A multi-channel sar enhanced imaging method based on low-rank tensor decomposition

Abstract

The application discloses a kind of based on low-rank tensor chain decomposition multi-channel millimeter wave SAR enhanced imaging method, including the following steps, to the two-dimensional SAR imaging of multi-channel echo, image is carried out phase difference compensation processing;The image of all channels is stacked into three-dimensional tensor, constructs tensor image stack;Inherent low-rank characteristics in SAR image tensor are extracted using tensor chain decomposition;Using TT kernel norm minimization establishes the multi-channel joint enhanced imaging problem model with TTNN constraint;Ket augmentation method is introduced in model, and local features of image neighborhood are strengthened;Based on ADMM framework iteration solution, enhanced imaging result is obtained.The application is processed to multi-channel millimeter wave SAR image by the method of low-rank tensor chain decomposition, realizes image enhancement, obtains clear and complete imaging result, achieves good sidelobe suppression effect, and obtains the effect superior to other algorithms in peak sidelobe ratio, structural similarity, equivalent view number.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and in particular to a multi-channel SAR enhancement imaging method based on low-rank tensor decomposition. Background Technology

[0002] With the rapid development of millimeter-wave technology, millimeter-wave radar systems, especially Synthetic Aperture Radar (SAR), have been widely used in autonomous driving, geological exploration, and urban mapping due to their advantages of high resolution, long range, and multi-channel array gain. However, due to the high spatial loss, limited transmit power, and antenna size limitations of the millimeter-wave band, millimeter-wave radar systems face challenges such as limited imaging range and low signal-to-noise ratio in certain applications, especially on platforms such as UAVs and ground-based rails. To address these issues, researchers have begun exploring how to improve imaging quality and range while maintaining high resolution.

[0003] Digital array technology offers an effective approach to addressing these challenges. Multi-channel digital arrays, through multiple receiving channels combined with digital beamforming (DBF), can acquire full-aperture echoes without beam scanning, improving system gain and range. Currently, traditional digital beamforming techniques primarily rely on linear methods, such as conventional beamforming (CBF), which improves the image signal-to-noise ratio by coherently accumulating the signal. However, this linear processing approach struggles to fully extract the potential structural features and low-rank information from multi-channel data when facing complex imaging scenarios.

[0004] Tensor decomposition (TD), a powerful signal processing tool, can effectively extract and represent the intrinsic structure of high-dimensional data, and has been widely used in video imaging, interferometric SAR, and other fields in recent years. Different TD models, such as the CANDECOMP / PARAFAC (CP) model, the Tucker model, and the Tensor Train (TT) model, each have their own characteristics. Among them, the TT model can balance global information extraction and local feature characterization in a more efficient way, and is particularly suitable for complex multi-channel SAR imaging scenarios. Compared with other TD models, the TT model has more accurate low-rank feature mining, which helps to better characterize redundant information and target features of interest in multi-channel radar images.

[0005] In millimeter-wave SAR systems, multi-channel arrays not only effectively improve imaging resolution and signal-to-noise ratio, but also uncover low-rank prior features in complex imaging environments. By deeply mining the low-rank characteristics of tensor data, image quality can be further improved, enabling radar systems to handle more complex imaging tasks.

[0006] In summary, the main challenge currently facing millimeter-wave SAR imaging technology lies in how to improve image quality and resolution through nonlinear and multidimensional data processing methods. Against this backdrop, tensor decomposition techniques, especially tensor chain decomposition models, have become an important research direction in multi-channel SAR imaging due to their powerful data processing capabilities. Summary of the Invention

[0007] Technical Problem: To further improve the image quality and resolution of multi-channel SAR imaging, this invention provides a multi-channel millimeter-wave SAR enhancement imaging method based on low-rank tensor chain decomposition, which can improve the imaging quality of multi-channel SAR.

[0008] Technical Solution: To achieve the above-mentioned objectives, this invention provides a multi-channel SAR enhancement imaging method based on low-rank tensor decomposition, comprising the following steps:

[0009] Step 1: Perform two-dimensional synthetic aperture radar (SAR) imaging on the multi-channel echoes and perform phase difference compensation processing on the images.

[0010] Step 2: Stack the images from all channels into a 3D tensor to construct an image tensor stack;

[0011] Step 3: Use tensor chain decomposition to extract the inherent low-rank characteristics in the SAR image tensor stack, providing a basic data structure for subsequent modeling.

