] Using the formula d(k) = ‖(S(k)-S(k-1)) / S(k-1)‖ F , calculate the relative change rate of the target image d(k), where S(k) and S(k-1) are the target images updated in the kth and k-1th iterations, ‖·‖ F represents the matrix Fibonacci norm.

[0066] If d(k) ≥ ε, repeat the steps and proceed to the next iteration; otherwise, stop the iteration. At this time, S(k) is the final near-field SAR interference suppression result, where ε is the iterative convergence threshold.

[0067] The innovation of the present invention lies in: adopting a near-field SAR image domain interference suppression method that is different from background cancellation. The innovation realizes interference suppression from the perspective of image decomposition. By taking advantage of the different characteristics of the interference image and the target image, the nuclear norm and L1 norm are used to describe them respectively, which can effectively decompose the original image and achieve effective interference suppression.

[0068] The advantages of this invention are that it fully considers the characteristics of near-field SAR images containing interference, enabling more accurate decomposition and achieving excellent interference suppression, accurately extracting the target image with minimal residual clutter and noise, and high image quality. It also eliminates the need for background cancellation methods that rely on two consecutive imaging sessions, significantly improving efficiency. Furthermore, it is applicable to interference suppression of both two- and three-dimensional near-field SAR images. Images processed by this method can be used for subsequent applications such as interpreting target scattering characteristics and identifying targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a flow chart of the present invention.

[0070] Figure 2 This is the verification result of the simulation experiment of the present invention. DETAILED DESCRIPTION

[0071] This paper mainly uses the simulation experiment method for verification. All steps and conclusions are verified to be correct on the mathematical calculation software Matlab2019b. The specific implementation steps are as follows:

[0072] Step 1. Initialize relevant parameters

[0073] Number of pixels in the image direction N a =256; image distance pixel N r =512, the image height is the number of pixels N h = 256, the original near-field SAR image containing interference is obtained by processing the back-projection algorithm described in Definition 2, and is denoted as I 256×512×256 ; Initialize target image component S(0) = 0 (256×512)×256 ,0 (256×512)×256 Represents a matrix with dimensions of (256×512)×256 and all elements are 0; initialize the interference image component J(0)=0 (256×512)×256 ; Lagrange multiplier initialization matrix Y(0)=0 (256×512)×256 ; Interference image decomposition weight coefficient ξ=0.5; Iteration convergence threshold ε=0.001.

[0074] Step 2. Height Rearrangement

[0075] The original near-field SAR image I containing interference obtained by initialization in step 1 is 256×512×256 Each height slice in is rearranged into a column vector d(i) by the matrix vectorization operator described in Definition 3, and the dimension of the vector is (256×512)×1, i=1, 2, ..., 256. Then the column vectors corresponding to each height slice are arranged from left to right to form the rearranged near-field SAR original image I containing interference (256×512)×256 , I (256×512)×256 =[d(1) d(2)…d(256)].

[0076] Step 3. Construct the target and interference image decomposition equations

[0077] According to the rearranged near-field SAR original image I containing interference obtained by initialization in step 2 (256×512)×256 , the interference image decomposition weight coefficient ξ=0.5, and the target and interference image decomposition equations are established.

[0078]

[0079] where argmin J,S,Y Indicates Take the minimum values ​​of J, S and Y, where J, S and Y are the interference image, target image and Lagrange multiplier matrix respectively. I is the rearranged near-field SAR original image containing interference obtained in step 2. ‖·‖1 represents the matrix L1 norm, ‖·‖ * represents the matrix nuclear norm, represents the square of the matrix Fibonacci norm, Tr(·) represents the matrix trace, (·) H represents the matrix transpose conjugate.

[0080] Step 4. Iterative decomposition of target and interference images

[0081] Using the interference image decomposition weight coefficient ξ = 0.5 and the iterative convergence threshold ε = 0.001 initialized in step 1, the target and interference image decomposition equations constructed in step 3 are solved iteratively to achieve iterative decomposition of the target and interference images. In the kth iteration, the following steps are performed:

[0082] Step 4.1. Establish the denoising equation based on the L1 norm regularization of the target image:

[0083]

[0084] O=IJ(k-1)+Y(k-1)

[0085] where argmin S Indicates Take the minimum value of S, where S is the target image and O is the noisy target image; I is the rearranged near-field SAR original image with interference obtained in step 2, and J(k-1) and Y(k-1) are the interference image and Lagrange multiplier matrix obtained in the k-1th iteration, respectively.

