A radar high-resolution two-dimensional imaging method based on low-rank and sparse constrained tensor completion

Abstract

The present invention proposes a tensor completion method based on low-rank and sparse joint constraints and applies it to radar high-resolution two-dimensional sparse reconstruction imaging to enhance sparse imaging performance. The present invention realizes radar high-resolution two-dimensional imaging through the following steps: first, a tensor model of radar data is constructed by a sliding window method to capture the intrinsic structure of high-dimensional data and mine the low-rank characteristics of the data. Secondly, a tensor low-rank and sparse joint constraint model based on Kronecker basis representation is used to characterize the enhanced low-rank and sparse characteristics of the constructed radar tensor data. Then, the alternating direction multiplier method is used to efficiently solve the optimal solution of the constraint model in an iterative manner and update the relevant parameters by a closed-form solution method. The present invention verifies the superiority of the tensor completion method based on low-rank and sparse joint constraints proposed in the present invention in radar high-resolution two-dimensional imaging through comparative experiments on electromagnetic simulation and measured radar data.

Description

Technical Field

[0001] The present invention relates to the field of radar signal processing technology, and in particular to a tensor completion radar high-resolution two-dimensional imaging method based on low rank and sparse constraints. Background Art

[0002] As all-day, all-weather active microwave remote sensing systems, synthetic aperture radar (SAR) and inverse synthetic aperture radar (ISAR) imaging technologies have been widely used in fields such as topographic mapping, environmental monitoring, and military reconnaissance. Traditional radar imaging techniques achieve high resolution and output signal-to-noise ratio (SNR) by coherently integrating echo data, thereby producing range-Doppler images. Higher-resolution ISAR imaging, on the other hand, requires a wide bandwidth for the transmitter signal, necessitating a longer synthetic aperture time. However, practical applications present challenges such as high system complexity, large data volumes, and complex target motion. Furthermore, continuous monitoring of multiple moving targets distributed over a large area requires switching between different targets, resulting in sparse aperture data. Therefore, achieving unambiguous imaging using traditional radar imaging methods alone is difficult.

[0003] In recent years, compressed sensing (CS) and matrix completion (MC) methods have been proposed as solutions to sparse sampling issues in radar imaging and have received extensive discussion. However, radar imaging based on CS is limited by the potential mismatch between the discrete dictionary used and the discrete data model grid. Relatively speaking, matrix completion methods do not suffer from this grid mismatch problem, but the attendant problem is that traditional matrix completion methods are only applicable to randomly sampled sparse dictionaries, and sparse reconstruction under block sparse sampling can lead to blurred imaging. To further exploit the low-rank and sparse properties of data, this paper proposes a tensor completion method with joint sparse and low-rank constraints, which utilizes the effective high-dimensional structure of the data to characterize data characteristics and improve imaging performance. A tensor model is constructed by locally stacking radar data using a sliding window method, and a tensor representation method based on a Kronecker basis is used to facilitate the reconstruction of radar data under sparse sampling. Based on the solution to the convex optimization problem, the alternating direction multiplier method is used to efficiently and optimally solve the model. Summary of the Invention

[0004] Purpose of the invention: In order to further improve the utilization of the low-rank and sparse characteristics of data, thereby further improving the resolution of radar sparse imaging, the present invention provides a radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion, which can improve the resolution of radar two-dimensional sparse imaging.

[0005] Technical solution: To achieve the above-mentioned purpose, the present invention proposes a radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion, which includes the following steps:

[0006] Step 1: receiving an echo signal corresponding to a linear frequency modulation signal transmitted by a radar, and preprocessing the echo signal to obtain echo data;

[0007] Step 2: constructing a radar data tensor model using a sliding window method based on the echo data;

[0008] Step 3, unfolding the tensor model along different modes to obtain an unfolding matrix, and performing Tucker decomposition on the tensor model to obtain a kernel tensor and a factor matrix;

[0009] Step 4, using a tensor characterization method based on a Kronecker basis to jointly characterize the sparse characteristics of the kernel tensor and the low-rank characteristics of the unfolded matrix;

[0010] Step 5: Filling the tensor based on the Kronecker basis-based tensor representation model to obtain a filled tensor model;

[0011] Step 6: Based on the filled tensor model, the filled matrix data is obtained by inverting the sliding window method to obtain a reconstructed high-resolution radar two-dimensional image.