[0012] Step 4: Based on the low-rank characteristic, a multi-channel joint enhancement imaging problem model with tensor chain nuclear norm TTNN constraints is established by minimizing the tensor chain nuclear norm TTNN.

[0013] Step 5: Based on the multi-channel joint enhancement imaging problem model, the Ket augmentation method is introduced to enhance the local features of the image neighborhood;

[0014] Step 6: Iteratively solve the optimization problem after introducing Ket augmentation based on the alternating direction multiplier ADMM framework to obtain the enhanced imaging results.

[0015] The step of performing two-dimensional synthetic aperture radar SAR imaging on multi-channel echoes and performing phase difference compensation processing on the images includes:

[0016] Because the echo corresponding to the p-th transmitting element after decoding by a multi-input multi-output synthetic aperture radar (SAR) is

[0017]

[0018] Where c is the electromagnetic wave propagation speed, {x,r} represents the target's azimuth and distance information, and R... p,q Let Ω represent the sum of the distances from the q-th element to the target and the target to the p-th element, and let τ and t represent the imaging area. m T represents fast time and slow time, respectively. p G represents the synthesis aperture time, γ represents the frequency modulation, λ represents the wavelength, and G represents the synthesis aperture time. p and G q Let σ(x,r) represent the channel gain of the p-th transmitting element and the q-th receiving element, respectively; let σ(x,r) represent the scattering cross-section at position (x,r); p and q represent the serial numbers of the transmitting and receiving elements, respectively, p = 1, 2, 3, ..., Pq = 1, 2, 3, ..., Q; and let P and Q represent the total number of transmitting and receiving elements, respectively.

[0019] Using the Back Projection Algorithm (BPA), the resulting image at (x, r) is expressed as follows:

[0020]

[0021] Where I represents the single-channel imaging result, x p and x q The p-th and q-th array elements represent their azimuth positions, respectively, and θ represents the incident angle of the target echo. Phase difference compensation processing is performed on the image of each channel to ensure phase consistency between images.

[0022] The step of stacking all channels of the image into a three-dimensional tensor to construct the image tensor stack includes:

[0023] Stack the images from each channel into a third-order tensor. Denotes the field of complex numbers, where l = (p-1)Q + q, L = PQ, where P and Q represent the total number of transmitting and receiving array elements, respectively; correspondingly, x is defined... l =x p +x q At this point, the image tensor stack is represented as

[0024]

[0025] in It is a column vector in which all elements are 1. Represents the real number field. It is a third-order tensor composed of the phase difference between channels. It is additive Gaussian noise. The symbol ⊥ represents the outer product, and ⊙ represents element-wise multiplication. This represents the image tensor stack.

[0026] The method of extracting the inherent low-rank characteristics of the SAR image tensor stack using tensor chain decomposition includes:

[0027] For image tensor stacks Its dimensions are represented as {I1,I2,I3}={N,M,L}; the tensor chain TT decomposition of this SAR image tensor stack includes two rearrangements and two singular value decompositions, and the TT-rank in each decomposition is defined as...

[0028] {R0=T0=1, R1=T1, R2=T2, R3=T3=1}

[0029] R0, R1, R2, and R3 represent the ranks of each core tensor obtained from the two rearrangements and two singular value decompositions, respectively; T0, T1, T2, and T3 represent the truncation positions, and by selecting appropriate values, the low-rank characteristics of the image tensor stack are adapted.

[0030] Where T1 < min(N,ML), T2 < min(T1M,L), The specific steps of tensor chain decomposition are as follows: First, decompose the tensor chain into its components. Matrixing is performed, and this process is represented as follows:

[0031]

[0032] X1 is... The result of matrix transformation is then used to compute the tensor SVD of X1, i.e.:

[0033] X1=U1S1V1 H

[0034] In the formula, U1, S1, and V1 are the tensor SVD decomposition results of X1, the first kernel tensor. Represented as Then for S1V1 H To truncate, that is:

[0035] A1=S1(1:T1,1:T1)V1 H (:,1:T1)

[0036] A represents the result of the truncation, and T1 represents the truncation position. After truncation, ... Rearrange to obtain The relationship between the (i1, i2)th element of A1 and the (j1, j2)th element of X2 is:

[0037]

[0038] T1 is for S1V1 H The truncation points, M and L represent the image stack, respectively. The second and third dimensions U2, S2, and V2 are the SVD decomposition results of X2; the second kernel tensor From the matrix Vectorization yields its relational expression. In the formula, T2 is the position where the second tensor is truncated; the third kernel tensor Represented as in In the above formula, S and V both represent the results of tensor SVD decomposition.

