Inverse Synthetic Aperture Radar Imaging Method and System Based on Co-prime Dual-channel Downsampling

Abstract

The present invention relates to a radar imaging method and system, and specifically to an inverse synthetic aperture radar imaging method and system based on co-prime dual-channel downsampling. It overcomes the problems existing in the inverse synthetic aperture radar imaging method under existing downsampling, such as large sampling difficulty, large time error, high hardware implementation difficulty, inability to guarantee imaging performance under low signal-to-noise ratio, and low reliability of sparse reconstruction. First, a co-prime dual-channel ADC sampling combination is used to downsample the inverse synthetic aperture radar echo; then, based on the reconstruction method, a high-resolution range image of sparse reconstruction is obtained, and further a two-dimensional ISAR image is obtained; compared with random sampling, the co-prime dual-channel ADC sampling proposed by the present invention is easy to implement in hardware and has small system error, and it is easier to ensure the accuracy of sampling; at the same time, the influence of noise on inverse synthetic aperture radar imaging is considered, and the influence of noise is considered in the sparse solution process, realizing the reconstruction of a high-performance and high-resolution radar range image under low signal-to-noise ratio.

Description

Technical Field

[0001] The present invention relates to a radar imaging method and system, specifically an inverse synthetic aperture radar imaging method and system based on co-prime dual-channel downsampling. Background Art

[0002] Radar imaging technology is an information acquisition technology that uses electromagnetic waves as a carrier and high-resolution radar to obtain information on the electromagnetic scattering characteristics of observed targets. With the gradual improvement of radar resolution, modern radars have gradually acquired the capabilities of target tracking, recognition, imaging, and anti-jamming. Compared with optical imaging, radar imaging has the advantages of long-range detection, all-weather operation, etc., and is widely used in target detection and radar astronomy. The idea of Inverse Synthetic Aperture Radar (ISAR) originated in the 1950s and was developed on the basis of Synthetic Aperture Radar (SAR). ISAR imaging generally detects non-cooperative targets, and its signal processing is more difficult and complex.

[0003] In the range dimension, ISAR transmits a linear frequency modulation signal and performs matched filtering and pulse compression at the receiving end to achieve range resolution of target scattering points. High range resolution is achieved by increasing the bandwidth of the linear frequency modulation signal. The virtual aperture of ISAR is formed by the relative rotation between the target and the radar. The azimuth resolution depends on the imaging accumulation angle formed by the relative rotation between the target and the radar. The longer the coherent accumulation time, the larger the imaging accumulation angle, and the higher the target azimuth resolution. However, a large signal bandwidth and a long coherent accumulation time will both cause a sharp increase in the data volume of the radar system, requiring a large amount of hardware resources and stronger signal real-time processing capabilities. In addition, since most of the targets observed by ISAR are non-cooperative moving targets with strong mobility, ISAR may not be able to ensure sufficient observation time, resulting in incomplete radar echo data and reduced imaging quality.

[0004] Currently, most of the research on ISAR imaging is based on the radar echo sampling satisfying the Nyquist sampling theorem. However, for radar signals with high range resolution and long coherent accumulation time, the amount of echo sampling data is extremely large and occupies a large amount of hardware resources. Existing sampling and signal processing equipment is difficult to process radar signals with high resolution and long coherent accumulation time.

[0005] To overcome the above problems, Li Wenjing et al. applied compressive sensing to the inverse synthetic aperture radar (ISAR) echo imaging in their published paper "An ISAR Imaging Method Based on Compressive Sensing" (Li Wenjing, Chen Hongwei. An ISAR Imaging Method Based on Compressive Sensing [J]. Computer Simulation, 2015, 32(8): 10 - 13, 62.). For high-resolution ISAR echo signals with large bandwidth and long coherent integration time, they proposed an idea and method for ISAR imaging under the condition lower than the Nyquist sampling theorem, obtaining high-quality target images with less observation information. First, a signal model of the ISAR two-dimensional image was established; second, the radar echo signal was randomly undersampled to obtain a radar signal that does not satisfy the Nyquist sampling theorem; finally, the orthogonal matching pursuit algorithm was used for signal reconstruction, and post-processing was performed on the reconstructed signal to obtain a high-resolution two-dimensional image. This method has the following three deficiencies: First, when downsampling the target echo received by the ISAR, random sampling was performed, but in practical applications, random downsampling is difficult, with large time sampling errors and hard to implement in hardware; second, the situation of the existence of noise was not considered, and the performance of sparse reconstruction cannot be guaranteed under low signal-to-noise ratio conditions; third, the sparse reconstruction evaluation results are not persuasive, and only the results of one random sampling are used for sparse evaluation. When the sampling positions change during the next random sampling, the results of sparse reconstruction cannot be guaranteed. Summary of the Invention

[0006] The object of the present invention is to provide an inverse synthetic aperture radar imaging method and system based on co-prime dual-channel downsampling, which overcomes the problems of large sampling difficulty, large time error, large hardware implementation difficulty, inability to guarantee imaging performance under low signal-to-noise ratio, and low reliability of sparse reconstruction evaluation results existing in the inverse synthetic aperture radar imaging method under existing downsampling.

[0007] The technical solution of the present invention is to provide an inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling, including the following steps:

[0008] Step 1: Use a co-prime dual-channel ADC sampling combination to downsample the inverse synthetic aperture radar echo;

[0009] Step 2: Reconstruct based on the downsampled data to obtain a sparse reconstructed range image vector S, and then obtain a two-dimensional ISAR image;

[0010] Step 2.1: Establish a weighted range image compressive sensing model and an optimization function:

[0011] The weighted range image compressive sensing model is: min(||WS||1), subject to ||s f12 - ΨS|| ≤ ξ;

[0012] Among them, W represents the diagonal weight matrix; ξ is the noise level; s f12 is the reduced-dimensional observation signal vector of the co-prime dual-channel ADC sampling combination; Ψ is the dictionary matrix of the co-prime dual-channel ADC sampling combination under the entire scene;

[0013] The optimization function is:

[0014]

[0015] Among them, is the estimated value of the range profile vector for sparse reconstruction, and μ is the sparse constraint coefficient;

[0016] Step 2.2, Solve the Hessian matrix (Hessian matrix) and conjugate gradient function of the optimization function, and obtain the range profile vector of sparse reconstruction based on the weighted l1 norm minimization method;

[0017] Step 2.21, Solve the initial Hessian matrix H(S 0 ):

[0018] H(S 0 ) = 2(Ψ) H Ψ + μU(S 0 )W 0

[0019] Among them, W 0 is the initial diagonal weight matrix, 2 ≤ i ≤ NM, where N is the number of points of each column range profile under Nyquist sampling, and M is the number of azimuth points; S 0 is the coarse range profile vector, which is obtained by performing an inverse Fourier transform on the reduced-dimensional observation signal matrix of the co-prime dual-channel ADC sampling combination to obtain a coarse range profile matrix, and then vectorizing the coarse range profile matrix by column; are the 1st, 2nd, up to the ith elements in S 0 respectively; τ is a positive number; (Ψ) H is the conjugate transpose of Ψ;

[0020] Step 2.22, Based on the initial Hessian matrix H(S 0 ), obtain the initial conjugate gradient function of the optimization function

[0021] Step 2.23, Based on the initial conjugate gradient function, when the conjugate gradient function is 0, obtain the estimated value of the range profile vector for sparse reconstruction

[0022] Step 2.24, Based on the judgment criterion, judge the estimated value of the range profile vector for sparse reconstruction Whether the requirement is met. If so, let the range image vector S of sparse reconstruction be equal to the estimated value of the range image vector of sparse reconstruction Arrange the range image vectors of sparse reconstruction in a matrix according to the corresponding echo order to obtain the high-resolution range image of sparse reconstruction, and calculate the 2D ISAR image. Otherwise, perform iteration, return to step 2.21, and update the range image vector of the Hessian matrix in step 2.21 to the estimated value of the range image vector of sparse reconstruction obtained in step 2.23 Until the estimated value of the range image vector of sparse reconstruction Meets the requirement.

