Multi-channel SAR enhanced imaging method based on low-rank tensor decomposition

Abstract

The invention discloses a multi-channel millimeter wave SAR enhanced imaging method based on low-rank tensor chain decomposition, and the method comprises the following steps: carrying out the two-dimensional SAR imaging of multi-channel echoes, and carrying out the phase difference compensation of an image; stacking the images of all the channels into a three-dimensional tensor, and constructing a tensor image stack; extracting inherent low-rank characteristics in the SAR image tensor by using tensor chain decomposition; establishing a multi-channel joint enhanced imaging problem model with TTNN constraint by using TT nuclear norm minimization; a Ket augmentation method is introduced into the model, and image neighborhood local features are enhanced; and performing iterative solution based on an ADMM framework to obtain an enhanced imaging result. According to the method, the multi-channel millimeter wave SAR image is subjected to combined processing through a low-rank tensor chain decomposition method, image enhancement is achieved, a clear and complete imaging result is obtained, a good side lobe suppression effect is achieved, and the effects superior to those of other algorithms are achieved in the aspects of peak side lobe ratio, structural similarity and equivalent looks.

Description

Technical Field

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

[0002] With the rapid development of millimeter wave technology, millimeter wave radar systems, especially synthetic aperture radar (SAR), have been widely used in fields such as 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 of the millimeter wave frequency band, limited transmission power, and antenna size limitations, millimeter wave radar systems face challenges of limited imaging distance and low signal-to-noise ratio in some application scenarios, especially on platforms such as drones and ground-based slides. To solve these problems, researchers began to explore how to improve imaging quality and range while maintaining high resolution.

[0003] Digital array technology provides an effective way to address these challenges. Multi-channel digital arrays use multiple receiving channels combined with digital beamforming (DBF) to collect full-aperture echoes without beam scanning, thereby improving the system's gain and range. Currently, traditional digital beamforming technology mainly relies on linear methods, such as conventional beamforming (CBF), which improves the image signal-to-noise ratio by coherently accumulating signals. However, this linear processing method is difficult to fully exploit the potential structural features and low-rank information in multi-channel data when faced with complex imaging scenes.

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

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

[0006] In general, the main challenge facing millimeter wave SAR imaging technology is how to improve image quality and resolution through nonlinear and multidimensional data processing methods. In this context, tensor decomposition technology, especially the tensor chain decomposition model, has become an important research direction in multi-channel SAR imaging due to its powerful data processing capabilities. Summary of the invention

[0007] Technical problem: In order to further improve the image quality and resolution of multi-channel SAR imaging, the present invention provides a multi-channel millimeter-wave SAR enhanced imaging method based on low-rank tensor chain decomposition, which can improve the imaging quality of multi-channel SAR.

[0008] Technical solution: In order to achieve the above-mentioned invention object, the present invention provides a multi-channel SAR enhanced imaging method based on low-rank tensor decomposition, comprising the following steps:

[0009] Step 1, performing two-dimensional synthetic aperture radar SAR imaging on the multi-channel echoes and performing phase difference compensation processing on the images;

[0010] Step 2, stack the images of all channels into a three-dimensional tensor to construct an image tensor stack;

[0011] Step 3, using 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 property, the tensor chain TT nuclear norm NN minimization is used to establish a multi-channel joint enhanced imaging problem model with tensor chain nuclear norm TTNN constraints;

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

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

[0015] The two-dimensional synthetic aperture radar SAR imaging is performed on the multi-channel echoes, and the phase difference compensation processing is performed on the image, which includes:

[0016] Since the echo corresponding to the pth transmitting array element after decoding of the multiple-input multiple-output synthetic aperture radar SAR is

[0017]