[0012] Furthermore, in step 1, preprocessing the echo signal corresponding to the received linear frequency modulation signal to obtain echo data includes the following steps:

[0013] Performing a delinear frequency modulation process on the echo signal to obtain a demodulated echo signal;

[0014] performing translation compensation on the demodulated echo signal to obtain a translation-compensated echo signal;

[0015] Sparse sampling is performed on the echo signal after translation compensation to obtain the echo data.

[0016] Furthermore, the echo data is composed of P scattering points, which can be expressed as:

[0017]

[0018] Among them, t r is the fast time within the pulse, t m is the pulse slow time, σ p represents the scattering coefficient of the pth scattering point, γ is the frequency slope of the linear FM wave, T is the pulse width of the linear FM wave, R ref is the reference distance for dechirping, c and fc are the propagation speed and carrier frequency of electromagnetic waves, respectively. j represents the imaginary number sign. Assuming that the distance from the center point of the target geometry to the radar is R0 and a scattering point (x p ,y p ) at pulse slow time t m The distance to the radar at the moment is R p (t m ), where (x p ,y p ) represents the horizontal and vertical coordinates of the p-th scattering point on the target in the radar coordinate system. Based on the assumption of small angle changes in target rotation, R is approximated by Taylor expansion. p (t m )=R0+y p +x p ·w·t m Express scatter point R p (t m ) distance, w represents the target’s rotation speed;

[0019] Performing sparse sampling processing on the echo signal after translation compensation to obtain the echo data:

[0020]

[0021] in, f s is the sampling frequency, PRF stands for pulse repetition frequency, σ′ p represents the simplified constant term, m = 1, 2, ..., M and n = 1, 2, ..., N represent the discrete samples of fast time and slow time, respectively, where M and N represent the total number of samples of the signal in the fast time and slow time dimensions, respectively.

[0022] Furthermore, in step 2, the method of constructing a radar data tensor model using a sliding window method based on the echo data is as follows:

[0023] Set the echo data size to in, Represents a set of matrices of size M×N. When constructed using the sliding window method, the echo data is first slid with a window of size I1×I2 with a step size of 1 to extract a data block of size I1×I2, where I1 and I2 represent the sizes of the first and second dimensions of the constructed tensor, respectively. The number of sliding blocks I3 satisfies I3=(M-I1+1)×(N-I2+1), and I3 represents the size of the third dimension of the tensor to be constructed. These extracted data blocks are stacked in sequence to obtain a tensor of size I1×I2×I3, which is recorded as the observed target echo data tensor. middle, Represents a set of tensors of size I1×I2×I3. The above tensorization operation is expressed as I1<M,I2<N。

[0024] Furthermore, in step 3, the expansion matrix is ​​set to Y (k) , which is the matrix along the k-th dimension of the tensor, expressed as:

[0025]

[0026] in, is the target echo data matrix to be reconstructed The tensor form is operated by sliding window get; Represents a tensor Expand the matrix in the kth dimension, represents a set of matrices of size I1×(I2I3), represents a set of matrices of size I2×(I1I3), represents a set of matrices of size I3×(I1I2); is the data block located in row i1 and column i2 extracted by the sliding window method in step 2, Representing a tensor In the second dimension, the transpose of the slice at position i2, where i1∈[1,M-I1+1], i2∈[1,N-I2+1], and k∈{1,2,3};

[0027] In step 3, the kernel tensor is obtained by Tucker decomposition, and its Tucker decomposition is expressed as:

[0028]

[0029] Among them, U1, U2, U3 are the factor matrices of the modulo-1, modulo-2 and modulo-3 expansion matrices, which are used to store the modulo-k expansion matrix Y (k) The principal left singular value of Represents a target tensor with reconstruction The kernel tensor of k Represents the kernel tensor in the kth dimension and the factor matrix U k The product of .