[0039] The expression for the multi-channel joint enhancement imaging problem model with tensor chain nuclear norm TTNN constraints, established by minimizing the TT nuclear norm, is as follows:

[0040]

[0041] ||*|| F The F-norm and TT-rank are actually composed of the ranks of tensors after matrix transformation according to different moduli; optimization problems with matrix rank constraints are nondeterministic polynomial-hard NP-hard problems, and relaxation is solved by nuclear norm; in the formula... Represents the original image stack. X1 is... The result of matrix transformation, X2 is the rearranged result, which represents the third-order tensor. The weighted TTNN, where ω is the weighting coefficient.

[0042] The introduction of the Ket augmentation method to enhance local features in the image neighborhood includes:

[0043] In Ket augmentation, The dimensions are first decomposed into N = N1 × N2 × … × N D-1 M = M1 × M2 × … × M D-1 and L=N D ×M D D represents the number of image patches, where and Let N represent the dimension size during block-by-block image structured addressing; furthermore, let N... D =L,M D =1, then rearrange the original tensor and swap dimensions to obtain After introducing Ket augmentation, the TTNN of higher-order tensors is defined as follows:

[0044]

[0045] ω is the weighting coefficient; similarly, the augmentation imaging problem with TTNN constraints can be modeled as follows:

[0046]

[0047] in This is the stack of the original images after Ket augmentation, where γ is a weighting coefficient and the optimization objective. It is a higher-order tensor after introducing Ket augmentation. To solve the objective.

[0048] The iterative solution based on the alternating direction multiplier ADMM framework includes:

[0049] The model is transformed into the optimization problem described below:

[0050]

[0051] The corresponding augmented Lagrangian function is

[0052]

[0053] A set of auxiliary variables introduced, That is, optimizing variables. This is the stack of the original images after Ket augmentation, where λ is the weighting coefficient, D represents the number of image patches, and ω... d These are the weights used for the d-th image. It is the introduced dual variable, representing the penalty coefficient. Similarly, the dual variables are also introduced. As an auxiliary variable introduced, λ is the weighting coefficient. The following subproblems are updated progressively to obtain the solution to the augmented Lagrangian function in the minimization optimization problem.

[0054]

[0055] In the formula, k is the iteration number, R and β represent the dual variables and penalty coefficients, η is the rising parameter used to adjust the penalty coefficient, and ω and λ are quantities introduced by the augmented Lagrangian function. The specific iterative update steps include:

[0056] renew

[0057]

[0058] in It is a singular value matrix, and a left singular value matrix. Right singular value matrix It is derived from singular value decomposition The obtained ; svt(·) represents the singular value thresholding operation, the r-th d The values ​​of the diagonal elements after SVT are updated to...

[0059] Then update

[0060]

[0061] fold <d>< / d> This is a rewrite for ease of expression. R and β represent the dual variables and penalty coefficients, D represents the number of image blocks, and δ is the quantity introduced by the augmented Lagrangian function. A set of auxiliary variables introduced, This is the original image stack after Ket augmentation;

[0062] Finally, update the dual variable and penalty coefficient.

[0063] Beneficial Effects: Compared with existing technologies, the beneficial effects of this invention are as follows: This invention stacks the two-dimensional SAR imaging results from multiple channels to form a tensor. The redundancy of the multi-channel image stack is characterized using a low-rank tensor chain decomposition model. The multi-channel SAR enhancement imaging problem is modeled and relaxed into a TTNN minimization problem, and an ADMM iterative solution process is provided, ultimately achieving SAR image enhancement. This invention proposes and solves an effective low-rank tensor chain decomposition model for SAR image enhancement. The algorithm not only effectively utilizes the array gain of multiple channels to improve the signal-to-noise ratio of SAR images but also reduces sidelobe levels, effectively achieving SAR image enhancement. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of the overall process of the SAR image compression method based on robust tensor decomposition proposed in this invention.

