Structured low-rank embedded meshless super-resolution ISAR imaging algorithm

Abstract

The invention discloses a meshless super-resolution ISAR (Inverse Synthetic Aperture Radar) imaging algorithm based on structured low-rank embedding. The meshless super-resolution ISAR imaging algorithm comprises the following steps: constructing an echo extrapolation model; according to the echo extrapolation model, using echoes of a low-resolution image to construct a structured echo matrix; obtaining a null-trapping filter based on the structured echo matrix; constructing an echo extrapolation problem, and performing echo extrapolation based on the null-trapping filter; iteratively carrying out null trap filter acquisition and echo extrapolation until convergence, and obtaining an echo extrapolation result; and imaging the echo extrapolation result to obtain a super-resolution imaging result. Based on the structured low-rank characteristic, echo extrapolation is realized by iteratively updating the null-trapping filter and the echo, so that super-resolution imaging is realized. Experimental results show that the target information of the structured target can be better reserved while the imaging resolution is improved, and meanwhile better visual effect and robustness are achieved.

Description

Technical Field

[0001] The present invention relates to the field of radar signal processing technology, and in particular to a structured low-rank embedded gridless super-resolution ISAR imaging algorithm. Background Art

[0002] As an all-day, all-weather active microwave remote sensing tool, ISAR (Inverse Synthetic Aperture Radar, ISAR) has the ability to provide two-dimensional high-resolution images of moving targets and is widely used in both civil and military fields. According to the basic principles of ISAR, high resolution in range and azimuth is obtained by broadband waveforms and the change in viewing angle between the radar and the target, respectively. Under appropriate imaging geometry, emitting broadband waveforms and increasing the coherent accumulation time to obtain more information on viewing angle changes can help improve range and azimuth resolution. However, in practical applications, this is often difficult to achieve, and the target can only be observed with a narrowband waveform for short-aperture observation. According to the ISAR imaging principle and the Rayleigh criterion, this will result in limited two-dimensional resolution of the image.

[0003] At present, using narrowband short-aperture echoes to achieve imaging resolution comparable to that of broadband long-aperture echoes has become a widely studied issue in the field of radar imaging, known as super-resolution imaging. Existing super-resolution ISAR imaging algorithms include spectrum estimation algorithms such as BURG and RELAX, as well as compressed sensing (CS) algorithms. However, CS algorithms have inherent limitations. When the dictionary between echoes and images is preset according to the imaging model, the image needs to be gridded, which inevitably leads to discretization model mismatch errors. In addition, the imaging performance of CS algorithms is limited by the restricted isometry property (RIP). There is a high similarity between dictionaries corresponding to overly fine grids, which cannot break through the limitations of RIP.

[0004] In order to overcome the model mismatch problem, the academic community has conducted research on gridless CS technology. Among them, matrix completion (MC) based on low-rank or structured low-rank characteristics is a typical gridless technology. The radar echo is modeled as a combination of multiple support bases that satisfy certain incoherence, thereby retaining the structural information in the echo. Atomic norm minimization (ANM) is another type of representation method for low-rank constraints. At present, there is a non-convex algorithm based on the two-dimensional ANM framework, which realizes gridless sparse ISAR imaging through reweighted two-dimensional ANM. At present, low-rank priors have been widely used in the field of sparse imaging, but their application in super-resolution ISAR imaging is still blank. According to the finite information rate theory, if the signal component corresponding to the target is considered to be in the low-dimensional subspace of the high-dimensional echo and is orthogonal to the remaining subspace (hereinafter referred to as the zero-trapping subspace), then the orthogonality of this subspace is described as the zero-trapping characteristic, that is, there is a zero-trapping filter corresponding to the signal distribution. In order to estimate the nulling subspace, the echo of the low-resolution image can be used to construct a structured echo matrix, and the singular value vectors corresponding to the smaller singular values ​​can be extracted by singular value decomposition of the matrix, and then the vectors are re-weighted. Then the super-resolution imaging problem is transformed into an echo extrapolation problem with nulling constraints, and the echo extrapolation is realized by iteratively updating the nulling filter and the echo, thereby achieving super-resolution imaging. Summary of the invention

[0005] Technical problem: In order to overcome the basis mismatch problem caused by the gridded dictionary and further improve the performance of super-resolution ISAR imaging using narrow-band short-aperture echoes, the present invention provides a structured low-rank embedded gridless super-resolution ISAR imaging algorithm, which can achieve effective ISAR high-resolution imaging under limited bandwidth and short aperture.