[0086] Step 4.2 Target image decomposition:

[0087] According to the target image L1 norm regularization denoising equation established in step 4.1, the formula

[0088] S(k)=sign(O)⊙thr(|O|-1 (256×512)×256 )

[0089] O=IJ(k-1)+Y(k-1)

[0090] where sign(·) is the element-wise sign operator defined in Definition 5, thr(·) is the element-wise hard threshold operator defined in Definition 6, and ⊙ represents the matrix Hadamard product; 1 (256×512)×256 represents a matrix of dimensions (256 × 512) × 256 with all elements set to 1. O is the noisy target image, and |·| represents the matrix 1-norm. I is the permuted near-field SAR original image containing interference obtained in step 2. J(k-1) and Y(k-1) are the interference image and Lagrange multiplier matrix obtained in the k-1th iteration, respectively. S(k) is the target image updated in the kth iteration.

[0091] Step 4.3. Establish a regularized denoising equation based on the interference image nuclear norm:

[0092]

[0093] P=IS(k)+Y(k-1)

[0094] where argmin J Indicates Take the minimum value of J, where J is the interference image and P is the interference image containing noise; I is the rearranged interference-containing near-field SAR original image obtained in step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, and S(k) is the updated target image obtained in step 4.2.

[0095] Step 4.4 Interference image decomposition:

[0096] According to the regularized denoising equation based on the interference image nuclear norm established in step 4.3, the formula

[0097] J(k)=U·M·V H

[0098]

[0099] ∑=diag(σ(P))

[0100] P=IS(k)+Y(k-1)

[0101] Among them, U and V H are the left singular matrix and right singular matrix obtained by decomposing the matrix P according to Definition 7, P is the interference image containing noise; ∑ is the singular value matrix of P, σ(P) is the singular value vector of P, represents a matrix of dimension (256×512)×256 with all elements set to 0.5, sign(·) is the element-wise sign operator defined in Definition 5, diag(·) is the vector matrix diagonal operator defined in Definition 4, and M is the singular value matrix after P denoising. I is the permuted near-field SAR original image containing interference obtained in Step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, and S(k) is the updated target image obtained in Step 4.2. J(k) is the interference image updated in the kth iteration. Step 4.5. Lagrange multiplier matrix update:

[0102] Y(k)=Y(k-1)+IJ(k)-S(k)

[0103] Y(k) is the Lagrange multiplier matrix updated in the kth iteration. I is the permuted near-field SAR original image containing interference obtained in step 2, S(k) is the updated target image obtained in step 4.2, J(k) is the updated interference image obtained in step 4.4, and Y(k-1) is the Lagrange multiplier matrix updated in the k-1th iteration.

[0104] Step 4.6. Iteration stop judgment:

[0105] According to the formula d(k) = ‖(S(k)-S(k-1)) / S(k-1)‖ F Calculate the relative change rate of the target image d(k), where S(k) and S(k-1) are the target images updated in the kth and k-1th iterations, ‖·‖ F represents the matrix Fibonacci norm. If d(k) ≥ 0.001, repeat the steps and proceed to the next iteration; otherwise, the iteration is terminated. At this point, S(k) is the final near-field SAR interference suppression result.

[0106] The computer simulation results are Figure 2 shown.

[0107] Computer simulation results show that the present invention realizes near-field SAR interference suppression in the image domain by decomposing the target and interference. The method of the present invention can achieve good interference suppression effect and can extract the target image. Compared with the background cancellation suppression method, the target image error magnitude is comparable, while the clutter and noise residues are less and the image quality is higher.