[0018] Where c is the propagation speed of electromagnetic waves, {x, r} represents the direction and distance information of the target, and R p,q represents the sum of the distance from the qth array element to the target and the distance from the target to the pth array element, Ω represents the imaging area, τ and t m Denote fast time and slow time respectively, T p represents the synthetic aperture time, γ represents the modulation frequency, λ represents the wavelength, G p and G q denote the channel gains of the pth transmitting element and the qth receiving element, respectively; σ(x,r) denotes the scattering cross-sectional area at the position (x,r); p and q denote the serial numbers of the transmitting and receiving elements, respectively; p=1,2,3,...,Pq=1,2,3,...,Q, and P and Q denote the total number of transmitting and receiving elements, respectively;

[0019] Using the back-projection algorithm BPA, the imaging result expression at (x, r) is:

[0020]

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

[0022] The images of all channels are stacked into a three-dimensional tensor, and the image tensor stack is constructed including:

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

[0024]

[0025] in is a column vector whose elements are all 1, represents the field of real numbers, is a third-order tensor consisting of the phase difference between channels, is additive Gaussian noise, represents the outer product, ⊙ represents element-by-element multiplication, Represents a stack of image tensors.

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

[0027] For image tensor stacks Its dimension is expressed as {I1, I2, I3} = {N, M, L}; the tensor chain TT decomposition of the 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 rank of each core tensor obtained by two rearrangements and two singular value decompositions, respectively; T0, T1, T2, and T3 represent the truncation positions, and by selecting appropriate values, they adapt to the low-rank characteristics of the image tensor stack;

[0030] Where T1<min(N,ML), T2<min(T1M,L), The specific steps of tensor chain decomposition are as follows: First, Matrixization is performed, and the process is expressed as

[0031]

[0032] X1 The result of matrixization is then used to calculate the tensor SVD of X1, namely:

[0033] X1=U1S1V1 H

[0034] U1, S1, and V1 in the formula are the tensor SVD decomposition results of X1. The first core tensor Expressed as Then for S1V1 H Truncate, that is:

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

[0036] A is the result of truncation, T1 is the position of truncation, after truncation, Rearrange to get 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 position of the cutoff, M, L represent the image stack The second and third dimensions, U2, S2, V2 are the SVD decomposition results of X2; the second core tensor By matrix Vectorization results in the relational expression T2 in the formula is the position where the second tensor is truncated; the third core tensor Expressed as in In the above formula, S and V both represent the results of tensor SVD decomposition.

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

[0040]

[0041] ||*|| F represents the F-norm, and the TT-rank is actually composed of the ranks of the tensors after matrixing according to different moduli; the optimization problem with matrix rank constraints is a non-deterministic polynomial NP-hard problem, which is relaxed to the nuclear norm solution; represents the original image stack, X1 The result of matrixization, X2 is the result after rearrangement, which represents a third-order tensor The weighted TTNN of , where ω is the weighting coefficient.

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

[0043] In Ket augmentation, The dimension is 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 blocks, where and Indicates the dimension size of the block-by-block image structured addressing; in addition, let N D =L,M D = 1, then rearrange the original tensor and swap the dimensions to get After introducing Ket augmentation, the TTNN of high-order tensor is defined as

[0044]

[0045] ω is the weighting coefficient. Similarly, the enhanced imaging problem with TTNN constraints can be modeled as

[0046]

[0047] in is the original image stack after Ket augmentation, γ is a weight coefficient, and the optimization objective is a high-order tensor after the introduction of Ket augmentation, To solve the goal.

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

[0049] The model is transformed into an optimization problem as follows:

[0050]

[0051] The corresponding augmented Lagrangian function is

[0052]

[0053] is a set of auxiliary variables introduced, That is, the optimization variable, is the original image stack after Ket augmentation, λ is the weight coefficient, D represents the number of image blocks, ω d is the weight used for the d-th image, is the introduced dual variable, which represents the penalty coefficient, The dual variable is also introduced. is a set of auxiliary variables introduced, λ is the weight coefficient, and the following sub-problems are gradually updated to obtain the solution of the augmented Lagrangian function in the minimization optimization problem:

[0054]

[0055] Where k is the number of iterations, R and β represent the dual variables and penalty coefficients, η is the rise parameter used to adjust the penalty coefficient, ω and λ are the quantities introduced by the augmented Lagrangian function, and the specific iterative update steps include:

[0056] renew

[0057]

[0058] in is the singular value matrix, and the left singular value matrix Right singular value matrix Singular value decomposition obtained; svt(·) represents the singular value threshold operation, the rth d The values ​​of the diagonal elements after SVT are updated to

[0059] Then update

[0060]

[0061] fold <d>< / d> It is a rewrite for the convenience 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; is a set of auxiliary variables introduced, is the original image stack after Ket augmentation;

[0062] Finally, update the dual variables and penalty coefficients.

[0063] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects: the present invention uses the two-dimensional SAR imaging results of multiple channels to stack and form a tensor, characterizes the redundancy of the multi-channel image stack through a low-rank tensor chain decomposition model, models the multi-channel SAR enhanced imaging problem and relaxes it into a TTNN minimization problem, and gives an ADMM iterative solution process, and finally realizes SAR image enhancement. The present invention proposes and solves an effective low-rank tensor chain decomposition model for SAR image enhancement. The inventive algorithm can not only effectively utilize the array gain of multiple channels to improve the signal-to-noise ratio of SAR images, but also reduce the sidelobe level, effectively realizing SAR image enhancement. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0065] Figure 2 This is a schematic diagram of the comparison between TTNN and other algorithms in the MIMO multi-channel SAR simulation experiment scenario. The lower left corner is the integrated sidelobe ratio (ISLR). Among them, (a) is the TTNN simulation imaging result, (b) is the Tucker result, (c) is the DBF result, and (d) is the single-channel result.

[0066] Figure 3 The figure is a schematic diagram of the quantitative analysis of TTNN compared with other algorithms in the MIMO multi-channel SAR simulation experiment scenario. Among them, (a) is the peak sidelobe ratio (PSNR), (b) is the structural similarity (SSIM), and (c) is the equivalent number of views (ENL). DETAILED DESCRIPTION

[0067] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0068] The present invention may be implemented in many different forms and should not be considered limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0069] like Figure 1 As shown, Figure 1 The overall process diagram of a multi-channel millimeter wave SAR enhanced imaging method based on low-rank tensor chain decomposition proposed by the present invention is as follows:

[0070] Step 1, perform two-dimensional SAR imaging on the multi-channel echoes and perform phase difference compensation processing on the images;

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

[0072] The echo corresponding to the pth transmission channel after MIMO-SAR decoding is

[0073]

[0074] Where c is the propagation speed of electromagnetic waves, {x, r} represents the direction and distance information of the target, and R p,q represents the sum of the distance from the qth array element to the target and the distance from the target to the pth array element, Ω represents the imaging area, τ and t m Denote fast time and slow time respectively, T p represents the synthetic aperture time, γ represents the modulation frequency, λ represents the wavelength, G p and G q denote the channel gains of the p-th transmitting element and the q-th receiving element respectively, σ(x,r) denotes the scattering cross-sectional area at the position (x,r); p and q denote the serial numbers of the transmitting and receiving elements respectively, p=1,2,3,...,Pq=1,2,3,...,Q, and P and Q denote the total number of transmitting and receiving elements respectively.

[0075] Perform α-times interpolation FFT on the echo matrix along the fast time dimension to achieve range compression and obtain 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 image. After range compression, the Map Drift algorithm is first used to estimate the platform velocity, and then the radial distance from (x,r) to the radar at the mth pulse moment is obtained based on the slant range expression:

[0078]

[0079] The corresponding distance unit index is

[0080]

[0081] Where round(·) indicates rounding operation. After obtaining the index in the range image, the corresponding phase compensation is performed and accumulated to achieve back projection imaging. The process can be expressed as

[0082]

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

[0084]

[0085] Where I is the single-channel imaging result, x p and x q They respectively represent the azimuth position of the array element.