[0006] Technical solution: In order to achieve the above-mentioned invention object, the present invention provides a structured low-rank embedded gridless super-resolution ISAR imaging method, the specific steps are:

[0007] Step 1, receiving an echo signal corresponding to a linear frequency modulation signal emitted by a radar, and preprocessing the echo signal, and then entering an iterative process;

[0008] Step 2: In the first iteration, the preprocessed echo signal is used to construct a structured echo matrix, and in the subsequent iteration, the echo extrapolation result obtained in the previous iteration is used to construct a structured echo matrix;

[0009] Step 3, using singular value decomposition and reweighted combination method to obtain a zero-pitching filter from the structured echo matrix;

[0010] Step 4, based on the zero-trapping filter, using the quasi-Newton method to obtain an echo extrapolation result;

[0011] Step 5, iteratively execute steps 2 to 4 until convergence to obtain the final echo extrapolation result;

[0012] Step 6: Imaging the final echo extrapolation result to obtain a super-resolution imaging result.

[0013] Furthermore, the steps of preprocessing the echo signal in step 1 are as follows:

[0014] Step 1.1, performing de-skewing processing on the echo signal to obtain a demodulated echo signal;

[0015] Step 1.2, compensating the residual video phase of the demodulated echo signal to obtain a compensated echo signal;

[0016] Step 1.3, sampling the compensated echo signal to obtain a discretized echo, the discretized echo is denoted as S, and is expressed as:

[0017]

[0018] in

[0019] ∑=diag([σ′1 σ′2…σ′ K ])

[0020]

[0021] Among them, a k (n) represents the frequency modulation phase vector a k The nth element in b is the fast time sequence number in discrete form, and n = 1, 2, ..., N, N is the number of sampling points in the pulse of the echo signal, b k (m) represents the pulse modulation phase vector b k The mth element in , m is the slow time sequence number in discrete form, and m = 1, 2, ..., M, M is the number of pulses of the echo signal, k is the number of scattering points on the target, and k = 1, 2 ..., K, K is the total number of scattering points on the target, σ′ k represents the product of the backscatter coefficient of the kth scattering point on the target and the constant phase, diag(·) is the diagonal matrix construction operation, (x k ,y k ) is the coordinate of the kth scattering point at the initial moment, γ is the modulation frequency of the linear frequency modulation waveform, f s represents the sampling rate, c is the propagation speed of electromagnetic waves, ω is the angular velocity of the target rotating uniformly around the origin, and f c is the center frequency, PRF is the pulse repetition frequency, and j represents the imaginary sign.

[0022] Furthermore, the method for constructing the structured echo matrix in step 2 is:

[0023] Assuming that the current iteration is the lth round, according to the echo Y in the lth round of iteration (l) The constructed structured matrix H Y It can be expressed as:

[0024]

[0025] Where Y is the broadband long aperture echo, (·) (l) represents the variable in the first iteration, is the number of sampling points in the pulse corresponding to the broadband, is the number of pulses corresponding to the long aperture, P and Q are constants, For structured operation, (l) The specific steps of taking the structured operation are:

[0026] Step 2.1, start from Y (l) Winning From Y (l) The (p,q)th block extracted from is expressed as:

[0027]

[0028] Among them, p and q are the row number and column number of the extracted block respectively, p=P+1,P+2,…, Y (l) The element in the i-th row and j-th column is denoted as Y (l) (i,j);

[0029] Step 2.2, Vectorize the operation to get Wherein, vec(·) represents a vectorized operation, and the vectorized operation is performed by vertically stacking each column of the matrix to be vectorized;

[0030] Step 2.3, Construct H in a horizontal stacking manner Y , H Y It is expressed as:

[0031]

[0032] When the iteration is in round 1, treat S as Y (1) ,at this time

[0033] Furthermore, in step 3, the step of obtaining a zero-trapping filter from the structured echo matrix is:

[0034] Step 3.1, H Y Do SVD in, H Y The left singular matrix obtained by SVD decomposition, H Y The conjugate transpose of the right singular matrix obtained by SVD decomposition, (·) H represents the conjugate transpose operation, H Y The singular value matrix obtained by SVD decomposition;