[0065] Figure 2 This diagram illustrates the comparison of TTNN's performance with other algorithms in a MIMO multi-channel SAR simulation scenario. The bottom left corner shows the integral sidelobe ratio (ISLR). (a) shows the TTNN simulation imaging result, (b) shows the Tucker result, (c) shows the DBF result, and (d) shows the single-channel result.

[0066] Figure 3 This diagram illustrates the quantitative analysis of TTNN compared to other algorithms in a MIMO multi-channel SAR simulation scenario. (a) represents the peak-to-sidelobe ratio (PSNR), (b) represents structural similarity (SSIM), and (c) represents the equivalent number of looks (ENL). Detailed Implementation

[0067] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0068] This invention can be implemented in many different forms and should not be considered as limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully express the scope of the invention to those skilled in the art.

[0069] like Figure 1 As shown, Figure 1 This is a schematic diagram of the overall process of a multi-channel millimeter-wave SAR enhancement imaging method based on low-rank tensor chain decomposition proposed in this invention. The method includes the following steps:

[0070] Step 1: Perform two-dimensional SAR imaging on the multi-channel echo and perform phase difference compensation processing on the image;

[0071] Specifically, multi-channel echo 2D SAR imaging includes the following steps:

[0072] The echo corresponding to the p-th transmit channel after MIMO-SAR decoding is

[0073]

[0074] Where c is the electromagnetic wave propagation speed, {x,r} represents the target's azimuth and distance information, and R... p,q Let Ω represent the sum of the distances from the q-th element to the target and the target to the p-th element, and let τ and t represent the imaging area. m T represents fast time and slow time, respectively. p G represents the synthesis aperture time, γ represents the frequency modulation, λ represents the wavelength, and G represents the synthesis aperture time. p and G q Let σ(x,r) represent the channel gain of the p-th transmitting element and the q-th receiving element, respectively, and let σ(x,r) represent the scattering cross-section at position (x,r). Let p and q represent the serial numbers of the transmitting and receiving elements, respectively, p = 1, 2, 3, ..., Pq = 1, 2, 3, ..., Q, and let P and Q represent the total number of transmitting and receiving elements, respectively.

[0075] Performing an α-fold interpolation FFT along the fast time dimension on the echo matrix achieves range compression, yielding a one-dimensional range image:

[0076]

[0077] Where B is the effective bandwidth of the waveform, c is the propagation speed of electromagnetic waves in vacuum, and n'∈[1,2,…,αN] is the index of the range profile. After range compression, the platform velocity is first estimated using the Map Drift algorithm, and then, based on the slant range expression, the radial distance from (x,r) to the radar at the m-th pulse moment is obtained as follows:

[0078]

[0079] Its corresponding distance cell index is

[0080]

[0081] Where round(·) represents the rounding operation. After obtaining its index in the range image, corresponding phase compensation is performed and the results are accumulated to achieve back projection imaging. This process can be represented as follows:

[0082]

[0083] The expression for the imaging result at (x,r) is:

[0084]

[0085] Where I represents the single-channel imaging result, x p and x q These represent the directional positions of the array elements.

[0086] Step 2: Stack the images of all channels into a 3D tensor to construct a tensor image stack;

[0087] Specifically, the images from each channel are stacked into a third-order tensor. in l = (p-1)Q + q, L = PQ. Accordingly, define x l =x p +x q At this point, the image stack tensor can be represented as:

[0088]

[0089] in It is a column vector in which all elements are 1. It is a third-order tensor composed of the phase difference between channels. It is additive Gaussian noise. represents the outer product, and represents element-wise multiplication.

[0090] Step 3: Extract the inherent low-rank properties of SAR image tensors using tensor chain decomposition.

[0091] Specifically, for image stacks:

[0092]

[0093] Its dimensions can be represented as {I1,I2,I3}={N,M,L}. The TT decomposition of this tensor can contain two rearrangements and two singular value decompositions. The TT-rank in each decomposition is defined as:

[0094] {R0=T0=1, R1=T1, R2=T2, R3=T3=1}

[0095] Where T1 < min(N,ML), T2 < min(T1M,L), The specific steps for tensor chain decomposition (TT) are as follows: First, decompose the tensor chain (TT) into tensor chains. The matrix transformation process can be represented as follows:

[0096]

[0097] Then calculate the SVD of X1, that is:

[0098] X1=U1S1V1 H

[0099] First kernel tensor It can be represented as Then for S1V1 H To truncate, that is:

[0100] A1=S1(1:T1,1:T1)V1 H (:,1:T1)

[0101] After severance, Rearrange to obtain The relationship between the (i1, i2)th element of A1 and the (j1, j2)th element of X2 is:

[0102]

[0103] Similarly, calculate the SVD of X2, i.e. Second kernel tensor Can be derived from matrix Vectorization yields its relational expression. The third kernel tensor It can be represented as in

[0104] Step 4: Utilize TT nuclear norm minimization to establish a multi-channel joint enhancement imaging problem model with TTNN constraints;

[0105] Specifically, it includes the following steps:

[0106] The expression for the multi-channel joint enhancement imaging problem model with tensor chain nuclear norm (TTNN) constraints, established by minimizing the TT nuclear norm, is as follows:

[0107]

[0108] The TT-rank is actually composed of the ranks of tensors after matrix transformation according to different moduli. Optimization problems with matrix rank constraints are NP-hard problems; this invention relaxes them by solving for the nuclear norm. In the formula... That is, to represent a third-order tensor The weighted TTNN, where ω is the weighting coefficient.

[0109] Step 5: Introduce the Ket augmentation method to enhance local features in the image neighborhood.

[0110] Specifically, in Ket augmentation, The dimensions are first decomposed into N = N1 × N2 × … × N D-1 M = M1 × M2 × … × M D-1 and L=N D ×M D ,in and This represents the dimension size during block-by-block image structured addressing. Furthermore, let N... D =L,M D =1. Then rearrange the original tensor and swap its dimensions to obtain... After introducing Ket augmentation, the TTNN of higher-order tensors is defined as follows:

[0111]

[0112] Similarly, the augmentation imaging problem with TTNN constraints can be modeled as follows:

[0113]

[0114] in This is the stack of the original images augmented by Ket.

[0115] Step 6: Iteratively solve the problem based on the ADMM framework to obtain the enhanced imaging results.

[0116] Specifically, we first introduce a set of auxiliary variables. in The model is then transformed into the optimization problem described below:

[0117]

[0118] Then, dual variables are introduced. The corresponding augmented Lagrangian function is

[0119]

[0120] in This is the penalty coefficient. By progressively updating the following subproblems, we can obtain the solution to the augmented Lagrangian function in the optimization problem.

[0121]

[0122] In the formula, R and β represent the dual variables and penalty coefficients, respectively; η is the rising parameter used to adjust the penalty coefficient; and ω and λ are quantities introduced by the augmented Lagrangian function. The specific iterative update steps include:

[0123] renew about The subproblem can be represented as

[0124]

[0125] Its closed-form solution is: in It is a singular value matrix, derived from singular value decomposition. Obtained. `svt(·)` represents the singular value thresholding operation. The r-th... d The values ​​of the diagonal elements after SVT are updated to...

[0126] Then update about The subproblem can be represented as

[0127]

[0128] For ease of explanation, the above formula is rewritten as follows:

[0129]

[0130] make The closed-form solution is obtained as

[0131]

[0132] Finally, update the dual variable and penalty coefficient. After the maximum number of iterations or the set convergence condition is met, the obtained... This is the final result of multi-channel SAR enhanced imaging.

[0133] To verify the beneficial effects of the present invention, the following experiments were conducted:

[0134] 1. This invention designs multi-channel SAR simulation experiments. In the simulation, a 2-transmit, 2-receive DDMMIMO array is set up, and different algorithms (TTNN, Tucker, DBF) are used for imaging processing. After obtaining the enhanced imaging results, the image quality of different algorithms is compared by considering structure, sharpness, and clutter. Quantitative analysis is performed using three indicators: PSNR, SSIM, and equivalent number of looks.

[0135] The experimental results are as follows: (Refer to the diagram) Figure 2 3 Figure 2 The figure shows a comparison of simulation results for single-building SAR tomography using L1NM, ANM, and the algorithm of this invention. It can be seen from the figure that the tensor decomposition method can effectively suppress sidelobes and enhance target features. TTNN, Tucker, and DBF can all utilize array gain to achieve better image signal-to-noise ratios than single-channel imaging. Algorithms utilizing the low-rank properties of tensors can achieve better denoising performance than DBF. Based on this, the proposed algorithm has a lower sidelobe level and higher image quality than Tucker. Figure 3 Quantitative analysis results are presented. Similar to the qualitative analysis results, the proposed algorithm shows significant advantages in three metrics: Peak Sidelobe Ratio (PSNR), Structural Similarity to Image (SSIM), and Equivalent Number of Looks (ENL). These advantages are even more pronounced at high signal-to-noise ratios. This indicates that, in addition to denoising, the proposed algorithm can also suppress sidelobes and lateral levels, improving image quality and achieving enhanced imaging results.