[0086] Step 2, stack the images of all channels into a three-dimensional tensor to construct a tensor image stack;

[0087] Specifically, the images of 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 , then the image stack tensor can be expressed as:

[0088]

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

[0090] Step 3, using tensor chain decomposition to extract the inherent low-rank properties in the SAR image tensor;

[0091] Specifically, for an image stack:

[0092]

[0093] Its dimensions can be expressed as {I1, I2, I3} = {N, M, L}. The TT decomposition of this tensor can include 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 of tensor chain (TT) decomposition are as follows: First, Matrixing, the process can be expressed as:

[0096]

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

[0098] X1=U1S1V1 H

[0099] The first kernel tensor It can be expressed as Then for S1V1 H Truncate, that is:

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

[0101] After truncation, Rearrange to get 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, that is The second core tensor The matrix Vectorization results in the relational expression The third core tensor It can be expressed as in

[0104] Step 4, using TT nuclear norm minimization to establish a multi-channel joint enhanced imaging problem model with TTNN constraints;

[0105] Specifically, the following steps are included:

[0106] The multi-channel joint enhanced imaging problem model expression with tensor chain nuclear norm (TTNN) constraint is established by minimizing the TT nuclear norm:

[0107]

[0108] TT-rank is actually composed of the ranks of tensors after being matrixed according to different moduli. The optimization problem with matrix rank constraints is an NP-hard problem, and the present invention relaxes it to solve it in the nuclear norm. That is, it represents a third-order tensor The weighted TTNN of , where ω is the weighting coefficient.

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

[0110] Specifically, in Ket augmentation, The dimension is first decomposed into N = N1 × N2 × ... × N D-1 , M=M1×M2×…×M D-1 and L = N D ×M D ,in and Indicates the dimension size of the block-by-block image structured addressing. In addition, let N D =L,M D = 1. Then rearrange the original tensor and swap the dimensions to get After introducing Ket augmentation, the TTNN of high-order tensor is defined as:

[0111]

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

[0113]

[0114] in is the original image stack after Ket augmentation.

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

[0116] Specifically, we first introduce a set of auxiliary variables in The model is then transformed into an optimization problem as follows:

[0117]

[0118] Then introduce the dual variable The corresponding augmented Lagrangian function is

[0119]

[0120] in is the penalty coefficient. By gradually updating the following subproblems, we can get the solution of the augmented Lagrangian function in the minimization optimization problem.

[0121]

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

[0123] renew about The sub-problem can be expressed as

[0124]

[0125] Its closed-form solution is: in is the singular value matrix, which is decomposed by the singular value decomposition Get. svt(·) represents the singular value threshold operation. d The values ​​of the diagonal elements after SVT are updated to

[0126] Then update about The sub-problem can be expressed as

[0127]

[0128] For the convenience of expression, the above formula can be rewritten as

[0129]

[0130] make The closed-form solution is

[0131]

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

[0133] In order to verify the beneficial effects of the present invention, the following experiment was carried out:

[0134] 1. The present invention designs multi-channel SAR simulation experiments. In the simulation, a 2-transmitter 2-receiver 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 structure, clarity and stray points. And the three indicators of PSNR, SSIM and equivalent view number are used for quantitative analysis.

[0135] The experimental results are as follows: Figure 2 ,3, Figure 2 The simulation results of single building SAR tomography are compared with L1NM, ANM and the algorithm of the present invention. It can be seen from the figure that the tensor decomposition method can effectively suppress the side lobes and enhance the target features. TTNN, Tucker and DBF can all use array gain to obtain better image signal-to-noise ratio than single-channel imaging results. The algorithm using the low-rank characteristics of the tensor can obtain better denoising performance than DBF. On this basis, the proposed algorithm has lower sidelobe level and higher image quality than Tucker. Figure 3 The results of quantitative analysis are given. Similar to the results of qualitative analysis, the proposed algorithm has significant advantages in the three indicators of peak sidelobe ratio (PSNR), structural similarity (SSIM) and equivalent number of views (ENL). Its advantages are more obvious under high signal-to-noise ratio. This shows that in addition to denoising, the proposed algorithm can also suppress side lobes and side levels, improve image quality, and achieve enhanced imaging effects.