[0035] Step 3.2: Take the left singular value vector corresponding to the last K singular values ​​obtained by SVD decomposition As the singular value vector corresponding to the trapped null subspace, where The method of obtaining is to extract The hth column of , where h is the column number, h = K+1, K+2, …, (2P+1)(2Q+1);

[0036] Step 3.3, rearrange the singular value vectors corresponding to the trapped zero subspace and perform interpolation FFT to obtain:

[0037]

[0038] in, The result after rearrangement and interpolation of FFT, Indicates interpolation FFT operation. The number of interpolation points is 2 to 4 times the number of points corresponding to the extrapolated echo. Indicates that Rearrange the matrix into a matrix with 2P+1 rows and 2Q+1 columns by filling column by column;

[0039] Step 3.4, Reweighted

[0040]

[0041] Where W is the reweighted result, W(i1,i2) represents the element in the i1th row and i2th column of W, express The element in the i1th row and i2th column, i1=1,2…,2P+1, i2=1,2…,2Q+1, β is the exponential coefficient, Yes H Y The hth singular value of ;

[0042] Step 3.5, perform IFFT on W to obtain the zero-trapping filter E of the first iteration (l) , expressed as:

[0043]

[0044] in, Indicates IFFT operation.

[0045] Furthermore, the steps of using the quasi-Newton method to implement echo extrapolation in step 4 are:

[0046] Step 4.1, construct the echo extrapolation problem, and regard S as the result of Y shortening the observation window length, expressed as:

[0047]

[0048] D r for No. Go to The matrix composed of row elements represents the downsampling matrix of the distance dimension, D a for No. Go to The matrix composed of row elements represents the downsampling matrix of the azimuth dimension. is the identity matrix, Indicates rounding down. Indicates rounding up, (·) T represents the transpose operation, N is the noise matrix, and the echo extrapolation problem in the lth iteration is expressed as:

[0049]

[0050] Among them, Y (l+1) is the broadband long aperture echo to be extrapolated in the lth iteration, * represents the convolution operation, ‖·‖ F represents the Frobenius norm of the matrix, λ is the regularization coefficient;

[0051] Step 4.2, according to the echo extrapolation problem, let y (l+1) =vec(Y (l+1) ), and use the quasi-Newton method to solve for y (l +1) , the steps are:

[0052] Step 4.2.1, calculate y (l+1) The conjugate gradient of is expressed as:

[0053]

[0054] in, Represents y (l+1) The conjugate gradient of represents the Kronecker product, s = vec(S), Hess(y(l+1) ) is through y (l+1) The estimated Hessian matrix is ​​expressed as:

[0055]

[0056] ⊙ represents Hadamard product;

[0057] Step 4.2.2, use the conjugate gradient algorithm to calculate the conjugate gradient zero point and find the variable to be determined for the next iteration. In the i-th iteration of the conjugate gradient algorithm, the variable to be determined for the i+1th iteration is The calculation formula is:

[0058]

[0059] in,(·) (i) represents the variable in the i-th iteration of the conjugate gradient algorithm, It represents the variable to be determined in the i-th iteration of the conjugate gradient algorithm, and ζ is the iteration step length;

[0060] Step 4.2.3, iteratively execute steps 4.2.1 and 4.2.2 to a preset number of iterations, and the iteration terminates.

[0061] Furthermore, the judgment condition for whether the convergence is achieved in step 5 is: ∈ is the convergence threshold.

[0062] Furthermore, the method for imaging the echo extrapolation result in step 6 is a range-Doppler algorithm, and the specific method is to perform a 2D FFT on the echo extrapolation result.

[0063] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0064] Based on the structured low-rank characteristics, the present invention transforms the super-resolution imaging problem into an echo extrapolation problem with a zero-trapping constraint, and realizes echo extrapolation by iteratively updating the zero-trapping filter and the echo, thereby realizing super-resolution imaging. The present invention proposes an effective super-resolution ISAR imaging method based on structured low-rank characteristics. Compared with the traditional grid super-resolution method, the invention can effectively overcome the basis mismatch problem caused by the grid dictionary, and can better retain the target information of the structured target while improving the resolution, and has a higher peak signal-to-noise ratio (PSNR), correlation coefficient (CC) and structure similarity index measure (SSIM) at different super-resolutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a schematic diagram of the overall process of the structured low-rank embedded gridless super-resolution ISAR imaging algorithm proposed in the present invention.