[0136] It should be noted that the above-described embodiments only illustrate some implementation methods of the present invention, and their description should not be construed as limiting the scope of the present invention. It should be pointed out that those skilled in the art can make several improvements without departing from the concept of the present invention, and these improvements should all fall within the protection scope of the present invention.

Claims

1. A multi-channel SAR enhancement imaging method based on low-rank tensor decomposition, characterized in that: Includes the following steps, Step 1: Perform two-dimensional synthetic aperture radar (SAR) imaging on the multi-channel echoes and perform phase difference compensation processing on the images. Step 2: Stack the images from all channels into a 3D tensor to construct an image tensor stack; Step 3: Use tensor chain decomposition to extract the inherent low-rank characteristics in the SAR image tensor stack, providing a basic data structure for subsequent modeling. Step 4: Based on the low-rank property, a multi-channel joint enhancement imaging problem model with tensor chain nuclear norm TTNN constraints is established by minimizing the tensor chain nuclear norm TTNN; the expression is: ||*|| F The F-norm and TT-rank are actually composed of the ranks of tensors after matrix transformation according to different moduli; optimization problems with matrix rank constraints are nondeterministic polynomial-hard NP-hard problems, and relaxation is solved by nuclear norm; in the formula... Represents the original image stack. X1 is... The result of matrix transformation, X2 is the rearranged result, which represents the third-order tensor. The weighted TTNN, where ω is the weighting coefficient; Step 5: Based on the multi-channel joint enhancement imaging problem model, the Ket augmentation method is introduced to enhance the local features of the image neighborhood; Step 6: Iteratively solve the optimization problem after introducing Ket augmentation based on the alternating direction multiplier ADMM framework to obtain the enhanced imaging results.

2. The multi-channel SAR enhancement imaging method based on low-rank tensor decomposition as described in claim 1, characterized in that: The step of performing two-dimensional synthetic aperture radar SAR imaging on multi-channel echoes and performing phase difference compensation processing on the images includes: Because the echo corresponding to the p-th transmitting element after decoding by a multi-input multi-output synthetic aperture radar (SAR) is Where c is the electromagnetic wave propagation speed, {x,r} represents the target's azimuth and distance information, and R... p,q Let Ω represent the sum of the distances from the q-th element to the target and the target to the p-th element, and let τ and t represent the imaging area. m T represents fast time and slow time, respectively. p G represents the synthesis aperture time, γ represents the frequency modulation, λ represents the wavelength, and G represents the synthesis aperture time. p and G q Let σ(x,r) represent the channel gain of the p-th transmitting element and the q-th receiving element, respectively; let σ(x,r) represent the scattering cross-section at position (x,r); p and q represent the serial numbers of the transmitting and receiving elements, respectively, p = 1, 2, 3, ..., P, q = 1, 2, 3, ..., Q, and let P and Q represent the total number of transmitting and receiving elements, respectively. Using the Back Projection Algorithm (BPA), the resulting image at (x, r) is expressed as follows: Where I represents the single-channel imaging result, x p and x q The p-th and q-th array elements represent their azimuth positions, respectively, and θ represents the incident angle of the target echo. Phase difference compensation processing is performed on the image of each channel to ensure phase consistency between images.

3. The multi-channel SAR enhancement imaging method based on low-rank tensor decomposition as described in claim 2, characterized in that: The step of stacking all channels of the image into a three-dimensional tensor to construct the image tensor stack includes: Stack the images from each channel into a third-order tensor. Denotes the field of complex numbers, where l = (p-1)Q + q, L = PQ, where P and Q represent the total number of transmitting and receiving array elements, respectively; correspondingly, x is defined... l =x p +x q At this point, the image tensor stack is represented as in It is a column vector in which all elements are 1. Represents the real number field. It is a third-order tensor composed of the phase difference between channels. It is additive Gaussian noise. The symbol ⊙ represents the outer product, and ⊙ represents element-wise multiplication. This represents the image tensor stack.