[0136] It should be noted that the above-described embodiments only express some implementation methods of the present invention, and the description thereof cannot be understood as limiting the scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the concept of the present invention, and these should all fall within the scope of protection of the present invention.

Claims

1. A multi-channel SAR enhanced imaging method based on low-rank tensor decomposition, characterized by: The following steps are included: Step 1, performing two-dimensional synthetic aperture radar SAR imaging on the multi-channel echoes and performing phase difference compensation processing on the images; Step 2, stack the images of all channels into a three-dimensional tensor to construct an image tensor stack; Step 3, using 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, the tensor chain TT nuclear norm NN minimization is used to establish a multi-channel joint enhanced imaging problem model with tensor chain nuclear norm TTNN constraints; Step 5: Based on the multi-channel joint enhanced imaging problem model, the Ket augmentation method is introduced to enhance the local features of the image neighborhood; Step 6, based on the alternating direction multiplier ADMM framework, iteratively solve the optimization problem after introducing Ket augmentation to obtain enhanced imaging results.

2. The multi-channel SAR enhanced imaging method based on low-rank tensor decomposition according to claim 1, characterized in that: The performing two-dimensional synthetic aperture radar SAR imaging on the multi-channel echoes and performing phase difference compensation processing on the images comprises: Since the echo corresponding to the pth transmitting array element after decoding of the multiple-input multiple-output synthetic aperture radar SAR is Where c is the propagation speed of electromagnetic waves, {x, r} represents the direction and distance information of the target, and R p，q represents the sum of the distance from the qth array element to the target and the distance from the target to the pth array element, Ω represents the imaging area, τ and t m Denote fast time and slow time respectively, T p represents the synthetic aperture time, γ represents the modulation frequency, λ represents the wavelength, G p and G q denote the channel gains of the p-th transmitting element and the q-th receiving element, respectively; σ(x, r) denotes the scattering cross-sectional area at the position (x, r); p and q denote the serial numbers of the transmitting and receiving elements, respectively; p = 1, 2, 3, ..., Pq = 1, 2, 3, ..., Q; P and Q denote the total number of transmitting and receiving elements, respectively; Using the back-projection algorithm BPA, the imaging result expression at (x, r) is: Where I is the single-channel imaging result, x p and x q They represent the azimuth positions of the pth and qth array elements respectively, θ represents the incident angle of the target echo, and phase difference compensation is performed on the image of each channel to ensure phase consistency between images.

3. The multi-channel SAR enhanced imaging method based on low-rank tensor decomposition as claimed in claim 2, characterized in that: The images of all channels are stacked into a three-dimensional tensor, and the image tensor stack is constructed including: Stack the images of each channel into a third-order tensor represents the field of complex numbers, where l=(p-1)Q+q,L=PQ,P、Q represent the total number of transmitting and receiving array elements respectively; accordingly, define x l =x p +x q , then the image tensor stack is represented as Juzhong is a column vector whose elements are all 1, represents the field of real numbers, is a third-order tensor consisting of the phase difference between channels, is additive Gaussian noise, represents the outer product, ⊙ represents element-wise multiplication, and χ represents the image tensor stack.