[0066] Figure 2 Simulated satellite model and ISAR imaging results, where (a) is the satellite model and (b) is the ISAR imaging result.

[0067] Figure 3 This is a comparison diagram of the super-resolution imaging results of simulated satellite targets using the present invention and the RD, ANM, and ICS algorithms at different super-resolutions.

[0068] Figure 4 This is a comparison diagram of 1×2 times super-resolution imaging results of simulated satellite targets under different signal-to-noise ratios between the present invention and the RD, ANM, and ICS algorithms.

[0069] Figure 5 This is a comparison diagram of 2×2 times super-resolution imaging results of simulated satellite targets using the present invention and RD, ANM, and ICS algorithms at different signal-to-noise ratios.

[0070] Figure 6 This is a comparison chart of PSNR, CC and SSIM of the present invention, ANM and ICS algorithms when performing super-resolution imaging of simulated satellite targets at different super-resolutions and signal-to-noise ratios.

[0071] Figure 7 The figures are comparison diagrams of the results of double super-resolution extrapolation of the measured original echoes by the present invention and the RD algorithm, where (a) is the data of the Yak-42 aircraft and (b) is the data of the civil aircraft.

[0072] Figure 8 This is a comparison chart of the 2×2 and 4×4 super-resolution imaging results of the present invention and the RD, ANM, and ICS algorithms on the measured Yak-42 aircraft data.

[0073] Fig. 9 This is a comparison chart of the 2×2 and 4×4 super-resolution imaging results of the present invention and the RD, ANM, and ICS algorithms on the measured civil aircraft data. DETAILED DESCRIPTION

[0074] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0075] 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.

[0076] like Figure 1As shown, the present invention provides a structured low-rank embedded gridless super-resolution ISAR imaging method, the specific steps are:

[0077] Step 1, receiving an echo signal corresponding to a linear frequency modulation signal emitted by a radar, and preprocessing the echo signal, and then entering an iterative process;

[0078] Step 2: In the first iteration, the preprocessed echo signal is used to construct a structured echo matrix, and in the subsequent iteration, the echo extrapolation result obtained in the previous iteration is used to construct a structured echo matrix;

[0079] Step 3, using singular value decomposition and reweighted combination method to obtain a zero-pitching filter from the structured echo matrix;

[0080] Step 4, based on the zero-trapping filter, using the quasi-Newton method to obtain an echo extrapolation result;

[0081] Step 5, iteratively execute steps 2 to 4 until convergence to obtain the final echo extrapolation result;

[0082] Step 6: Imaging the final echo extrapolation result to obtain a super-resolution imaging result.

[0083] Furthermore, the steps of preprocessing the echo signal in step 1 are as follows:

[0084] Step 1.1, performing de-skewing processing on the echo signal to obtain a demodulated echo signal;

[0085] Step 1.2, compensating the residual video phase of the demodulated echo signal to obtain a compensated echo signal;

[0086] Step 1.3, sampling the compensated echo signal to obtain a discretized echo, the discretized echo is denoted as S, and is expressed as:

[0087]

[0088] in

[0089] ∑=diag([σ′1 σ′2…σ′ K ])

[0090]

[0091] Among them, a k (n) represents the frequency modulation phase vector a k The nth element in b is the fast time sequence number in discrete form, and n = 1, 2, ..., N, N is the number of sampling points in the pulse of the echo signal, b k (m) represents the pulse modulation phase vector bk The mth element in , m is the slow time sequence number in discrete form, and m = 1, 2, ..., M, M is the number of pulses of the echo signal, k is the number of scattering points on the target, and k = 1, 2 ..., K, K is the total number of scattering points on the target, σ k ′ represents the product of the backscatter coefficient of the kth scattering point on the target and the constant phase, diag(·) is the diagonal matrix construction operation, (x k ,y k ) is the coordinate of the kth scattering point at the initial moment, γ is the modulation frequency of the linear frequency modulation waveform, f s represents the sampling rate, c is the propagation speed of electromagnetic waves, ω is the angular velocity of the target rotating uniformly around the origin, and f c is the center frequency, PRF is the pulse repetition frequency, and j represents the imaginary sign.