[0030] Furthermore, in step 4, the method for jointly characterizing the sparse characteristics of the kernel tensor and the low-rank characteristics of the unfolded matrix using a tensor characterization method based on a Kronecker basis is as follows:

[0031]

[0032] Among them, 0<t<1, which is the compromise coefficient for balancing the two constraints, Y (k) is the expansion matrix modulo-k, is the kernel tensor obtained by Tucker decomposition, P ls (·) and P ls * (·) are convex relaxations of the sparse constraint and the low-rank constraint, respectively, as follows:

[0033]

[0034] Among them, ε is a preset positive number; Representing a tensor elements, σ m (Y (k) ) is defined as the expansion matrix Y (k) The mth singular value of ; 1≤i1≤I1,1≤i2≤I2,1≤i3≤I3;

[0035] According to the sparse characteristics of the kernel tensor and the low-rank characteristics of the unfolded matrix, the tensor representation model in step 4 can be expressed as:

[0036]

[0037] Where, λ = (1-t) / t, Represent the observed target echo data tensor respectively and the target echo data tensor to be reconstructed The tensor mapped under the sparse sampling dictionary Ω.

[0038] Furthermore, in step 5, filling the tensor model is performed by solving the constrained optimization problem using the alternating direction multiplier method, and the augmented Lagrangian function for the tensor representation model is expressed as:

[0039]

[0040] Among them, fold k (·) means unfold k The inverse operation of (·), M1, M2 and M3 are auxiliary variables for expanding the matrix along modulo-1, modulo-2 and modulo-3 respectively; and For tensors, and the matrix M k The Lagrange multiplier of express The Lagrange multiplier after mapping under the sparse sampling dictionary Ω, μ is the coefficient;

[0041] The iterative steps of the alternating direction multiplier method are:

[0042] First, the kernel tensor Perform update iteration, that is, the (i+1)th iteration It can be expressed as:

[0043]

[0044] Where b is a small constant coefficient, With the (i)th iteration U1, U2 and U3, and their corresponding Lagrange multipliers The Tucker decomposition formula in the three dimensions of the tensor is obtained, that is: in,(·) H Represents the conjugate transpose operation, using The expression for the kernel tensor Iterate using the closed-form solution method, namely:

[0045]

[0046] Among them, the D b,ε (·) represents the operation of finding a closed-form solution using soft thresholding under coefficient b;

[0047] During the update iteration process of U1, U2 and U3, the (i+1)th iteration of U1 is:

[0048]

[0049] Among them, F1 and Yes The left and right singular value matrices obtained by performing the singular value decomposition operation; the updates of U2 and U3 are the same as U1, and the U2 and U3 of the (i+1)th iteration are expressed as Among them, F2 and Yes The left and right singular value matrices obtained by performing the singular value decomposition operation, F3 and Yes Performing a singular value decomposition operation to obtain a left singular value matrix and a right singular value matrix;

[0050] To M k ,k∈{1,2,3} iterative update, M k Using the tensor of the (i)th iteration And the singular value decomposition of its Lagrange multiplier is obtained, that is:

[0051]

[0052] in, SVD(·) represents the singular value decomposition operation, is the singular value σ1,σ2,...,σ n In the coefficient a k Perform a soft threshold closed-form solution operation and construct a diagonalized matrix based on the singular value results of the closed-form solution;

[0053] The target echo data tensor to be reconstructed The update iterative process is based on the update results of all the variables mentioned above. The iteration is expressed as:

[0054]

[0055] in, K represents the dimension of the tensor, which is set to 3, Ω ⊥ Represents the complement matrix of the sparse sampling dictionary Ω.

[0056] Furthermore, the Lagrange multiplier in the iterative process of the alternating direction multiplier method is The iterative update is based on the coefficient μ of the (i+1)th iteration (i+1) as well as Expressed as:

[0057]

[0058] in, Represents the (i+1)th iteration represents the (i)th iteration

[0059] Furthermore, the steps of performing an inversion sliding window method on the filled tensor model to obtain filled matrix data, thereby obtaining a reconstructed high-resolution radar two-dimensional image include:

[0060] The filled tensor model is subjected to an inversion sliding window to obtain filled inverse transformation matrix data; the inverse transformation matrix data is subjected to imaging processing using a range-Doppler method to obtain the radar high-resolution two-dimensional image.