4. The multi-channel SAR enhancement imaging method based on low-rank tensor decomposition as described in claim 3, characterized in that: The method of extracting the inherent low-rank characteristics of the SAR image tensor stack using tensor chain decomposition includes: For image tensor stacks Its dimensions are represented as {I1,I2,I3}={N,M,L}; the tensor chain TT decomposition of this SAR image tensor stack includes two rearrangements and two singular value decompositions, and the TT-rank in each decomposition is defined as {R0=T0=1,R1=T1,R2=T2,R3=T3=1}. R0, R1, R2, and R3 represent the ranks of each core tensor obtained from the two rearrangements and two singular value decompositions, respectively; T0, T1, T2, and T3 represent the truncation positions, which are adjusted by selecting appropriate values ​​to fit the image tensor stack. The low-rank characteristic; Where T1 < min(N,ML), T2 < min(T1M,L), The specific steps of tensor chain decomposition are as follows: First, decompose the tensor chain into its components. Matrixing is performed, and this process is represented as follows: X1 is... The result of matrix transformation is then used to compute the tensor SVD of X1, i.e.: In the formula, U1, S1, and V1 are the tensor SVD decomposition results of X1, the first kernel tensor. Represented as Then to To truncate, that is: A represents the result of the truncation, and T1 represents the truncation position. After truncation, ... Rearranged to obtain The relationship between the (i1, i2)th element of A1 and the (j1, j2)th element of X2 is: T1 is a pair The truncation points, M and L represent the image stack, respectively. The second and third dimensions U2, S2, and V2 are the SVD decomposition results of X2; the second kernel tensor From the matrix Vectorization yields its relational expression. In the formula, T2 is the position where the second tensor is truncated; the third kernel tensor Represented as in In the above formula, S and V both represent the results of tensor SVD decomposition.

5. The multi-channel SAR enhancement imaging method based on low-rank tensor decomposition as described in claim 1, characterized in that: The introduction of the Ket augmentation method to enhance local features in the image neighborhood includes: In Ket augmentation, The dimensions are first decomposed into N = N1 × N2 × … × N D-1 M = M1 × M2 × … × M D-1 and L=N D ×M D D represents the number of image patches, where Let N represent the dimension size during block-by-block image structured addressing; furthermore, let N... D =L,M D =1, then rearrange the original tensor and swap dimensions to obtain After introducing Ket augmentation, the TTNN of higher-order tensors is defined as follows: ω is the weighting coefficient; similarly, the augmentation imaging problem with TTNN constraints can be modeled as follows: in This is the stack of the original images after Ket augmentation, where γ is a weighting coefficient and the optimization objective. It is a higher-order tensor after introducing Ket augmentation. To solve the objective.

6. The multi-channel SAR enhancement imaging method based on low-rank tensor decomposition as described in claim 5, characterized in that: The iterative solution based on the alternating direction multiplier ADMM framework includes: The model is transformed into the optimization problem described below: The corresponding augmented Lagrangian function is A set of auxiliary variables introduced, That is, optimizing variables. This is the stack of the original images after Ket augmentation, where λ is the weighting coefficient, D represents the number of image patches, and ω... d These are the weights used for the d-th image. The introduced dual variable represents the penalty coefficient. Similarly, dual variables are introduced. As an auxiliary variable introduced, λ is the weighting coefficient. The following subproblems are updated progressively to obtain the solution to the augmented Lagrangian function in the minimization optimization problem. In the formula, k is the iteration number, R and β represent the dual variables and penalty coefficients, η is the rising parameter used to adjust the penalty coefficient, and ω and λ are quantities introduced by the augmented Lagrangian function. The specific iterative update steps include: renew in It is a singular value matrix, and a left singular value matrix. Right singular value matrix It is derived from singular value decomposition The obtained ; svt(·) represents the singular value thresholding operation, the r-th d The values ​​of the diagonal elements after SVT are updated to... Then update fold <d>< / d> This is a rewrite for ease of expression. R and β represent the dual variables and penalty coefficients, D represents the number of image blocks, and δ is the quantity introduced by the augmented Lagrangian function. A set of auxiliary variables introduced, This is the stack of the original images after Ket augmentation; Finally, update the dual variable and penalty coefficient.

Images