[0092] Furthermore, the method for constructing the structured echo matrix in step 2 is:

[0093] Assuming that the current iteration is the lth round, according to the echo Y in the lth round of iteration (l) The constructed structured matrix H Y It can be expressed as:

[0094]

[0095] Where Y is the broadband long aperture echo, (·) (l) represents the variable in the first iteration, is the number of sampling points in the pulse corresponding to the broadband, is the number of pulses corresponding to the long aperture, P and Q are constants, For structured operation, (l) The specific steps of taking the structured operation are:

[0096] Step 2.1, start from Y (l) Winning From Y (l) The (p,q)th block extracted from is expressed as:

[0097]

[0098] Among them, p and q are the row number and column number of the extracted block respectively, p=P+1,P+2,…, Y (l) The element in the i-th row and j-th column is denoted as Y (l) (i,j);

[0099] Step 2.2, Vectorize the operation to get Wherein, vec(·) represents a vectorized operation, and the vectorized operation is performed by vertically stacking each column of the matrix to be vectorized;

[0100] Step 2.3, Construct H in a horizontal stacking manner Y , H Y It is expressed as:

[0101]

[0102] When the iteration is in round 1, treat S as Y (1) ,at this time

[0103] Furthermore, in step 3, the step of obtaining a zero-trapping filter from the structured echo matrix is:

[0104] Step 3.1, H Y Do SVD in, H Y The left singular matrix obtained by SVD decomposition, H Y The conjugate transpose of the right singular matrix obtained by SVD decomposition, (·) H represents the conjugate transpose operation, H Y The singular value matrix obtained by SVD decomposition;

[0105] Step 3.2: Take the left singular value vector corresponding to the last K singular values ​​obtained by SVD decomposition As the singular value vector corresponding to the trapped null subspace, where The method of obtaining is to extract The hth column of , where h is the column number, h = K+1, K+2, …, (2P+1)(2q+1);

[0106] Step 3.3, rearrange the singular value vectors corresponding to the trapped zero subspace and perform interpolation FFT to obtain:

[0107]

[0108] in, The result after rearrangement and interpolation of FFT, Indicates interpolation FFT operation. The number of interpolation points is 2 to 4 times the number of points corresponding to the extrapolated echo. Indicates that Rearrange the matrix into a matrix with 2P+1 rows and 2Q+1 columns by filling column by column;

[0109] Step 3.4, Reweighted

[0110]

[0111] Where W is the reweighted result, W(i1,i2) represents the element in the i1th row and i2th column of W, express The element in the i1th row and i2th column, i1=1,2…,2P+1, i2=1,2…,2Q+1, β is the exponential coefficient, Yes H Y The hth singular value of ;

[0112] Step 3.5, perform IFFT on W to obtain the zero-trapping filter E of the first iteration (l) , expressed as:

[0113]

[0114] in, Indicates IFFT operation.

[0115] Furthermore, the steps of using the quasi-Newton method to implement echo extrapolation in step 4 are:

[0116] Step 4.1, construct the echo extrapolation problem, and regard S as the result of Y shortening the observation window length, expressed as:

[0117]

[0118] D r for No. Go to The matrix composed of row elements represents the downsampling matrix of the distance dimension, D a for No. Go to The matrix composed of row elements represents the downsampling matrix of the azimuth dimension. is the identity matrix, Indicates rounding down. Indicates rounding up, (·) T represents the transpose operation, N is the noise matrix, and the echo extrapolation problem in the lth iteration is expressed as:

[0119]

[0120] Among them, Y (l+1) is the broadband long aperture echo to be extrapolated in the lth iteration, * represents the convolution operation, ‖·‖ F represents the Frobenius norm of the matrix, λ is the regularization coefficient;

[0121] Step 4.2, according to the echo extrapolation problem, let y (l+1) =vec(Y (l+1) ), and use the quasi-Newton method to solve for y (l +1) , the steps are:

[0122] Step 4.2.1, calculate y (l+1) The conjugate gradient of is expressed as:

[0123]

[0124] in, Represents y (l+1) The conjugate gradient of represents the Kronecker product, s = vec(S), Hess(y (l+1) ) is through y (l+1) The estimated Hessian matrix is ​​expressed as:

[0125]

[0126] ⊙ represents Hadamard product;

[0127] Step 4.2.2, use the conjugate gradient algorithm to calculate the conjugate gradient zero point and find the variable to be determined for the next iteration. In the i-th iteration of the conjugate gradient algorithm, the variable to be determined for the i+1th iteration is The calculation formula is:

[0128]

[0129] in,(·) (i) represents the variable in the i-th iteration of the conjugate gradient algorithm, It represents the variable to be determined in the i-th iteration of the conjugate gradient algorithm, and ζ is the iteration step length;

[0130] Step 4.2.3, iteratively execute steps 4.2.1 and 4.2.2 to a preset number of iterations, and the iteration terminates.