[0023] Further, in step 2.1, the reduced-dimension observation signal vector s of the co-prime dual-channel ADC sampling combination f12 and the dictionary matrix Ψ of the co-prime dual-channel ADC sampling combination in the whole scene are determined through the following process: According to the downsampled radar echo data s of the first channel in the co-prime dual-channel ADC sampling combination t1 , calculate the frequency-domain pulse compression data s of the first channel f1 ; According to the downsampled radar echo data s of the second channel in the co-prime dual-channel ADC sampling combination t2 , calculate the frequency-domain pulse compression data s of the second channel f2 ; Arrange s f1 and s f2 in a matrix according to the order of sampling time. The row direction of the matrix represents the range direction, and the column direction of the matrix represents the azimuth direction. Quantize the matrix column by column to obtain the reduced-dimension observation signal vector s of the co-prime dual-channel ADC sampling combination f12 ;

[0024] The dictionary matrix Ψ of the co-prime dual-channel ADC sampling combination in the whole scene:

[0025]

[0026] where F 12 is the dictionary matrix of each column range image, F 12 = U 12 F, U 12 is the observation matrix of the co-prime dual-channel ADC sampling combination, which is obtained by arranging each row of the observation matrix U1 of the first channel and the observation matrix U2 of the second channel in the co-prime dual-channel ADC sampling combination in a matrix according to the order of sampling time; F is the Fourier basis matrix.

[0027] Further, in step 2.21, calculate the initial diagonal weight matrix W through the following formula 0 ;

[0028]

[0029] where, is the initial diagonal weight matrix W 0 The diagonal elements in represent the rough range profile vector S 0 The i-th element in The weighted weight coefficient of, σ is a positive constant to prevent the phenomenon that false targets appear in non-target areas due to excessive weight values.

[0030] To further improve the reconstruction accuracy, in step 2.24, when returning to step 2.21, the diagonal weight matrix in the Hessian matrix in step 2.21 needs to be updated synchronously based on the following formula:

[0031]

[0032] where S i is the estimated value of the range profile vector for sparse reconstruction in step 2.23 The i-th element in, w i is the diagonal element in the updated diagonal weight matrix, representing the estimated value of the range profile vector after sparse reconstruction The weighted weight coefficient of the i-th element in

[0033] Furthermore, in step 2.1, by estimating the noise variance σ 2 and the Laplacian scale factor γ, the sparse constraint coefficient μ is calculated: μ = σ 2 γ; where: σ 2 = E{(s I ) H s I}; γ = NM / ||S 0 ||1; where, s I is the noise sample, obtained by taking the noise units that obviously do not contain the target signal from the rough range profile vector and vectorizing them; (s I ) H represents the conjugate transpose of s I

[0034] Furthermore, in step 2.24, the judgment criterion is:

[0035]

[0036] where, if the iteration number is 0, then is S 0 ; if the iteration number is greater than 0, then is the estimated value of the range profile vector for sparse reconstruction obtained in the previous iteration, and ρ represents the preset threshold.

[0037] ​Further, in step 2.24, arrange the range image vectors obtained by sparse reconstruction into a matrix according to the corresponding echo order to obtain the high-resolution range image after sparse reconstruction, and calculate the two-dimensional ISAR image. Specifically:

[0038] Arrange the range image vectors S obtained by sparse reconstruction into a matrix according to the corresponding echo order to obtain the high-resolution range image after sparse reconstruction; perform translational compensation on the high-resolution range image after sparse reconstruction, and perform azimuth compression on the result of translational compensation to obtain the high-resolution two-dimensional ISAR image.

[0039] Further, in step 1, through screening, obtain the optimal co-prime dual-channel ADC sampling combination, and use the optimal co-prime dual-channel ADC sampling combination to downsample the inverse synthetic aperture radar echo.

[0040] In order to further improve the sampling accuracy, before using the optimal co-prime dual-channel ADC sampling combination determined in step 1 to downsample the inverse synthetic aperture radar echo, it is necessary to determine the time delay error of the optimal co-prime dual-channel, and compensate the time delay error into the co-prime dual-channel ADC sampling combination, and then use the optimal co-prime dual-channel ADC sampling combination after time delay error compensation to downsample the inverse synthetic aperture radar echo;

[0041] Specifically, the time delay error of the optimal co-prime dual-channel is determined through the following process: use the optimal co-prime dual-channel ADC sampling combination to sample the reference signal, and based on the sampling time of the first channel, obtain the time delay error between the optimal co-prime dual-channels according to the position of the target in the range direction in the second channel; the bandwidth of the reference signal needs to meet: ensure that any sampling rate in the optimal co-prime dual-channel ADC sampling combination meets the Nyquist sampling rate of the reference signal.

[0042] Further, in step 1, the specific process of obtaining the optimal co-prime dual-channel ADC sampling combination through screening is as follows:

[0043] Step 1.1: Determine the range-direction dictionary matrix F of each column of each co-prime dual-channel ADC sampling combination in the current application scenario 12 0 ; F 12 0 =U 12 0 F; where U 12 0 is the observation matrix of each co-prime dual-channel ADC sampling combination;

[0044] Step 1.2: Based on the range image dictionary matrix F of each column of each co-prime dual-channel ADC sampling combination 12 0, determine the partial dictionary matrix of the range profile of each column of each group of co-prime dual-channel ADC sampling combinations related to the number and position of strong scattering points in the scene It means that the positions of k strong scattering points in the range profile vector of each column correspond to F 12 0 The matrix formed by the columns;

[0045] Step 1.3: Calculate the mean of the restricted isometry constants corresponding to the partial dictionary matrices of the range profiles of each column of each co-prime dual-channel ADC sampling combination under the condition that the number of strong scattering points is the same but the positions are different The corresponding mean of the restricted isometry constants;

[0046] Step 1.4: Compare the means of the restricted isometry constants corresponding to the partial dictionary matrices of the range profiles of each column of each co-prime dual-channel ADC sampling combination under the condition that the number of strong scattering points is the same but the positions are different Select the minimum mean of the restricted isometry constants;

[0047] Step 1.5: Determine whether the minimum mean of the restricted isometry constants satisfies the RIP criterion. If it meets the requirements, take the co-prime dual-channel ADC sampling combination corresponding to the minimum mean of the restricted isometry constants as the optimal co-prime dual-channel ADC sampling combination for the corresponding number of strong scattering points; if it does not meet the requirements, it is necessary to return and modify the co-prime dual-channel ADC sampling combination, and repeat the process from Step 1.1 to Step 1.4 until the requirements are met.