[0061] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0062] Thanks to the advantages of constructing tensors using a sliding window method and exploiting the low-rank and sparse characteristics of data based on tensor models, this method can effectively overcome the grid adaptation issues in traditional compressed sensing methods and the limitations of traditional matrix completion methods in sparse sampling methods. The proposed high-resolution two-dimensional radar imaging method based on low-rank and sparse joint constrained tensor completion can reconstruct high-resolution two-dimensional radar images under different sparse sampling methods and low signal-to-noise ratio conditions, improving the resolution and noise resistance of radar imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a flowchart of the radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion according to the present invention;

[0064] Figure 2 This is the sparse sampling method used in the experiment;

[0065] Figure 3 The ISAR imaging results of the measured Yak-42 aircraft data using L1, SLR, HaLRTC and the method of the present invention with a two-dimensional random sampling rate of 0.25 are shown;

[0066] Figure 4 The ISAR imaging results of the measured Yak-42 aircraft data using L1, SLR, HaLRTC and the method of the present invention with a two-dimensional block sampling rate of 0.25 are shown;

[0067] Figure 5 The ISAR imaging results of the measured Yak-42 aircraft data using L1, SLR, HaLRTC and the method of the present invention with a random mixed block sampling rate of 0.25. DETAILED DESCRIPTION

[0068] In order to illustrate the technical solution disclosed in the present invention in detail, further elaboration is given below in conjunction with the accompanying drawings and specific embodiments.

[0069] The present invention can 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.

[0070] like Figure 1 As shown, the present invention proposes a radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion, which includes the following steps:

[0071] Step 1: receiving an echo signal corresponding to a linear frequency modulation signal transmitted by a radar, and preprocessing the echo signal to obtain echo data;

[0072] Step 2: constructing a radar data tensor model using a sliding window method based on the echo data;

[0073] Step 3, unfolding the tensor model along different modes to obtain an unfolding matrix, and performing Tucker decomposition on the tensor model to obtain a kernel tensor and a factor matrix;

[0074] Step 4, using a tensor characterization method based on a Kronecker basis to jointly characterize the sparse characteristics of the kernel tensor and the low-rank characteristics of the unfolded matrix;

[0075] Step 5: Filling the tensor based on the Kronecker basis-based tensor representation model to obtain a filled tensor model;

[0076] Step 6: Based on the filled tensor model, the filled matrix data is obtained by inverting the sliding window method to obtain a reconstructed high-resolution radar two-dimensional image.

[0077] Furthermore, in step 1, preprocessing the echo signal corresponding to the received linear frequency modulation signal to obtain echo data includes the following steps:

[0078] Performing a delinear frequency modulation process on the echo signal to obtain a demodulated echo signal;

[0079] performing translation compensation on the demodulated echo signal to obtain a translation-compensated echo signal;

[0080] Sparse sampling is performed on the echo signal after translation compensation to obtain the echo data.

[0081] Furthermore, the echo data is composed of P scattering points, which can be expressed as:

[0082]

[0083] Among them, t r is the fast time within the pulse, t m is the pulse slow time, σ p represents the scattering coefficient of the pth scattering point, γ is the frequency slope of the linear FM wave, T is the pulse width of the linear FM wave, R ref is the reference distance for dechirping, c and f c are the propagation speed and carrier frequency of electromagnetic waves, respectively. j represents the imaginary number sign. Assuming that the distance from the center point of the target geometry to the radar is R0 and a scattering point (x p ,y p ) at pulse slow time t m The distance to the radar at the moment is R p (t m ), where (x p ,yp ) represents the horizontal and vertical coordinates of the p-th scattering point on the target in the radar coordinate system. Based on the assumption of small angle changes in target rotation, R is approximated by Taylor expansion. p (t m )=R0+y p +x p ·w·t m Express scatter point R p (t m ) distance, w represents the target’s rotation speed;

[0084] Performing sparse sampling processing on the echo signal after translation compensation to obtain the echo data:

[0085]

[0086] in, f s is the sampling frequency, PRF stands for pulse repetition frequency, σ′ p represents the simplified constant term, m = 1, 2, ..., M and n = 1, 2, ..., N represent the discrete samples of fast time and slow time, respectively, where M and N represent the total number of samples of the signal in the fast time and slow time dimensions, respectively.