[0131] Furthermore, the judgment condition for whether the convergence is achieved in step 5 is: ∈ is the convergence threshold.

[0132] Furthermore, the method for imaging the echo extrapolation result in step 6 is a range-Doppler algorithm, and the specific method is to perform a 2D FFT on the echo extrapolation result.

[0133] In order to verify the beneficial effects of the present invention, simulation and measured data experiments of ISAR imaging are carried out. The comparison algorithms include an algorithm based on atomic norm minimization (ANM) and an algorithm based on improved CS (ICS for short). PSNR, CC and SSIM are used for quantitative analysis. Two super-resolution imaging situations are considered, azimuth super-resolution and range-azimuth joint super-resolution. In the azimuth super-resolution situation, echoes under broadband and half aperture are used, which is recorded as 1×2. In the range-azimuth joint super-resolution situation, echoes under half bandwidth and half aperture are used, which is recorded as 2×2. In addition, echoes under quarter bandwidth and quarter aperture are considered, which is recorded as 4×4. The specific experimental contents are as follows:

[0134] 1. Use simulated satellite data to verify the super-resolution ISAR imaging performance, uniformly set the echo SNR to 20dB, use different algorithms to perform ISAR super-resolution imaging on the simulated satellite data, and evaluate the imaging performance of each algorithm at different super-resolutions.

[0135] 2. Use simulated satellite data to verify the super-resolution ISAR imaging performance. Set the echo signal-to-noise ratio to 5dB and 10dB respectively. Use different algorithms to perform 1×2 and 2×2 super-resolution on the simulated satellite data, and evaluate the imaging performance of each algorithm under different echo SNRs.

[0136] 3. The super-resolution imaging performance is verified using the measured data of the Yak-42 aircraft and the civil aircraft. The two types of measured data are directly extrapolated with two times super-resolution using the RD algorithm and the present invention respectively, and the original echo direct extrapolation imaging performance is compared.

[0137] 4. The super-resolution imaging performance was verified using measured data from the Yak-42 aircraft and civil aircraft. The two types of measured data were truncated to simulate 2×2 and 4×4 times super-resolution. Different algorithms were used to perform ISAR super-resolution imaging on the truncated data, and the imaging performance of each algorithm was evaluated.

[0138] The experimental results are as follows:

[0139] Reference Figure 2 , Figure 2 The simulated satellite model and ISAR imaging results used in the experiment are Figure 2 (b) The ISAR imaging result shown is a high-resolution image used as a reference.

[0140] Reference Figure 3 , Figure 3This is a comparison diagram of the super-resolution imaging results of simulated satellite targets under different super-resolutions of the present invention and the RD, ANM, and ICS algorithms. It can be seen from the figure that under different super-resolution conditions, the imaging results of the present invention are closer to the reference high-resolution image, and while improving the resolution, the target information of the structured target can be better retained.

[0141] Reference Figure 4 and Figure 5 , Figure 4 This is a comparison chart of the 1×2 times super-resolution imaging results of the simulated satellite target under different signal-to-noise ratios between the present invention and the RD, ANM, and ICS algorithms. Figure 5 This is a comparison diagram of 2×2 times super-resolution imaging results of simulated satellite targets under different signal-to-noise ratios between the present invention and the RD, ANM, and ICS algorithms. It can be seen from the figure that even when the SNR is low, the present invention can still obtain high-resolution imaging results using limited bandwidth and aperture, and the additional Gaussian noise does not affect the protection of the target contour and structural information by the present invention, and can still reflect the typical components of the target.

[0142] Reference Figure 6 , Figure 6 The figure is a comparison of PSNR, CC and SSIM between the present invention and the ANM and ICS algorithms for super-resolution imaging of simulated satellite targets at different super-resolutions and signal-to-noise ratios. The present invention has the best PSNR, CC and SSIM indicators at high SNR and still has good robustness at low SNR.

