Radar high-resolution two-dimensional imaging method based on low-rank and sparse constraint tensor completion

Abstract

The invention provides a tensor completion method based on low-rank and sparse combined constraint, and the method is applied to radar high-resolution two-dimensional sparse reconstruction imaging so as to enhance sparse imaging performance. Radar high-resolution two-dimensional imaging is realized through the following steps: firstly, constructing a tensor model of radar data through a sliding window method to capture an internal structure of high-dimensional data and mine low-rank characteristics of the data; secondly, representing enhanced low-rank and sparse characteristics of the constructed radar tensor data by using a tensor low-rank and sparse combined constraint model represented based on a Kronecker basis; and then an optimal solution of the constraint model is efficiently solved in an iteration mode by using an alternating direction multiplier method, and related parameters are updated through a closed-form solution method. According to the method, the superiority of the tensor completion method based on the low-rank and sparse joint constraint in radar high-resolution two-dimensional imaging is verified through comparison experiments on electromagnetic simulation and actually 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 an all-day, all-weather active microwave remote sensing detection system, Synthetic Aperture Radar (SAR) and Inverse Synthetic Aperture Radar (ISAR) have been widely used in many fields such as terrain mapping, environmental monitoring and military reconnaissance. Traditional radar imaging technology obtains a range-Doppler image by coherently accumulating echo data to obtain a higher resolution and output signal-to-noise ratio (SNR). Higher-resolution ISAR imaging requires the transmitter signal to have a wide bandwidth and requires more synthetic aperture time. However, in practical applications, there are problems such as high system complexity, large data volume and complex target motion. In addition, when a multifunctional radar beam is continuously monitoring multiple moving targets distributed over a large area, it is necessary to introduce switching scans of different targets to obtain sparse aperture data. Therefore, it is difficult to achieve unambiguous imaging using only traditional radar imaging methods in this case.

[0003] In recent years, compressed sensing (CS) and matrix completion (MC) methods have been proposed to solve the sparse sampling problem in radar imaging and have been widely discussed. However, radar imaging based on compressed sensing methods is limited to the problem of grid mismatch between the discrete dictionary used and the discrete data model. Relatively speaking, the matrix completion method does not have the problem of grid mismatch, but the problem that follows is that the traditional matrix completion method is only applicable to sparse dictionaries with random sampling, and the sparse reconstruction under block sparse sampling will cause fuzzy imaging. In order to further utilize the low rank and sparse characteristics of data, the present invention proposes a tensor completion method with sparse and low rank joint constraints, which uses effective high-dimensional structure of data to characterize data characteristics to improve imaging performance. A tensor model is constructed by locally stacking radar data through a sliding window method, and a tensor representation method based on Kronecker basis is used to promote the reconstruction of radar data under sparse sampling. According to 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 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 emitted 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 according to 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, based on the tensor representation model based on the Kronecker basis, fill the tensor 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] The echo signal after translation compensation is subjected to sparse sampling processing 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, and R ref is the reference distance for de-chirping, c and fc are the propagation speed and carrier frequency of electromagnetic waves, respectively. j represents the imaginary sign. Assume that the distance from the center of the target geometry to the radar is R0 and the distance from a scattering point on the target (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 pth 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 Expression scatter point R p (t m ), w represents the target’s rotation speed;

[0019] The echo signal after translation compensation is subjected to sparse sampling processing to obtain the echo data:

[0020]

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

[0022] Furthermore, in step 2, the method of constructing a radar data tensor model using a sliding window method according to 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, first use a window of size I1×I2 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 size of the first dimension and the second dimension 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 In tensor form, through sliding window operation get; Represents a tensor Expand the matrix in the kth dimension, represents the set of matrices of size I1×(I2I3), represents the set of matrices of size I2×(I1I3), represents a set of matrices of size I3×(I1I2); is the data block located in the i1th row and the i2th column 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], 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, respectively, 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 of 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 of 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 sparse constraints and low-rank constraints, 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, Respectively represent the observed target echo data tensor 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 an 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 Lagrange multiplier after mapping under 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, Using 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 singular value matrix and the right singular value matrix obtained by the singular value decomposition operation; the update of U2 and U3 is 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 singular value decomposition, F3 and Yes A left singular value matrix and a right singular value matrix obtained by performing a singular value decomposition operation;

[0050] To M k ,k∈{1,2,3} in 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 values ​​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 above variables. 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 It is 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 sliding window methods and mining the low-rank and sparse characteristics of data based on tensor models, it can effectively make up for the grid adaptation problem in traditional compressed sensing methods and the applicability limitations of traditional matrix completion methods to sparse sampling methods. The radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion proposed in the present invention can reconstruct high-resolution two-dimensional radar images under different sparse sampling methods and low signal-to-noise ratio conditions, thereby improving the resolution and noise resistance of radar imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 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 by L1, SLR, HaLRTC and the method of the present invention when the two-dimensional random sampling rate is 0.25;

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

[0067] Figure 5 ISAR imaging results of measured Yak-42 aircraft data using L1, SLR, HaLRTC and the method of the present invention when the random mixed block sampling rate is 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 of the specification.