[0087] Furthermore, in step 2, the method of constructing a radar data tensor model using a sliding window method based on the echo data is as follows:

[0088] Set the echo data size to in, Represents a set of matrices of size M×N. When constructed using the sliding window method, the echo data is first slid with a window of size I1×I2 with a step size of 1 to extract a data block of size I1×I2, where I1 and I2 represent the sizes of the first and second dimensions of the constructed tensor, respectively. The number of sliding blocks I3 satisfies I3=(M-I1+1)×(N-I2+1), and I3 represents the size of the third dimension of the tensor to be constructed. These extracted data blocks are stacked in sequence to obtain a tensor of size I1×I2×I3, which is recorded as the observed target echo data tensor. middle, Represents a set of tensors of size I1×I2×I3. The above tensorization operation is expressed as I1<M,I2<N。

[0089] Furthermore, in step 3, the expansion matrix is ​​set to Y (k) , which is the matrix along the k-th dimension of the tensor, expressed as:

[0090]

[0091] in, is the target echo data matrix to be reconstructed The tensor form is operated by sliding window get; Represents a tensor Expand the matrix in the kth dimension, represents a set of matrices of size I1×(I2I3), represents a set of matrices of size I2×(I1I3), represents a set of matrices of size I3×(I1I2); is the data block located in row i1 and column i2 extracted by the sliding window method in step 2, Representing a tensor In the second dimension, the transpose of the slice at position i2, where i1∈[1,M-I1+1], i2∈[1,N-I2+1], and k∈{1,2,3};

[0092] In step 3, the kernel tensor is obtained by Tucker decomposition, and its Tucker decomposition is expressed as:

[0093]

[0094] Among them, U1, U2, U3 are the factor matrices of the modulo-1, modulo-2 and modulo-3 expansion matrices, which are used to store the modulo-k expansion matrix Y (k) The principal left singular value of Represents a target tensor with reconstruction The kernel tensor of k Represents the kernel tensor in the kth dimension and the factor matrix U k The product of .

[0095] Furthermore, in step 4, the method for jointly characterizing the sparse characteristics of the kernel tensor and the low-rank characteristics of the unfolded matrix using a tensor characterization method based on a Kronecker basis is as follows:

[0096]

[0097] Among them, 0<t<1, which is the compromise coefficient for balancing the two constraints, Y (k) is the expansion matrix modulo-k, is the kernel tensor obtained by Tucker decomposition, P ls (·) and P ls * (·) are convex relaxations of the sparse constraint and the low-rank constraint, respectively, as follows:

[0098]

[0099] Among them, ε is a preset positive number; Representing a tensor elements, σ m (Y (k) ) is defined as the expansion matrix Y (k) The mth singular value of ; 1≤i1≤I1,1≤i2≤I2,1≤i3≤I3;

[0100] According to the sparse characteristics of the kernel tensor and the low-rank characteristics of the unfolded matrix, the tensor representation model in step 4 can be expressed as:

[0101]

[0102] Where, λ = (1-t) / t, Represent the observed target echo data tensor respectively and the target echo data tensor to be reconstructed The tensor mapped under the sparse sampling dictionary Ω.

[0103] Furthermore, in step 5, filling the tensor model is performed by solving the constrained optimization problem using the alternating direction multiplier method, and the augmented Lagrangian function for the tensor representation model is expressed as:

[0104]

[0105] Among them, fold k (·) means unfold k The inverse operation of (·), M1, M2 and M3 are auxiliary variables for expanding the matrix along modulo-1, modulo-2 and modulo-3 respectively; and For tensors, and the matrix M k The Lagrange multiplier of express The Lagrange multiplier after mapping under the sparse sampling dictionary Ω, μ is the coefficient;

[0106] The iterative steps of the alternating direction multiplier method are:

[0107] First, the kernel tensor Perform update iteration, that is, the (i+1)th iteration It can be expressed as:

[0108]

[0109] Where b is a small constant coefficient, With the (i)th iteration U1, U2 and U3, and their corresponding Lagrange multipliers The Tucker decomposition formula in the three dimensions of the tensor is obtained, that is: in,(·) H Represents the conjugate transpose operation, using The expression for the kernel tensor Iterate using the closed-form solution method, namely:

[0110]

[0111] Among them, the D b,ε (·) represents the operation of finding a closed-form solution using soft thresholding under coefficient b;

[0112] During the update iteration process of U1, U2 and U3, the (i+1)th iteration of U1 is:

[0113]

[0114] Among them, F1 and Yes The left and right singular value matrices obtained by performing the singular value decomposition operation; the updates of U2 and U3 are the same as U1, and the U2 and U3 of the (i+1)th iteration are expressed as Among them, F2 and Yes The left and right singular value matrices obtained by performing the singular value decomposition operation, F3 and Yes Performing a singular value decomposition operation to obtain a left singular value matrix and a right singular value matrix;

[0115] To M k ,k∈{1,2,3} iterative update, M k Using the tensor of the (i)th iteration And the singular value decomposition of its Lagrange multiplier is obtained, that is:

[0116]

[0117] in, SVD(·) represents the singular value decomposition operation, is the singular value σ1,σ2,...,σ n In the coefficient a k Perform a soft threshold closed-form solution operation and construct a diagonalized matrix based on the singular value results of the closed-form solution;

[0118] The target echo data tensor to be reconstructed The update iterative process is based on the update results of all the variables mentioned above. The iteration is expressed as:

[0119]

[0120] in, K represents the dimension of the tensor, which is set to 3, Ω ⊥ Represents the complement matrix of the sparse sampling dictionary Ω.

[0121] Furthermore, the Lagrange multiplier in the iterative process of the alternating direction multiplier method is The iterative update is based on the coefficient μ of the (i+1)th iteration (i+1) as well as Expressed as:

[0122]

[0123] in, Represents the (i+1)th iteration represents the (i)th iteration

[0124] Furthermore, the steps of performing an inversion sliding window method on the filled tensor model to obtain filled matrix data, thereby obtaining a reconstructed high-resolution radar two-dimensional image include:

[0125] The filled tensor model is subjected to an inversion sliding window to obtain filled inverse transformation matrix data; the inverse transformation matrix data is subjected to imaging processing using a range-Doppler method to obtain the radar high-resolution two-dimensional image.

[0126] In order to verify the beneficial effects of the present invention, the following experiments were performed:

[0127] (1) Use electromagnetic simulation to construct experimental data for ISAR satellite imaging. Under the same data conditions, use different methods to process the data sets for ISAR two-dimensional imaging and provide specific numerical analysis.

[0128] (2) Under the same experimental conditions, different methods were used to perform ISAR two-dimensional imaging processing on the measured Yak-42 aircraft dataset.

[0129] The experimental results are as follows: Figure 2 , Figure 2 Indicates the three different sparse sampling methods used in this experiment, namely two-dimensional random sampling, two-dimensional block sampling, and random mixed block sampling. Figure 3 , Figure 3The ISAR imaging results of the measured Yak-42 aircraft data using L1, SLR, HaLRTC and the method of the present invention with a two-dimensional random sampling rate of 0.25 are shown in Figure 2. Figure 4 , Figure 4 The ISAR imaging results of the measured Yak-42 aircraft data using L1, SLR, HaLRTC and the method of the present invention with a two-dimensional block sampling rate of 0.25 are shown in Figure 2. Figure 5 , Figure 5 Figure 2 shows the ISAR imaging results of measured Yak-42 aircraft data using L1, SLR, HaLRTC, and the method described in the present invention at a random mixed block sampling rate of 0.25. As can be seen from the accompanying figures, the sparsely reconstructed imaging results of the measured data using the method described in the present invention at different sparse sampling rates also achieve clearer and more complete structure and contours, and also achieve the most significant sidelobe and noise suppression effects.

[0130] It should be noted that the above-described embodiments only represent some embodiments of the present invention, and their descriptions should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the scope of the present invention, and these improvements should fall within the scope of protection of the present invention.