[0143] Reference Figure 7 , Figure 7 The figure is a comparison diagram of the results of the direct double super-resolution extrapolation of the measured original echo by the present invention and the RD algorithm, where (a) is the Yak-42 aircraft data, and (b) is the civil aircraft data. Compared with the results of the traditional RD algorithm, the present invention can make the imaging results of the target more finely focused, the adjacent strong scattering points can be better resolved, and has a narrower main lobe and a lower side lobe level.

[0144] Reference Figure 8 and Fig. 9 , Figure 8 This is a comparison chart of the 2×2 and 4×4 super-resolution imaging results of the present invention and the RD, ANM, and ICS algorithms on the measured Yak-42 aircraft data. Fig. 9 The following is a comparison chart of 2×2 and 4×4 super-resolution imaging results of measured civil aircraft data by the present invention and the RD, ANM, and ICS algorithms. By comparison, the imaging results of the present invention have better visual effects and better robustness to different types of aerospace targets.

[0145] 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 gridless super-resolution ISAR imaging method with structured low-rank embedding, characterized in that: The specific steps are: Step 1, receiving an echo signal corresponding to a linear frequency modulation signal emitted by a radar, and preprocessing the echo signal, and then entering an iterative process; Step 2: In the first iteration, the preprocessed echo signal is used to construct a structured echo matrix, and in the subsequent iteration, the echo extrapolation result obtained in the previous iteration is used to construct a structured echo matrix; Step 3, using singular value decomposition and reweighted combination method to obtain a zero-pitching filter from the structured echo matrix; Step 4, based on the zero-trapping filter, using the quasi-Newton method to obtain an echo extrapolation result; Step 5, iteratively execute steps 2 to 4 until convergence to obtain the final echo extrapolation result; Step 6: Imaging the final echo extrapolation result to obtain a super-resolution imaging result.

2. The structured low-rank embedded gridless super-resolution ISAR imaging method according to claim 1, characterized in that: The steps of preprocessing the echo signal in step 1 are as follows: Step 1.1, performing de-skewing processing on the echo signal to obtain a demodulated echo signal; Step 1.2, compensating the residual video phase of the demodulated echo signal to obtain a compensated echo signal; Step 1.3, sampling the compensated echo signal to obtain a discretized echo, the discretized echo is denoted as S, and is expressed as: in ∑=diag([σ′1 σ′2 … σ′ K ]) Among them, a k (n) represents the frequency modulation phase vector a k The nth element in b is the fast time sequence number in discrete form, and n = 1, 2, ..., N, where N is the number of sampling points in the pulse of the echo signal, and b k (m) represents the pulse modulation phase vector b k The mth element in , m is the slow time sequence number in discrete form, and m = 1, 2, ..., M, M is the number of pulses of the echo signal, k is the number of scattering points on the target, and k = 1, 2 ..., K, K is the total number of scattering points on the target, σ′ k represents the product of the backscatter coefficient of the kth scattering point on the target and the constant phase, diag(·) is the diagonal matrix construction operation, (x k ,y k ) is the coordinate of the kth scattering point at the initial moment, γ is the modulation frequency of the linear frequency modulation waveform, f s represents the sampling rate, c is the propagation speed of electromagnetic waves, ω is the angular velocity of the target rotating uniformly around the origin, and f c is the center frequency, PRF is the pulse repetition frequency, and j represents the imaginary sign.