[0048] Furthermore, in Step 1.1, the observation matrix U of each group of co-prime dual-channel ADC sampling combinations is determined through the following process 12 0 : Calculate the observation matrix of each channel in each group of co-prime dual-channel ADC sampling combinations, and arrange each row of the observation matrices of the two channels in the same matrix according to the sampling order and sampling position to obtain the observation matrix U formed by each group of co-prime dual-channel ADC sampling combinations 12 0 .

[0049] Furthermore, if the two channels in the co-prime dual-channel ADC sampling combination have the same sampling time, when arranging each row of the observation matrices of the two channels in the same matrix according to the sampling order and sampling position, only keep the rows of the observation matrix corresponding to any one of the channels at this sampling time.

[0050] Further, in step 1.1, the observation matrix of each channel in each pair of co-prime dual-channel ADC sampling combinations is determined through the following process: First, based on the number of sampling points N at the Nyquist sampling rate, the observation matrix U corresponding to each column of echoes under the Nyquist sampling theorem and the Fourier basis matrix F corresponding to the scene are calculated; then, according to the sampling times of each channel in each pair of co-prime dual-channel ADC sampling combinations, the corresponding rows in the observation matrix U corresponding to the sampling times are retained to obtain the observation matrix of each channel in each pair of co-prime dual-channel ADC sampling combinations.

[0051] Further, step 1.2 specifically includes the following steps:

[0052] Step 1.21: Determine the number and positions of strong scattering points in the scene; according to the scene requirements, determine the maximum number K of strong scattering points included in the scene; among the K strong scattering points, select k strong scattering points as a group of strong scattering points, where k traverses from 1 to K, and K is an integer greater than 1; for each group of strong scattering points, randomly select its position in the scene; for each group of strong scattering points, determine P random positions, where P is an integer greater than 1;

[0053] Step 1.22: Obtain the partial dictionary matrix of each pair of co-prime dual-channel ADC sampling combinations according to the number and positions of strong scattering points in the scene; according to the number k of strong scattering points included in each group of strong scattering points determined in step 1.21 and the positions of each strong scattering point in the scene, extract the corresponding regions in the range image dictionary matrix F of each column of each pair of co-prime dual-channel ADC sampling combinations to obtain multiple partial dictionary matrices of each column of range image of each pair of co-prime dual-channel ADC sampling combinations 12 0 It refers to the matrix formed by the columns in F corresponding to the positions of k strong scattering points in each column of range image vector. 12 0 in the matrix.

[0054] Step 1.3 specifically includes the following steps:

[0055] Step 1.31: Calculate the eigenvalues of, and determine the range of eigenvalues;

[0056] Step 1.32: According to the range of eigenvalues [1 - δ k , 1 + δ k , determine the restricted isometry constant δ corresponding to each partial dictionary matrix of each pair of co-prime dual-channel ADC sampling combinations k ;

[0057] Step 1.33: Calculate the mean value of the restricted isometry constants corresponding to the partial dictionary matrices of each co-prime dual-channel ADC sampling combination under the condition that the number of strong scattering points is the same and the positions are different.

[0058] The present invention also provides an inverse synthetic aperture radar imaging system based on co-prime dual-channel downsampling, including a memory and a processor. The special feature lies in that: a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the above-mentioned inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling are realized.

[0059] The beneficial effects of the present invention are as follows:

[0060] 1. The present invention uses a co-prime dual-channel ADC sampling combination to downsample the inverse synthetic aperture radar echo. Compared with random sampling, the co-prime dual-channel ADC sampling proposed by the present invention samples uniformly within each channel, is easy to implement in hardware and has small system errors, and is more likely to ensure the accuracy of sampling; the present invention also considers the influence of noise on inverse synthetic aperture radar imaging. During the sparse solution process, the influence of noise on ISAR imaging is considered, the noise variance and Laplace scale factor are estimated using the coarse distribution range profile result, and the sparse constraint coefficient is obtained. The influence of noise is considered during the sparse solution process of the range profile, realizing high-performance and high-resolution radar range profile reconstruction under low signal-to-noise ratio, and further improving the performance of the ISAR two-dimensional image.

[0061] 2. The present invention uses a co-prime dual-channel dictionary matrix to evaluate the sparse reconstruction performance, and selects an optimal co-prime dual-channel combination from the available co-prime dual-channel combinations for ISAR echo downsampling to further improve the accuracy of sampling.

[0062] 3. The present invention considers the system error problem existing in the co-prime dual-channel ADC sampling process, calculates the error and compensates for the error, improves the accuracy of the range profile, and further enhances the performance of the ISAR two-dimensional image. Description of the Drawings

[0063] Figure 1 is the flowchart of the inverse synthetic aperture radar imaging method based on co-prime dual-channel ADC downsampling Figure 1 ;

[0064] Figure 2 is the flowchart of the inverse synthetic aperture radar imaging method based on co-prime dual-channel ADC downsampling Figure 2 ;

[0065] Figure 3 is the flowchart of the inverse synthetic aperture radar imaging method based on co-prime dual-channel ADC downsampling Figure 3 ;

[0066] Figure 4 is the statistical average graph of the maximum eigenvalue and the minimum eigenvalue;

[0067] Figure 5 is δ k Statistical average graph;

[0068] Figure 6(a) is the one-dimensional range image of the reference signal obtained using the first channel;

[0069] Figure 6(b) is the one-dimensional range image of the reference signal obtained using the second channel;

[0070] Figure 7(a) and Figure 7(b) are respectively the ISAR imaging results (contour graph) under ideal sampling and the ISAR imaging results under ideal sampling; Figure 7(c) and Figure 7(d) are the ISAR imaging results (contour graph) under sampling using the first channel of combination 2 and the ISAR imaging results under sampling using the first channel of combination 2; Figure 7(e) and Figure 7(f) are the ISAR imaging results (contour graph) under sampling using the second channel of combination 2 and the ISAR imaging results under sampling using the second channel of combination 2; Figure 7(g) and Figure 7(h) are the ISAR imaging results (contour graph) under sampling using combination 2 and the ISAR imaging results under sampling using combination 2; Figure 7(i) is the comparison graph of the range images reconstructed based on the co-prime dual channels; Figure 7(j) and Figure 7(k) are the ISAR imaging results (contour graph) based on the range images reconstructed by the co-prime dual channels and the ISAR imaging results based on the range images reconstructed by the co-prime dual channels;