Claims

1. A radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion, characterized by: The method comprises the following steps: Step 1: receiving an echo signal corresponding to a linear frequency modulation signal transmitted by a radar, and preprocessing the echo signal to obtain echo data; Step 2: constructing a radar data tensor model using a sliding window method based on the echo data; Step 3, unfolding the tensor model along different modes to obtain an unfolding matrix, and performing Tucker decomposition on the tensor model to obtain a kernel tensor and a factor matrix; Step 4, using a tensor characterization method based on a Kronecker basis to jointly characterize the sparse characteristics of the kernel tensor and the low-rank characteristics of the unfolded matrix; Step 5: Filling the tensor based on the Kronecker basis-based tensor representation model to obtain a filled tensor model; Step 6: Based on the filled tensor model, the filled matrix data is obtained by inverting the sliding window method to obtain a reconstructed high-resolution radar two-dimensional image.

2. The radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion according to claim 1, characterized in that: In step 1, preprocessing the echo signal corresponding to the received linear frequency modulation signal to obtain echo data includes the following steps: Performing a delinear frequency modulation process on the echo signal to obtain a demodulated echo signal; performing translation compensation on the demodulated echo signal to obtain a translation-compensated echo signal; Sparse sampling is performed on the echo signal after translation compensation to obtain the echo data.

3. The radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion according to claim 2, characterized in that: The echo data is composed of P scattering points, which can be expressed as: Among them, t r is the fast time within the pulse, t m is the pulse slow time, σ p represents the scattering coefficient of the pth scattering point, γ is the frequency slope of the linear FM wave, T is the pulse width of the linear FM wave, R ref is the reference distance for dechirping, c and f c are the propagation speed and carrier frequency of electromagnetic waves, respectively. j represents the imaginary number sign. Assuming that the distance from the center point of the target geometry to the radar is R0 and a scattering point (x p ,y p ) at pulse slow time t m The distance to the radar at the moment is R p (t m ), where (x p ,y p ) represents the horizontal and vertical coordinates of the p-th scattering point on the target in the radar coordinate system. Based on the assumption of small angle changes in target rotation, R is approximated by Taylor expansion. p (t m )=R0+y p +x p ·w·t m Express scatter point R p (t m ), w represents the target's rotational speed; performing sparse sampling processing on the echo signal after translation compensation to obtain the echo data: in, f s is the sampling frequency, PRF stands for pulse repetition frequency, σ p ′ represents the simplified constant term, m = 1, 2, ..., M and n = 1, 2, ..., N represent the discrete samples of fast time and slow time respectively, where M and N represent the total number of samples of the signal in the fast time and slow time dimensions respectively, and rect[x] represents the rectangular wave about x.

4. The radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion according to claim 3, characterized in that: In step 2, the method of constructing a radar data tensor model using a sliding window method based on the echo data is as follows: Set the echo data size to in, Represents a set of matrices of size M×N. When constructed using the sliding window method, a window of size I1×I2 is used to slide the echo data with a step size of 1 to extract a data block of size I1×I2, where I1 and I2 represent the sizes of the first and second dimensions of the constructed tensor, respectively. The number of sliding blocks I3 satisfies I3=(M-I1+1)×(N-I2+1), and I3 represents the size of the third dimension of the tensor to be constructed. These extracted data blocks are stacked in sequence to obtain a tensor of size I1×I2×I3, which is recorded as the observed target echo data tensor. middle, Represents a set of tensors of size I1×I2×I3. The above tensorization operation is expressed as I1<M,I2<N。 5. The radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion according to claim 4, characterized in that: In step 3, set the expansion matrix to Y (k) , which is the matrix along the k-th dimension of the tensor, expressed as: in, is the target echo data matrix to be reconstructed In tensor form, through sliding window operation get; Represents a tensor Expand the matrix in the kth dimension, represents a set of matrices of size I1×(I2I3), represents a set of matrices of size I2×(I1I3), represents a set of matrices of size I3×(I1I2); is the data block located in row i1 and column i2 extracted by the sliding window method in step 2, Representing a tensor In the second dimension, the transpose of the slice at position i2, where i1∈[1,M-I1+1], i2∈[1,N-I2+1], and k∈{1,2,3}; In step 3, the kernel tensor is obtained by Tucker decomposition, and its Tucker decomposition is expressed as: Among them, U1, U2, U3 are the factor matrices of the modulo-1, modulo-2 and modulo-3 expansion matrices, which are used to store the modulo-k expansion matrix Y (k) The principal left singular value of Represents a target tensor with reconstruction The kernel tensor of k Represents the kernel tensor in the kth dimension and the factor matrix U k The product of .