4. The multi-channel SAR enhanced imaging method based on low-rank tensor decomposition as claimed in claim 3, characterized in that: The method of extracting the inherent low-rank characteristics in the SAR image tensor stack by using tensor chain decomposition includes: For image tensor stacks Its dimension is expressed as {I1, I2, I3} = {N, M, L}; the tensor chain TT decomposition of the 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 rank of each core tensor obtained by two rearrangements and two singular value decompositions, respectively; T0, T1, T2, and T3 represent the truncation positions, and by selecting appropriate values, they adapt to the low-rank characteristics of the image tensor stack; Where T1<min(N,ML), T2<min(T1M,L), The specific steps of tensor chain decomposition are as follows: First, Matrixization is performed, and the process is expressed as X1 The result of matrixization is then used to calculate the tensor SVD of X1, namely: U1, S1, and V1 in the formula are the tensor SVD decomposition results of X1. The first core tensor Expressed as Then Truncate, that is: A is the result of truncation, T1 is the position of truncation, after truncation, Rearrange to get The relationship between the (i1, i2)th element of A1 and the (j1, j2)th element of X2 is T1 is for The position of the cutoff, M, L represent the image stack The second and third dimensions, U2, S2, V2 are the SVD decomposition results of X2; the second core tensor By matrix Vectorization results in the relational expression T2 in the formula is the position where the second tensor is truncated; the third core tensor Expressed as Start In the above formula, S and V both represent the results of tensor SVD decomposition.

5. The multi-channel SAR enhanced imaging method based on low-rank tensor decomposition as claimed in claim 4, characterized in that: The multi-channel joint enhanced imaging problem model expression established by minimizing the TT nuclear norm with tensor chain nuclear norm TTNN constraints is: ||*|| F represents the F-norm, and the TT-rank is actually composed of the ranks of the tensors after matrixing according to different moduli; the optimization problem with matrix rank constraints is a non-deterministic polynomial NP-hard problem, which is relaxed to the nuclear norm solution; represents the original image stack, X1 The result of matrixization, X2 is the result after rearrangement, which represents a third-order tensor The weighted TTNN of , where ω is the weighting coefficient.

6. The multi-channel SAR enhanced imaging method based on low-rank tensor decomposition as claimed in claim 5, characterized in that: The introduction of the Ket augmentation method to strengthen the local features of the image neighborhood includes: In Ket augmentation, The dimension is 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 blocks, where and Indicates the dimension size of the block-by-block image structured addressing; in addition, let N D =L,M D = 1, then rearrange the original tensor and swap the dimensions to get After introducing Ket augmentation, the TTNN of high-order tensor is defined as ω is the weighting coefficient. Similarly, the enhanced imaging problem with TTNN constraints can be modeled as Juzhong is the original image stack after Ket augmentation, γ is a weight coefficient, and the optimization objective is a high-order tensor after the introduction of Ket augmentation, To solve the goal.

7. The multi-channel SAR enhanced imaging method based on low-rank tensor decomposition according to claim 6, characterized in that: The iterative solution based on the alternating direction multiplier ADMM framework includes: The model is transformed into an optimization problem as follows: The corresponding augmented Lagrangian function is is a set of auxiliary variables introduced, That is, the optimization variable, is the original image stack after Ket augmentation, λ is the weight coefficient, D represents the number of image blocks, ω d is the weight used for the d-th image, is the introduced dual variable, which represents the penalty coefficient, The dual variable is also introduced. is a set of auxiliary variables introduced, λ is the weight coefficient, and the following sub-problems are gradually updated to obtain the solution of the augmented Lagrangian function in the minimization optimization problem: Where k is the number of iterations, R and β represent the dual variables and penalty coefficients, η is the rise parameter used to adjust the penalty coefficient, ω and λ are the quantities introduced by the augmented Lagrangian function, and the specific iterative update steps include: renew Juzhong is the singular value matrix, and the left singular value matrix Right singular value matrix Singular value decomposition obtained; svt(·) represents the singular value threshold operation, the rth d The values ​​of the diagonal elements after SVT are updated to Then update fold <d>< / d> It is a rewrite for the convenience 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; is a set of auxiliary variables introduced, is the original image stack after Ket augmentation; Finally, update the dual variables and penalty coefficients.

Images