Claims

1. A method for suppressing interference in near-field SAR image domain by decomposing target and interference, characterized in that it The following steps are involved: Step 1. Initialize relevant parameters The number of pixels in the image direction, denoted as N a ; The number of pixels in the image distance direction, recorded as N r , the image height is the number of pixels, recorded as N h , for a two-dimensional image, its N h =1; the original near-field SAR image containing interference obtained by the traditional back-projection algorithm is denoted as Initialize the target image component, denoted as S(0); initialize the interference image component, denoted as J(0); initialize the Lagrange multiplier matrix, denoted as Y(0); the interference image decomposition weight coefficient, denoted as ξ; the iterative convergence threshold, denoted as ε; Step 2. Height Rearrangement The original near-field SAR image containing interference obtained by initialization in step 1 is Each height slice in the matrix is ​​rearranged into a column vector using the traditional matrix vectorization operator method, denoted as d(i), and the dimension of the vector is (N a ×N r )×1, i=1, 2,…, N h ; Then the column vectors corresponding to each height slice are arranged from left to right to form a rearranged near-field SAR original image containing interference Step 3. Construct the target and interference image decomposition equations According to the rearranged near-field SAR original image containing interference obtained by initialization in step 2 Interference image decomposition weight coefficient ξ, constructing the target and interference image decomposition equation; where argmin J,s,Y Indicates Take the minimum values ​​of J, S and Y, where J, S and Y are the interference image, target image and Lagrange multiplier matrix respectively. I is the rearranged near-field SAR original image containing interference obtained in step 2; ‖·‖1 represents the matrix L1 norm, ‖·‖ * represents the matrix nuclear norm, represents the square of the matrix Fibonacci norm, Tr(·) represents the matrix trace, (·) H represents the matrix transpose conjugate; Step 4. Iterative decomposition of target and interference images For the interference image decomposition weight coefficient ξ and iterative convergence threshold ε initialized in step 1, the target and interference image decomposition equations constructed in step 3 are solved iteratively to achieve iterative decomposition of the target and interference images. In the kth iteration, the following steps are performed: Step 4.

1. Establish the denoising equation based on the L1 norm regularization of the target image: O=IJ(k-1)+Y(k-1) where argmin S Indicates Take the minimum value of S, where S is the target image and O is the target image containing noise; I is the rearranged near-field SAR original image containing interference obtained in step 2, J(k-1) and Y(k-1) are the interference image and Lagrange multiplier matrix obtained in the k-1th iteration respectively; Step 4.2 Target image decomposition: According to the target image L1 norm regularization denoising equation established in step 4.1, the target image decomposition is achieved using the following formula; O=IJ(k-1)+Y(k-1) where sign(·) is the element-wise sign operator, thr(·) is the element-wise hard threshold operator, and ⊙ represents the matrix Hadamard product. The dimension is (N a ×N r )×N h The matrix whose elements are all 1, O is the target image with noise, |·| represents the matrix 1 norm; I is the rearranged near-field SAR original image with interference obtained in step 2, J(k-1) and Y(k-1) are the interference image and Lagrange multiplier matrix obtained in the k-1th iteration respectively; S(k) is the target image updated in the kth iteration; Step 4.

3. Establish a regularized denoising equation based on the interference image nuclear norm: P=IS(k)+Y(k-1) where argmin J Indicates Take the minimum value of J, where J is the interference image, P is the interference image containing noise; I is the rearranged interference-containing near-field SAR original image obtained in step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, S(k) is the updated target image obtained in step 4.2, and ξ is the interference image decomposition weight coefficient; Step 4.4 Interference image decomposition: According to the interference image nuclear norm regularization denoising equation established in step 4.3, the interference image decomposition is achieved using the following formula; J(k)=U·M·V H ∑=diag(σ(P)) P=IS(k)+Y(k-1) Among them, U and V H are the left singular matrix and right singular matrix obtained by matrix singular value decomposition of P, P is the interference image containing noise; ∑ is the singular value matrix of P, σ(P) is the singular value vector of P, ξ is the decomposition weight coefficient of the interference image, The dimension is (N a ×N r )×N h where is a matrix whose elements are all 1, sign(·) is the element-wise sign operator, diag(·) is the vector matrix diagonal operator, and M is the singular value matrix after P denoising. I is the rearranged near-field SAR original image containing interference obtained in step 2, Y(k-1) is the Lagrange multiplier matrix obtained in the k-1th iteration, S(k) is the updated target image obtained in step 4.2, and J(k) is the interference image updated in the kth iteration. Step 4.

5. Use the following formula to update the Lagrange multiplier matrix: Y(k)=Y(k-1)+IJ(k)-S(k) Y(k) is the Lagrange multiplier matrix updated in the k-th iteration; I is the rearranged near-field SAR original image containing interference obtained in step 2, S(k) is the updated target image obtained in step 4.2, J(k) is the updated interference image obtained in step 4.4, and Y(k-1) is the Lagrange multiplier matrix updated in the k-1-th iteration; Step 4.

6. Iteration stop judgment: Using the formula d(k) = ‖(S(k)-S(k-1)) / S(k-1)‖ F , calculate the relative change rate of the target image d(k), where S(k) and S(k-1) are the target images updated in the kth and k-1th iterations, ‖·‖ F represents the matrix Fibonacci norm; If d(k)≥ε, repeat the steps and proceed to the next iteration; Otherwise, the iteration is stopped. At this time, S(k) is the final near-field SAR interference suppression result, where ε is the iterative convergence threshold.

Images