[0071] Figure 8(a) is the comparison graph of the range images reconstructed under the 15 dB noise condition; Figure 8(b) is the ISAR imaging result (fixed weight) (contour graph) under the 15 dB noise condition; Figure 8(c) is the ISAR imaging result (fixed weight) under the 15 dB noise condition; Figure 8(d) is the ISAR imaging (adaptive weighting) (contour graph) under the 15 dB noise condition; Figure 8(e) is the ISAR imaging (adaptive weighting) under the 15 dB noise condition; Figure 8(f) is the comparison graph of the range images reconstructed under the 5 dB noise condition; Figure 8(g) is the ISAR imaging (adaptive weighting) (contour graph) under the 5 dB noise condition; Figure 8(h) is the ISAR imaging (adaptive weighting) under the 5 dB noise condition; Figure 8(i) is the ISAR imaging (fixed weight) (contour graph) under the 5 dB noise condition; Figure 8(j) is the ISAR imaging (fixed weight) under the 5 dB noise condition. Specific implementation mode

[0072] In order to reduce the difficulty of downsampling while ensuring the accuracy of downsampling and the imaging accuracy under low signal-to-noise ratio, this embodiment uses a co-prime dual-channel ADC sampling combination to downsample the inverse synthetic aperture radar echo. Then, based on the weighted l1-norm minimization method, a sparse reconstructed range image is obtained, and then a two-dimensional ISAR image is obtained; it meets the requirements of high-performance range image reconstruction under sub-Nyquist sampling and low signal-to-noise ratio, and a high-resolution two-dimensional ISAR image is obtained, which has high application value. It can be implemented by an inverse synthetic aperture radar imaging system based on co-prime dual-channel ADC downsampling. The system includes a memory and a processor. When the computer program stored in the memory is executed by the processor, the steps of the inverse synthetic aperture radar imaging method based on co-prime dual-channel ADC downsampling are implemented.

[0073] As Figure 1 shown, the imaging method of this embodiment specifically includes the following steps:

[0074] Step 1. Input the inverse synthetic aperture radar parameters, reference signal, and co-prime dual-channel ADC sampling combination.

[0075] The inverse synthetic aperture radar parameters include the carrier frequency f c of the inverse synthetic aperture radar, wavelength λ, bandwidth B, pulse width T p , pulse repetition frequency PRF, and Nyquist sampling rate F s and other basic parameters; the reference signal needs to make any sampling rate in the co-prime dual-channel combination meet the Nyquist sampling rate; there are multiple selectable co-prime dual-channel ADC sampling combinations. The co-prime dual-channel ADC sampling combination means using dual-channel ADC for signal sampling. The sampling intervals of both channels are uniform and relatively prime to each other, and the signal is sampled co-primely. The sampling intervals of the two channels of ADC are U / F s and V / F s respectively. U and V are a pair of relatively prime numbers, and the corresponding sampling rates of the two channels are F s / U and F s / V.

[0076] If the selectable co-prime dual-channel ADC sampling combination is the system-required co-prime dual-channel ADC sampling combination, or the RIP performance differences of each co-prime dual-channel ADC sampling combination are small, then any group of co-prime dual-channel ADC sampling combinations can be directly used to downsample the inverse synthetic aperture radar echo, and step 5 is executed; otherwise, the optimal co-prime dual-channel ADC sampling combination is selected based on the process from step 2 to step 4 to downsample the inverse synthetic aperture radar echo.

[0077] Step 2. Calculate the RIP performance of the dictionary matrix corresponding to each co-prime dual-channel ADC sampling combination.

[0078] Step 2.1: Calculate the Nyquist sampling theorem observation matrix U and the corresponding basis matrix F of the scene based on the number of sampling points N at the Nyquist sampling rate; according to the sampling time of each channel in each pair of co-prime dual-channel ADC sampling combinations, retain the corresponding rows in the observation matrix U corresponding to the sampling time, and obtain the observation matrix of each channel in each pair of co-prime dual-channel ADC sampling combinations.

[0079] Step 2.2: Arrange each row of the observation matrices of the two channels in the same matrix according to the sampling order and sampling position to obtain the observation matrix U formed by each pair of co-prime dual-channel ADC sampling combinations. 12 0 . If the two channels in the co-prime dual-channel ADC sampling combination have the same sampling time, when arranging each row of the observation matrices of the two channels in the same matrix according to the sampling order and sampling position, only retain the rows of the observation matrix corresponding to any one of the channels at that sampling time.

[0080] Step 2.3: Determine the column distance image dictionary matrix F of each pair of co-prime dual-channel ADC sampling combinations in the current application scenario. 12 0 ; F 12 0 = U 12 0 F;

[0081] Step 2.4: Based on the column distance image dictionary matrix F of each pair of co-prime dual-channel ADC sampling combinations, determine the partial dictionary matrix of the column distance image of each pair of co-prime dual-channel ADC sampling combinations related to the number and position of strong scattering points in the scene. 12 0 , determine the partial dictionary matrix of the column distance image of each pair of co-prime dual-channel ADC sampling combinations related to the number and position of strong scattering points in the scene.

[0082] First, according to the scene requirements, determine the maximum number of strong scattering points K included in the scene (determined according to the requirements and specific application scenarios); among the K strong scattering points, select k strong scattering points as a group of strong scattering points, where k traverses from 1 to K, and K is an integer greater than 1; for each group of strong scattering points, randomly select its position in the scene; for each group of strong scattering points, determine P random positions, where P is an integer greater than 1; according to the number of strong scattering points k included in each determined group of strong scattering points and the positions of each strong scattering point in the scene, extract the corresponding regions in the column distance image dictionary matrix F 12 0 of each pair of co-prime dual-channel ADC sampling combinations to obtain multiple partial dictionary matrices of the column distance image of each pair of co-prime dual-channel ADC sampling combinations. refers to the matrix formed by the columns corresponding to the positions of k strong scattering points in the column distance image vector in F 12 0 .

[0083] Step 2.5: Calculate the partial dictionary matrices of each pair of co-prime dual-channel ADC sampling combinations under the condition that the number of strong scattering points is the same but the positions are different. Calculate the corresponding mean of the restricted isometry constants.

[0084] First, calculate the eigenvalues to determine the range of the eigenvalues. Then, according to the range of the eigenvalues [1 - δ k , 1 + δ k , determine the restricted isometry constant δ corresponding to each partial dictionary matrix of each pair of co-prime dual-channel ADC sampling combinations. k Finally, calculate the mean of the restricted isometry constants corresponding to the partial dictionary matrices of each pair of co-prime dual-channel ADC sampling combinations under the condition that the number of strong scattering points is the same but the positions are different.

[0085] Step 3: Determine the optimal pair of co-prime dual-channel ADC sampling combinations.

[0086] The closer to 0, the better the RIP performance of the dictionary matrix. Select the pair of co-prime dual-channels corresponding to the one closest to 0 as the optimal pair of co-prime dual-channels.

[0087] Step 4: Use the reference signal to obtain the time-delay error between the two channels in the optimal pair of co-prime dual-channel ADC sampling combinations.

[0088] Use the optimal pair of co-prime dual-channel ADC sampling combinations to sample the reference signal. Taking the sampling time of the first channel as the reference, according to the position of the target in the range direction in the second channel, obtain the time-delay error between the optimal pair of co-prime dual-channels. If the error between the co-prime dual-channels in the optimal pair of co-prime dual-channel ADC sampling combinations is very small, much smaller than the error that the system needs to consider, this step can be omitted. As shown in Figure 2 , directly use the optimal pair of co-prime dual-channel ADC sampling combinations to downsample the inverse synthetic aperture radar echo. Correspondingly, there is no need to compensate for the time-delay error in the next acquisition process either.