6. The radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion according to claim 5, characterized in that: In step 4, the method for jointly characterizing the sparse characteristics of the kernel tensor and the low-rank characteristics of the unfolded matrix using a tensor characterization method based on a Kronecker basis is as follows: Among them, 0<t<1, which is the compromise coefficient for balancing the two constraints, Y (k) is the expansion matrix modulo-k, P ls (·) and P ls * (·) are convex relaxations of the sparse constraint and the low-rank constraint, respectively, as follows: Among them, ε is a preset positive number; Representing a tensor elements, σ m (Y (k) ) is defined as the expansion matrix Y (k) The mth singular value of ; 1≤i1≤I1,1≤i2≤I2,1≤i3≤I3; According to the sparse characteristics of the kernel tensor and the low-rank characteristics of the unfolded matrix, the tensor representation model in step 4 is expressed as: Where, λ = (1-t) / t, Represent the target echo data tensor to be reconstructed and the observed target echo data tensor The tensor mapped under the sparse sampling dictionary Ω.

7. The radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion according to claim 6, characterized in that: In step 5, filling the tensor model is performed by solving the constrained optimization problem using the alternating direction multiplier method, and the augmented Lagrangian function for the tensor representation model is expressed as: Among them, fold k (·) means unfold k The inverse operation of (·), M1, M2 and M3 are auxiliary variables for expanding the matrix along modulo-1, modulo-2 and modulo-3 respectively; and For tensors, and the matrix M k The Lagrange multiplier of express The Lagrange multiplier after mapping under the sparse sampling dictionary Ω, μ is the coefficient; The iterative steps of the alternating direction multiplier method are: For the kernel tensor Perform update iteration, that is, the (i+1)th iteration It can be expressed as: Where b is a constant coefficient, With the (i)th iteration U1, U2 and U3, and their corresponding Lagrange multipliers The Tucker decomposition formula in the three dimensions of the tensor is obtained, that is: in,(·) H Represents the conjugate transpose operation, using The expression for the kernel tensor Iterate using the closed-form solution method, namely: Among them, the D b,ε (·) represents the operation of finding a closed-form solution using soft thresholding under coefficient b; During the update iteration process of U1, U2 and U3, the (i+1)th iteration of U1 is: Among them, F1 and Yes The left and right singular value matrices obtained by performing the singular value decomposition operation; the updates of U2 and U3 are the same as U1, and the U2 and U3 of the (i+1)th iteration are expressed as Among them, F2 and Yes The left and right singular value matrices obtained by performing the singular value decomposition operation, F3 and Yes Performing a singular value decomposition operation to obtain a left singular value matrix and a right singular value matrix; To M k ,k∈{1,2,3} iterative update, M k Using the tensor of the i-th iteration And the singular value decomposition of its Lagrange multiplier is obtained, that is: in, SVD(·) represents the singular value decomposition operation, is the singular value σ1,σ2,...,σ n In the coefficient a k Perform a soft threshold closed-form solution operation and construct a diagonalized matrix based on the singular value results of the closed-form solution; The target echo data tensor to be reconstructed The update iterative process is based on the update results of all the variables mentioned above. The iteration is expressed as: in, K represents the dimension of the tensor, which is set to 3, Ω ⊥ Represents the complement matrix of the sparse sampling dictionary Ω.

8. The radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion according to claim 7, characterized in that: Lagrange multipliers in the iterative process of the alternating direction multiplier method The iterative update is based on the coefficient μ of the (i+1)th iteration (i+1) as well as Expressed as: in, Represents the (i+1)th iteration represents the (i)th iteration 9. The radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion according to claim 8, characterized in that: The steps of performing an inversion sliding window method on the filled tensor model to obtain filled matrix data, thereby obtaining a reconstructed high-resolution radar two-dimensional image include: The filled tensor model is subjected to an inversion sliding window to obtain filled inverse transformation matrix data; the inverse transformation matrix data is subjected to imaging processing using a range-Doppler method to obtain the radar high-resolution two-dimensional image.

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