3. The structured low-rank embedded gridless super-resolution ISAR imaging method according to claim 2, characterized in that: The method for constructing the structured echo matrix in step 2 is: Assuming that the current iteration is the lth round, according to the echo Y in the lth round of iteration (l) The constructed structured matrix H Y It can be expressed as: Where Y is the broadband long aperture echo, (·) (l) represents the variable in the first iteration, is the number of sampling points in the pulse corresponding to the broadband, is the number of pulses corresponding to the long aperture, P and Q are constants, For structured operation, (l) The specific steps of taking the structured operation are: Step 2.1, start from Y (l) Winning From Y (l) The (p, q)th block extracted from is expressed as: Among them, p and q are the row number and column number of the extracted block respectively. Y (l) The element in the i-th row and j-th column is denoted as Y (l) (i, j); Step 2.2, Vectorize the operation to get Wherein, vec(·) represents a vectorized operation, and the vectorized operation is performed by vertically stacking each column of the matrix to be vectorized; Step 2.3, Construct H in a horizontal stacking manner Y , H Y It is expressed as: When the iteration is in round 1, treat S as Y (1) ,at this time 4. The structured low-rank embedded gridless super-resolution ISAR imaging method according to claim 3, characterized in that: In step 3, the step of obtaining the null filter from the structured echo matrix is: Step 3.1, H Y Do SVD in, H Y The left singular matrix obtained by SVD decomposition, H Y The conjugate transpose of the right singular matrix obtained by SVD decomposition, (·) H represents the conjugate transpose operation, H Y The singular value matrix obtained by SVD decomposition; Step 3.2: Take the left singular value vector corresponding to the last K singular values ​​obtained by SVD decomposition As the singular value vector corresponding to the trapped null subspace, where The method of obtaining is to extract The h-th column of , where h is the column number, h = K+1, K+2, ..., (2P+1)(2Q+1); Step 3.3, rearrange the singular value vectors corresponding to the trapped zero subspace and perform interpolation FFT to obtain: in, for The result after rearrangement and interpolation of FFT, Indicates interpolation FFT operation. The number of interpolation points is 2 to 4 times the number of points corresponding to the extrapolated echo. Indicates that Rearrange the matrix into a matrix with 2P+1 rows and 2Q+1 columns by filling column by column; Step 3.4, Reweighted Where W is the re-weighted result, W(i1, i2) represents the element in the i1th row and i2th column of W, express The element in the i1th row and i2th column, i1=1,2…,2P+1, i2=1,2…,2Q+1, β is the exponential coefficient, Yes H Y The hth singular value of ; Step 3.5, perform IFFT on W to obtain the zero-trapping filter E of the first iteration (l) , expressed as: in, Indicates IFFT operation.

5. The structured low-rank embedded gridless super-resolution ISAR imaging method according to claim 4, characterized in that: The steps of using the quasi-Newton method to implement echo extrapolation in step 4 are: Step 4.1, construct the echo extrapolation problem, and regard S as the result of Y shortening the observation window length, expressed as: D r for No. Go to The matrix composed of row elements represents the downsampling matrix of the distance dimension, D a for No. Go to The matrix composed of row elements represents the downsampling matrix of the azimuth dimension. and is the identity matrix, Indicates rounding down. Indicates rounding up, (·) T represents the transpose operation, N is the noise matrix, then the echo extrapolation problem in the lth iteration is expressed as: Among them, Y (l+1) is the broadband long aperture echo to be extrapolated in the lth iteration, * represents the convolution operation, ||·|| F represents the Frobenius norm of the matrix, λ is the regularization coefficient; Step 4.2, according to the echo extrapolation problem, let y (l+1) =vec(Y (l+1) ), and use the quasi-Newton method to solve for y (l+1) , the steps are: Step 4.2.1, calculate y (l+1) The conjugate gradient of is expressed as: in, Represents y (l+1) The conjugate gradient of represents the Kronecker product, s = vec(S), Hess(y (l+1) ) is through y (l+1) The estimated Hessian matrix is ​​expressed as: ⊙ represents Hadamard product; Step 4.2.2, use the conjugate gradient algorithm to calculate the conjugate gradient zero point and find the variable to be determined for the next iteration. In the i-th iteration of the conjugate gradient algorithm, the variable to be determined for the i+1th iteration is The calculation formula is: in,(·) (i) represents the variable in the i-th iteration of the conjugate gradient algorithm, It represents the variable to be determined in the i-th round of iteration of the conjugate gradient algorithm, and ζ is the iteration step length; Step 4.2.3, iteratively execute steps 4.2.1 and 4.2.2 to a preset number of iterations, and the iteration terminates.

6. The structured low-rank embedded gridless super-resolution ISAR imaging method according to claim 5, characterized in that: The judgment condition for whether the step 5 converges is: ∈ is the convergence threshold.

7. The structured low-rank embedded gridless super-resolution ISAR imaging method according to claim 6, characterized in that: The method for imaging the echo extrapolation result in step 6 is the range-Doppler algorithm, and the specific method is to perform 2D FFT on the echo extrapolation result.

Images