[0089] Step 5: Use the optimal pair of co-prime dual-channel ADC sampling combinations to downsample the inverse synthetic aperture radar echo.

[0090] Use the first channel in the optimal pair of co-prime dual-channel ADC sampling combinations to downsample the inverse synthetic aperture radar echo to obtain the observation matrix U1 of the first channel and the downsampled radar echo data s of the first channel t1 ; Compensate the system error of the co-prime dual-channels into the system, and use the second channel after compensating the time-delay error to downsample the inverse synthetic aperture radar echo to obtain the observation matrix U2 of the second channel and the downsampled radar echo data s of the second channel​t2 。

[0091] Step 6. Obtain the reduced-dimension observation signal, observation matrix, and dictionary matrix of the entire scene for the optimal co-prime dual-channel ADC sampling combination.

[0092] (6a) Based on the downsampled radar echo data s t1 , s t2 , calculate the frequency-domain pulse compression data s f1 and s f2 corresponding to the co-prime dual-channel;

[0093] (6b) Arrange the s f1 and s f2 obtained in step (6a) in a matrix according to the sequence of sampling times in the entire scene. The row direction of the matrix represents the range direction, and the column direction represents the azimuth direction. Vectorize the matrix, s f12 = vect{S}, where vect{} means arranging the matrix into a vector by columns, to obtain the reduced-dimension observation signal vector s f12 of the co-prime dual-channel ADC sampling combination;

[0094] (6c) At the same time, arrange each row in the observation matrix U1 of the first channel and the observation matrix U2 of the second channel in the same matrix according to the sequence of sampling times, then the observation matrix U 12 of the optimal co-prime dual-channel ADC sampling combination can be obtained. If the two channels have the same sampling time, only keep the rows of the observation matrix corresponding to the first channel at that sampling time; according to the observation matrix U 12 and the Fourier basis matrix F, obtain the dictionary matrix F 12 = U 12 F of the range profile of each column of this co-prime dual-channel. According to the dictionary matrix F 12 of the range profile of each column, construct the dictionary matrix Ψ of the entire scene as shown in formula (1):

[0095]

[0096] Step 7. Establish a weighted range profile compressive sensing model and solve the optimization function.

[0097] (7a) Based on the dictionary matrix Ψ of the co-prime dual-channel ADC sampling combination of the entire scene and the reduced-dimension observation signal vector s f12 obtained in step 6, establish a weighted range profile compressive sensing model as shown in formula (2):

[0098] min(||WS||1), subject to ||s f12 - ΨS|| ≤ ξ (2)

[0099] Among them, W represents the diagonal weight matrix, and the diagonal elements of the diagonal weight matrix are represented as w i . ξ is the corresponding noise level. To restore the signal in the target area while suppressing the signal in the non-target area, a lower weight is applied to the support area corresponding to the target area, and a larger weight is applied to the non-target area.

[0100] (7b) According to the weighted range image compressive sensing model in (7a), an optimization function is established, as shown in formula (3):

[0101]

[0102] In the formula, is the estimated value of the range image vector for sparse reconstruction, μ is the l1 constraint coefficient, which depends on the statistical parameters of the noise and the target. To avoid the problem that S is not differentiable at 0, the following approximation is made: |S i |≈(|S i | 2 +τ) 1 / 2 , where τ is a small component, generally about 2 orders of magnitude smaller than the mean of the range image.

[0103] To solve the optimization function, formula (2) can be written in the following form:

[0104]

[0105] Derive the above formula:

[0106]

[0107] In the formula, U(S) = diag[1 / (|S1| 2 +τ) 1 / 2 , 1 / (|S2| 2 +τ) 1 / 2 , …, 1 / (|S i | 2 +τ) 1 / 2 .

[0108] Step 8. Calculate the coarse range image vector, estimate the noise variance and the Laplacian scale factor, and calculate the sparse constraint coefficient;

[0109] (8a) Perform an inverse Fourier transform on the dimensionality-reduced observation signal matrix of the co-prime dual-channel ADC sampling combination obtained in step 6 to obtain the coarse range image matrix, and vectorize the coarse range image matrix column by column to obtain the coarse range image vector S 0 .

[0110] (8b) Extract the noise units that obviously do not contain the target signal from the coarse range image vector S 0 , and after vectorization, use s IIt means that by using the noise sample s I the noise variance can be accurately estimated, as shown in Equation (6):

[0111] σ 2 = E{(s I ) H s I} (6)

[0112] (8c) Assume that the elements in S follow the same distribution and each point has the same Laplacian factor, as shown in Equation (7):

[0113] γ = NM / ||S 0 ||1 (7)

[0114] In the formula, (s I ) H denotes the conjugate transpose of s I ; N is the number of range samples per column under the condition of satisfying the Nyquist sampling theorem, and M is the number of azimuth samples.

[0115] (8d) According to the estimated noise variance σ 2 in (8b) and the Laplacian factor γ obtained in (8c), the sparse constraint coefficient μ = σ 2 γ is obtained.

[0116] Step 9. Calculate the initial diagonal weight matrix W 0 ;

[0117] According to the coarse range profile vector S 0 obtained in Step (8a), let the weight 0 of the i-th element in the initial diagonal weight matrix W be equal to the reciprocal of the i-th element 0 in S , then the weight coefficient can be set as:

[0118]

[0119] σ is expressed as a small constant. To prevent the phenomenon that false targets appear in non-target areas due to excessive weights, σ can be set as the mean value.

[0120] Step 10. Calculate the Hessian matrix and conjugate gradient function of the optimization function

[0121] (10a) According to the optimization function in Step 7, the coarse range profile vector S 0 obtained in Step (8), and the initial weighted coefficient W 0 , the initial Hessian matrix H(S 0 ) can be calculated:

[0122] H(S 0 ) = 2(Ψ) H Ψ + μU(S 0 )W 0 (8)

[0123] Wherein, 2 ≤ i ≤ NM;

[0124] (10b) According to the optimization function in step 7 and the initial Hessian matrix in step (10a), the initial conjugate gradient function of the optimization function can be obtained as follows:

[0125]

[0126] Step 11. Use the method of minimizing the weighted l1 norm to obtain the range image of sparse reconstruction;

[0127] To require the minimum value of the optimization function, when its conjugate gradient function of the optimization function is 0, it is the optimal solution, that is:

[0128] H(S 0 )S - 2(Ψ) H s f12 = 0 (10)

[0129] The estimated value of the range image vector after sparse reconstruction can be obtained

[0130]

[0131] Step 12. Determine whether the reconstructed range image vector meets the requirements?

[0132] (12a) According to the estimated value of the range image vector after sparse reconstruction to determine whether it meets the requirements:

[0133]

[0134] Among them, if the number of iterations is 0, then is S 0 , if the number of iterations is greater than 0, then is the estimated value of the range image vector of sparse reconstruction obtained in the previous iteration, ρ represents a preset threshold, and its value is a small threshold discrimination constant.