[0069] The present invention can be implemented in many different forms and should not be considered limited to the embodiments described 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, the method comprising the following steps:

[0071] Step 1, receiving an echo signal corresponding to a linear frequency modulation signal emitted 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 according to 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, based on the tensor representation model based on the Kronecker basis, fill the tensor 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] The echo signal after translation compensation is subjected to sparse sampling processing 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, and R ref is the reference distance for de-chirping, c and f c are the propagation speed and carrier frequency of electromagnetic waves, respectively. j represents the imaginary sign. Assume that the distance from the center of the target geometry to the radar is R0 and the distance from a scattering point on the target (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 pth 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 Expression scatter point R p (t m ), w represents the target’s rotation speed;

[0084] The echo signal after translation compensation is subjected to sparse sampling processing to obtain the echo data:

[0085]

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

[0087] Furthermore, in step 2, the method of constructing a radar data tensor model using a sliding window method according to 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, first use a window of size I1×I2 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 size of the first dimension and the second dimension 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 In tensor form, through sliding window operation get; Represents a tensor Expand the matrix in the kth dimension, represents the set of matrices of size I1×(I2I3), represents the set of matrices of size I2×(I1I3), represents a set of matrices of size I3×(I1I2); is the data block located in the i1th row and the i2th column 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], 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, respectively, 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 of 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 of 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 sparse constraints and low-rank constraints, 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, Respectively represent the observed target echo data tensor 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 an 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 Lagrange multiplier after mapping under 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, Using 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, that is:

[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 singular value matrix and the right singular value matrix obtained by the singular value decomposition operation; the update of U2 and U3 is 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 singular value decomposition, F3 and Yes A left singular value matrix and a right singular value matrix obtained by performing a singular value decomposition operation;

[0115] To M k ,k∈{1,2,3} in 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 values ​​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 above variables. 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 It is 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 experiment was carried out:

[0127] (1) Use electromagnetic simulation to construct simulation experimental data of ISAR satellite imaging, use different methods to process the data sets with ISAR two-dimensional imaging under the same data conditions, and give 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 sampled in this experiment, namely two-dimensional random sampling, two-dimensional block sampling, and random mixed block sampling. Figure 3 , Figure 3 The ISAR imaging results of the measured Yak-42 aircraft data using L1, SLR, HaLRTC and the method of the present invention when the two-dimensional random sampling rate is 0.25. 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 when the two-dimensional block sampling rate is 0.25. Figure 5 , Figure 5 The ISAR imaging results of the measured Yak-42 aircraft data by L1, SLR, HaLRTC and the method of the present invention under the condition of random mixed block sampling rate of 0.25. According to the attached drawings, it can be seen that the sparse reconstruction imaging results of the measured data by the method of the present invention under different sparse sampling rates also have clearer and more complete structure and contour, and the sidelobe and noise suppression effects are also the most obvious.

[0130] 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 radar high-resolution two-dimensional imaging method based on low-rank and sparse joint constrained tensor completion, characterized in that: The method comprises the following steps: Step 1, receiving an echo signal corresponding to a linear frequency modulation signal emitted 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 according to 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, based on the tensor representation model based on the Kronecker basis, fill the tensor 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; The echo signal after translation compensation is subjected to sparse sampling processing 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, and R ref is the reference distance for de-chirping, c and f c are the propagation speed and carrier frequency of electromagnetic waves, respectively. j represents the imaginary sign. Assume that the distance from the center of the target geometry to the radar is R0 and the distance from a scattering point on the target (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 pth 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 Expression scatter point R p (t m ), w represents the target's rotation speed; sparse sampling is performed 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 constant term after simplification, m=1,2,...,M and n=1,2,...,N represent the discrete sampling 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 a 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 according to 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, wherein I1 and I2 represent the size of the first dimension and the second dimension 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 the set of matrices of size I1×(I2I3), represents the set of matrices of size I2×(I1I3), represents a set of matrices of size I3×(I1I2); is the data block located in the i1th row and the i2th column 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], 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, respectively, 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 of 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 of 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 sparse constraints and low-rank constraints, 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, Respectively represent the observed target echo data tensor and the target echo data tensor to be reconstructed 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 Lagrange multiplier after mapping under 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, Using 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 singular value matrix and the right singular value matrix obtained by the singular value decomposition operation; the update of U2 and U3 is 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 singular value decomposition, F3 and Yes A left singular value matrix and a right singular value matrix obtained by performing a singular value decomposition operation; To M k ,k∈{1,2,3} in 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 values ​​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 above variables. 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 It is 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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