[0135] If the estimated value of the range image vector of sparse reconstruction meets the requirements, let the range image vector S of sparse reconstruction be equal to the estimated value of the range image vector of sparse reconstruction Arrange the range image vectors of sparse reconstruction in a matrix according to the corresponding echo order to obtain the high-resolution range image of sparse reconstruction, and calculate the two-dimensional ISAR image:

[0136] Arrange the estimated values of the reconstructed range image vectors in a matrix according to the corresponding echo order to obtain the high-resolution range image of sparse reconstruction;

[0137] Perform translational compensation on the high-resolution range image of sparse reconstruction, including envelope alignment and autofocus, and compensate for the envelope offset and phase error caused by translation respectively.

[0138] Perform azimuth compression on the result of translational compensation to obtain a high-resolution two-dimensional ISAR image.

[0139] If the estimated value of the range image vector of sparse reconstruction does not meet the requirements, perform iteration, return to step 10, update the Hessian matrix, and update the range image vector of the Hessian matrix in step 10 to the estimated value of the range image vector of sparse reconstruction obtained in step 11 until the estimated value of the range image vector of sparse reconstruction meets the requirements. At the same time, the diagonal weight matrix in the Hessian matrix can also be updated synchronously based on the following formula:

[0140]

[0141] where S i is the i-th element in the estimated value of the range image vector of sparse reconstruction in step 11 , w i is the diagonal element in the updated diagonal weight matrix, representing the weighted coefficient of the i-th element in the estimated value of the range image vector after sparse reconstruction . Of course, when the requirement for reconstruction accuracy is not high, the diagonal weight matrix can also not be updated, and the initial diagonal weight matrix can be directly used to calculate the Hessian matrix, as shown in Figure 3 .

[0142] The beneficial effects of this embodiment are verified through the following simulation experiments:

[0143] I. Determine the inverse synthetic aperture radar parameters, reference signal, and co-prime dual-channel ADC sampling combination;

[0144] In this embodiment, an inverse synthetic aperture radar with a carrier frequency f c of 10 GHz, a wavelength λ of 0.03 m, a bandwidth B of 800 MHz, a pulse width T p of 1 μs, and a pulse repetition frequency PRF of 300 is taken as an example. The Nyquist sampling rate F sIt is 1.2 times the signal bandwidth B, and the specific parameters are shown in Table 1; there are 5 groups of selectable co-prime dual-channel ADC sampling combinations, and the sampling rates of each group of co-prime dual-channel ADC sampling combinations are shown in Table 2; the bandwidth of the reference signal cannot exceed 0.85×F s / 9;

[0145] Table 1 Basic Parameters of Inverse Synthetic Aperture Radar

[0146]

[0147] Table 2 Co-prime Dual-channel Combinations

[0148]

[0149] Second, calculate the RIP performance of the dictionary matrix corresponding to each group of co-prime dual-channel ADC sampling combinations, and select the optimal co-prime dual-channel ADC sampling combination;

[0150] According to the pulse width T of the inverse synthetic aperture radar p , Nyquist sampling rate F s and the sampling rate of each group of co-prime dual-channel ADC sampling combinations, calculate the dictionary matrix F corresponding to each group of co-prime dual-channel ADC sampling combinations under each column range profile 12 0 ; Under each group of co-prime dual-channel ADC sampling combinations, the number k of strong scattering points traverses from 1 to 80, It refers to the matrix composed of the columns corresponding to the positions of k strong scattering points in each column range profile vector in F 12 0 . For each k, 1000 random trials are carried out, and the maximum eigenvalue and minimum eigenvalue of are statistically averaged, and the results are shown in Figure 4 . At the same time, calculate δ of each group of co-prime dual-channels k , and take the average value of δ k to obtain As shown in Figure 5 . The specific results are shown in Table 3.

[0151] Table 3 RIP Performance of Co-prime Dual-channel ADC Sampling Combinations

[0152]

[0153] Note:

[0154] The average value is the average value of corresponding to strong scattering points from 1 to 80;

[0155] δ k The closer to 0, the better the RIP performance of the dictionary matrix. Select the one closest to 0 The relatively prime dual-channel combination corresponding to the average value is used as the optimal relatively prime dual-channel combination. As can be seen from Table 3 and Figure 5 both, the average value of combination 2 is the smallest. It can be known that combination 2 is the optimal relatively prime dual-channel combination in the entire inverse synthetic aperture radar imaging scenario, and the sampling rate F of the first channel is obtained s / 5, and the sampling rate F of the second channel is s / 6; if the number of targets in the inverse synthetic aperture radar imaging scenario is determined, the corresponding to this number of targets should be used to select the relatively prime dual-channel ADC sampling combination.

[0156] III. Reconstruct the high-resolution range profile based on the weighted compressive sensing model;

[0157] (3a) Use the optimal relatively prime dual-channel ADC sampling combination to sample the reference signal and calculate the time delay error between channels. The results are shown in Figures 6(a) and 6(b). The range profile positions of the target under different sampling channels can be obtained. In the first channel, the relative position of the range profile corresponding to the target is 0 m, and in the second channel, the relative position of the range profile corresponding to the target is 1.875 m. Then, according to the relative position difference of 1.875 m of the target in the range profile between the two channels, the time error between the two channels can be obtained as 1.25e-8 s.

[0158] (3b) After compensating for the channel error, use the relatively prime dual-channel ADC sampling combination to downsample the inverse synthetic aperture radar echo. According to the sampling results, the downsampled observation signal vector s f12 under the optimal relatively prime dual-channel ADC sampling combination is obtained, the dictionary matrix F 12 of each column of the range profile, and the dictionary matrix Ψ of the entire scenario. Calculate the reconstructed range profile vector:

[0159]

[0160] IV. Simulation results and analysis;

[0161] According to the range profile vector reconstructed by formula (12), arrange this range profile vector into a matrix according to the corresponding echo order to obtain the high-resolution range profile; perform translational compensation on the high-resolution range profile, including envelope alignment and autofocus, and compensate for the envelope offset and phase error caused by translation respectively; perform azimuth compression on the compensated result to obtain the high-resolution two-dimensional ISAR image. The specific results are as Figures 7(a) to 7(k) shown. Figure 7(a) and 7(b) are the ideal one-dimensional range profiles obtained under the Nyquist sampling condition. Using the results of imaging with the ideal one-dimensional range profile, it can be seen that there are 13 target points; Figure 7(c) and 7(d) are for the sampling rate of Fs / 5 (the first channel of combination 2), the one-dimensional range profile obtained under the undersampling condition, and the result of two-dimensional imaging using this one-dimensional range profile; Figure 7(e) and 7(f) is the sampling rate of F s / 6 (the second channel of combination 2), the one-dimensional range profile obtained under the undersampling condition, and the result of two-dimensional imaging using this one-dimensional range profile; Figure 7(g) and 7(h) is co-prime dual-channel sampling, and the sampling rates are F s / 5 and F s / 6 (combination 2), the one-dimensional range profile obtained under the undersampling condition, and the result of two-dimensional imaging using this range profile; Fig. 7(i) is the high-resolution range profile obtained by reconstructing the range profile according to formula (12), and one column of the reconstructed high-resolution range profile is taken out; Figs. 7(j) and (k) are the result images of two-dimensional imaging of the reconstructed range profile obtained based on formula (12). It can be seen from Figures 7(a) to 7(k) that by using the proposed inverse synthetic aperture radar imaging method based on co-prime dual-channel ADC downsampling, the high-resolution one-dimensional range profile of the target can be accurately reconstructed, and further the high-resolution inverse synthetic aperture radar two-dimensional image of the target can be obtained.

[0162] In the case of noise, according to the data sampled by the optimal co-prime dual-channel ADC, the high-resolution range profile is reconstructed using formula (12), and ISAR two-dimensional imaging is performed based on this high-resolution range profile. The method used in the present invention is compared with the fixed weight algorithm (the initial diagonal weight matrix constructed using the coarse range profile), and the results Figures 8(a) to 8(j) are shown as follows.

[0163] From the restored image Figures 8(a) to 8(i) when there is noise, it can be seen that the fixed weight method estimates the target position in the one-dimensional range profile relatively accurately, but compared with the adaptive weighting method, the amplitude difference from the ideal sampling is relatively large. In contrast, the inverse synthetic aperture radar imaging method based on compressive sensing co-prime dual-channel ADC sampling proposed in the present invention can not only reduce the sampling rate, but also can better ensure the accuracy of the target amplitude and position of the one-dimensional range profile under downsampling, and at the same time has good noise suppression ability, and further a high-resolution ISAR two-dimensional image can be obtained.

Claims

1. An inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling, characterized in that, Including the following steps: Step 1: Downsample the inverse synthetic aperture radar echo using a co-prime dual-channel ADC sampling combination; Step 2: Reconstruct based on the downsampled data to obtain the sparse reconstructed range image vector S, and then obtain the two-dimensional ISAR image; Step 2.1: Establish a weighted range image compressive sensing model and an optimization function: The weighted range image compressive sensing model is: min(||WS||1), subject to ||s f12 -ΨS|| ≤ ξ; where W represents a diagonal weight matrix; ξ is the noise level; s f12 is the reduced-dimensional observation signal vector of the co-prime dual-channel ADC sampling combination; Ψ is the dictionary matrix of the co-prime dual-channel ADC sampling combination under the entire scenario; The optimization function is: Among them, is the estimated value of the range image vector for sparse reconstruction, and μ is the sparse constraint coefficient; Step 2.2: Solve the Hessian matrix and conjugate gradient function of the optimization function, and obtain the sparse reconstructed range image vector S based on the weighted l1-norm minimization method; Step 2.21, solve the initial Hessian matrix H(S 0 ): H(S 0 ) = 2(Ψ) H Ψ + μU(S 0 )W 0 Among them, W 0 is the initial diagonal weight matrix, 2 ≤ i ≤ NM, where N is the number of points of the range profile per column under Nyquist sampling, and M is the number of points in the azimuth direction; S 0 is the coarse range profile vector, which is obtained by performing an inverse Fourier transform on the reduced-dimensional observation signal matrix of the co-prime dual-channel ADC sampling combination to obtain the coarse range profile matrix, and then vectorizing the coarse range profile matrix column by column; are the first, second, up to the i-th elements in S 0 respectively; τ is a positive number; (Ψ) H is the conjugate transpose of Ψ; Step 2.

22. Based on the initial Hessian matrix H(S 0 ), obtain the initial conjugate gradient function ▽J(S 0 ) of the optimization function; ▽J(S 0 ) = -2(Ψ) H s f12 +H(S 0 )S; Step 2.23: Based on the initial conjugate gradient function, when the conjugate gradient function is 0, obtain the estimated value of the range image vector for sparse reconstruction Step 2.24: Based on the judgment criterion, judge whether the estimated value of the range image vector of sparse reconstruction meets the requirements. If so, let the range image vector S of sparse reconstruction be equal to the estimated value of the range image vector of sparse reconstruction Arrange the range image vectors of sparse reconstruction into a matrix according to the corresponding echo order to obtain the high-resolution range image of sparse reconstruction, and calculate the 2D ISAR image. Otherwise, perform iteration, return to Step 2.21, and update the range image vector of the Hessian matrix in Step 2.21 to the estimated value of the range image vector of sparse reconstruction obtained in Step 2.23 until the estimated value of the range image vector of sparse reconstruction meets the requirements.

2. The inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling according to claim 1, wherein In Step 2.1, the reduced-dimension observation signal vector s of the co-prime dual-channel ADC sampling combination f12 , and the dictionary matrix Ψ of the co-prime dual-channel ADC sampling combination under the entire scenario is determined through the following process: According to the downsampled radar echo data \(s\) of the first channel in the co-prime dual-channel ADC sampling combination t1 , calculate the frequency-domain pulse compression data \(s\) of the first channel f1 ; according to the downsampled radar echo data \(s\) of the second channel in the co-prime dual-channel ADC sampling combination t2 , calculate the frequency-domain pulse compression data \(s\) of the second channel f2 ; arrange \(s\) f1 and \(s\) f2 in a matrix according to the order of sampling time. The row direction of the matrix represents the range direction, and the column direction of the matrix represents the azimuth direction. Quantize the matrix column-wise to obtain the dimensionality-reduced observation signal vector \(s\) of the co-prime dual-channel ADC sampling combination f12 ;​​ The dictionary matrix Ψ of the co-prime dual-channel ADC sampling combination under the entire scene: Among them, F 12 is the dictionary matrix of the distance images for each column, and F 12 = U 12 F, where U 12 is the observation matrix of the co-prime dual-channel ADC sampling combination, which is obtained by arranging each row of the observation matrix U1 of the first channel and the observation matrix U2 of the second channel in the co-prime dual-channel ADC sampling combination in a matrix according to the sequence of sampling times; F is the Fourier basis matrix.

3. The inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling according to claim 2, wherein In step 2.21, the initial diagonal weight matrix W is calculated by the following formula 0 ; Among them, is the initial diagonal weight matrix W 0 The diagonal elements in it represent the weighted weight coefficient of the i-th element in the coarse range image vector S 0 in σ is a constant to prevent the phenomenon that false targets appear in non-target areas due to excessive weight values, and it is a positive number; In Step 2.24, when returning to Step 2.21, synchronously update the diagonal weight matrix in the Hessian matrix of Step 2.21 based on the following formula: Among them, S i is the estimated value of the range image vector for sparse reconstruction in step 2.23 of the i-th element, and w i is the diagonal element in the updated diagonal weight matrix, representing the weighted weight coefficient of the i-th element in the estimated value of the range image vector after sparse reconstruction .

4. The inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling according to claim 3, wherein In step 2.1, by estimating the noise variance σ 2 and the Laplacian scale factor γ, calculate the sparse constraint coefficient μ: μ = σ 2 γ; where: σ 2 = E{(s I ) H s I}; γ = NM / ||S 0 ||1; where, s I is the noise sample, obtained by taking the noise cells that do not contain the target signal from the coarse range profile vector and vectorizing them; (s I ) H denotes the conjugate transpose of s I .

5. The inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling according to claim 4, wherein In Step 2.24, the judgment criterion is: wherein, if the number of iterations is 0, then is S 0 , if the number of iterations is greater than 0, then is the estimated value of the range image vector of the sparse reconstruction obtained in the previous iteration, and ρ represents a preset threshold; In Step 2.24, arrange the sparse reconstructed range image vectors in a matrix according to the corresponding echo order to obtain the sparse reconstructed high-resolution range image, and calculate the two-dimensional ISAR image. Specifically: Arrange the sparse reconstructed range image vector S in a matrix according to the corresponding echo order to obtain the sparse reconstructed high-resolution range image; perform translational compensation on the sparse reconstructed high-resolution range image, and perform azimuth compression on the result of the translational compensation to obtain the two-dimensional ISAR image.

6. The inverse synthetic aperture radar imaging method based on co - prime dual - channel downsampling according to any one of claims 1 to 5, characterized in that: In Step 1, obtain the optimal co-prime dual-channel ADC sampling combination through screening, and use the optimal co-prime dual-channel ADC sampling combination to downsample the inverse synthetic aperture radar echo.

7. The inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling according to claim 6, wherein: In Step 1, use the optimal co-prime dual-channel ADC sampling combination after delay error compensation to downsample the inverse synthetic aperture radar echo; Specifically, determine the optimal co-prime dual-channel time delay error through the following process: Use the optimal co-prime dual-channel ADC sampling combination to sample the reference signal. Taking the sampling time of the first channel as the reference, obtain the time delay error between the optimal co-prime dual-channels according to the position of the target in the range direction in the second channel; the bandwidth of the reference signal needs to satisfy: ensure that any sampling rate in the optimal co-prime dual-channel ADC sampling combination satisfies the Nyquist sampling rate of the reference signal.

8. The inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling according to claim 7, wherein In Step 1, the specific process of obtaining the optimal co-prime dual-channel ADC sampling combination through screening is as follows: Step 1.

1. Determine the dictionary matrix F of the range profiles of each column for each pair of relatively prime dual-channel ADC sampling combinations in the current application scenario 12 0 ; F 12 0 = U 12 0 F; where U 12 0 is the observation matrix of each group of relatively prime dual-channel ADC sampling combinations; Step 1.2, Based on the column range image dictionary matrix F of each group of mutually prime dual-channel ADC sampling combinations 12 0 , determine the partial dictionary matrix of the column range image of each group of mutually prime dual-channel ADC sampling combinations related to the number and position of strong scatterers in the scene refers to the matrix formed by the positions of k strong scatterers corresponding to the columns of the column range image vector in F 12 0 columns; Step 1.3: Calculate the mean of the restricted isometry constants corresponding to the partial dictionary matrices of the range profiles of each column of the co-prime dual-channel ADC sampling combinations under the condition that the number of strong scattering points is the same but the positions are different. The corresponding mean of the restricted isometry constants; Step 1.

4. Compare the partial dictionary matrices corresponding to the range profiles of each column of each pair of co-prime dual-channel ADC sampling combinations under the condition that the number of strong scattering points is the same but the positions are different corresponding to the mean of the restricted isometry constants, and select the minimum mean of the restricted isometry constants; Step 1.5: Judge whether the mean of the minimum restricted isometry constant satisfies the RIP criterion. If it meets the requirements, use the co-prime dual-channel ADC sampling combination corresponding to the mean of the minimum restricted isometry constant as the optimal co-prime dual-channel ADC sampling combination corresponding to the number of strong scatterers; if it does not meet the requirements, it is necessary to return and modify the co-prime dual-channel ADC sampling combination, and repeat the process from Step 1.1 to Step 1.4 until the requirements are met.

9. The inverse synthetic aperture radar imaging method based on co-prime dual-channel decimation according to claim 8, wherein In Step 1.1, the observation matrix U of each pair of relatively prime dual-channel ADC sampling combinations is determined through the following process 12 0 : Calculate the observation matrix of each channel in each group of relatively prime dual-channel ADC sampling combinations, and arrange each row of the observation matrices of the two channels in the same matrix according to the sampling order and sampling position to obtain the observation matrix U composed of each group of relatively prime dual-channel ADC sampling combinations 12 0 。 10. The inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling according to claim 9, wherein: If the two channels in the co-prime dual-channel combination have the same sampling time, when arranging each row of the observation matrices of the two channels in the same matrix according to the sampling order and sampling position, only retain the rows of the observation matrix corresponding to any one of the channels at this sampling time.

11. The inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling according to claim 10, wherein In Step 1.1, determine the observation matrix of each channel in each co-prime dual-channel ADC sampling combination through the following process: First, calculate the observation matrix U corresponding to each column of echoes under the Nyquist sampling theorem and the Fourier basis matrix F corresponding to the scene based on the number of sampling points N at the Nyquist sampling rate. After that, according to the sampling time of each channel in each pair of co-prime dual-channel ADC sampling combinations, retain the corresponding rows in the observation matrix U corresponding to the sampling time, and obtain the observation matrix of each channel in each pair of co-prime dual-channel ADC sampling combinations.

12. The inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling according to claim 11, wherein: Step 1.2 specifically includes the following steps: Step 1.21: Determine the number and positions of strong scatterers in the scene; according to the scene requirements, determine the maximum number of strong scatterers K included in the scene; among the K strong scatterers, select k strong scatterers as the strong scatterer group, where k traverses from 1 to K, and K is an integer greater than 1; for each strong scatterer group, randomly select its position in the scene; for each strong scatterer group, determine P random positions, where P is an integer greater than 1. Step 1.22: Obtain a partial dictionary matrix of each set of mutually prime dual-channel ADC sampling combinations according to the number and positions of strong scattering points in the scene; according to the number k of strong scattering points included in each set of strong scattering point groups determined in Step 1.21 and the positions of each strong scattering point in the scene, extract each column range image dictionary matrix F of each set of mutually prime dual-channel ADC sampling combinations 12 0 in the corresponding region, and obtain multiple partial dictionary matrices of each column range image corresponding to each set of mutually prime dual-channel ADC sampling combinations Step 1.3 specifically includes the following steps: Step 1.

31. Calculate the eigenvalues and determine the range of the eigenvalues; Step 1.

32. Determine the restricted isometry constant δ corresponding to each part of the dictionary matrix of each group of relatively prime dual-channel ADC sampling combinations according to the range of the eigenvalue [1 - δ k , 1 + δ k , k ; Step 1.33: Calculate the mean of the restricted isometry constants corresponding to the partial dictionary matrices of each pair of co-prime dual-channel ADC sampling combinations under the condition that the number of strong scatterers is the same but the positions are different.

13. An inverse synthetic aperture radar imaging system based on co-prime dual-channel downsampling, comprising a memory and a processor, characterized in that: The memory stores a computer program, and when the computer program is executed by a processor, the steps of the inverse synthetic aperture radar imaging method based on co-prime dual-channel downsampling according to any one of claims 1-12 are implemented.

Images