A micro-Doppler suppression method for millimeter-wave ISAR vehicle target imaging

Abstract

The present invention provides a micro-Doppler suppression method for millimeter-wave ISAR vehicle target imaging. The method constructs an optimization problem for micro-Doppler suppression by acquiring raw echo data. Based on the original RPCA model, a more generalized Schatten‑p norm is used to perform a non-convex approximation on the rank function. At the same time, a graph Laplace regularization term based on a custom graph adjacency weight matrix is ​​introduced into the optimization function to better distinguish the local features of the target and micro-motion range images between different pulses. While retaining the target's main scattering points as complete as possible, the micro-Doppler effect can be better suppressed to obtain a more ideal ISAR image.

Description

Technical Field

[0001] The present invention belongs to the technical fields of radar signal processing and ISAR imaging, and in particular relates to a millimeter-wave ISAR vehicle target imaging micro-Doppler suppression method. Background Art

[0002] Industrial-grade millimeter-wave radar equipment is low-cost, compact, and unaffected by weather and nighttime conditions. Its all-weather capabilities make it suitable for widespread use in transportation and public security. For example, millimeter-wave radars can be deployed along single- and double-lane roads to monitor and identify passing vehicles; they can also be deployed at the entrances of parking lots or underground garages to monitor and identify vehicles entering and exiting. However, during ISAR vehicle target imaging, the micro-Doppler effect generated by the rapid rotation of the wheels can disrupt the image of the vehicle's main body, reducing the quality of the final image and impacting subsequent applications based on ISAR images. Therefore, research on high-performance micro-Doppler suppression methods for millimeter-wave ISAR vehicle target imaging is of great significance.

[0003] Existing methods all perform a one-dimensional Fourier transform on the original time domain data collected by the radar in the range dimension to obtain the one-dimensional range image of the target, and use certain features of the target's one-dimensional range image to build a model to suppress micro-Doppler in ISAR imaging. Many existing model construction methods are improved based on robust principal component analysis (RPCA). The basic idea is to use the low-rank characteristics of the one-dimensional range image of the target's main scattering points and the sparse characteristics of the one-dimensional range image of the rapidly rotating scattering points, take the one-dimensional range image sequence as input, and use the idea of ​​matrix decomposition to decompose it into the one-dimensional range images of the target's main scattering points and the rapidly rotating scattering points.

[0004] Zhou et al. proposed a new ISAR imaging method for rotating targets based on RPCA in the paper “W. Zhou, C. Yeh, R. Jin, Z. Li, S. Song, J. Yang. ISAR imaging of targets with rotating parts based on robust principal component analysis, IET Radar Sonar Navigation, vol. 11, no. 4, pp. 563–569, Apr. 2017”, which mainly utilizes the low-rank characteristics of the target body scattering point echoes and the sparse characteristics of the rotation component within certain range units. Cheng et al. proposed a new method in the document "D. Cheng, S. Pei, H. Qu, C. Chen, W. Chen. Removing Micro-Doppler Effect in ISAR Imaging by Promoting JointSparsity in Range Profile Sequences and the Time-Frequency Domain, IEEE Sensors Journal, vol. 21, no. 21, pp. 24613-24630, 1Nov. 1, 2021" that utilizes the joint sparsity of the subject in the range unit sequence and time-frequency domain. By iteratively solving the convex optimization model of dual joint sparsity regularization, useful subject target signals are extracted from the original image to eliminate micro-Doppler interference. Zhang et al. proposed an improved RPCA model in "S. Zhang, Y. Liu, X. Li, D. Hu, Removal of Micro-Doppler Effect of ISAR Image Based on Laplacian Regularized Nonconvex Low-Rank Representation, IEEE Transactions on Image Processing, vol. 30, pp. 6446-6458, 2021" that uses matrix singular value functions and replaces nuclear norms to approximate the rank function, which also effectively suppresses the micro-Doppler effect.

[0005] Some of the above methods improved on RPCA still use the nuclear norm convex approximation to approximate the rank function, or use the nuclear norm definition to non-convexly approximate the rank function. However, if the matrix singular values ​​are large, according to the definition of the nuclear norm and the rank function, the nuclear norm convex approximation is too relaxed, resulting in an unsatisfactory approximation effect, which makes it unable to retain as much information about the target body scattering points as possible. In simulation and measured data, this is manifested in: in addition to suppressing micro-Doppler, it also suppresses too many signal components of the target body scattering points, resulting in poor imaging effects. As for the method of adding time-frequency domain joint sparse regularization to the model, if the simulation data is not ideal, the measured data has large errors, or the experimental observation time is short, the time-frequency spectrum described in the article may not have a very obvious joint sparsity, which may have a certain impact on the imaging results. Summary of the Invention

[0006] In order to solve the above problems existing in the prior art, the present invention provides a method for suppressing micro-Doppler in millimeter-wave ISAR vehicle target imaging. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0007] The present invention provides a millimeter wave ISAR vehicle target imaging micro-Doppler suppression method comprising:

[0008] Step 1: Collect raw echo data from the millimeter-wave radar device when the radar wave illuminates the vehicle target;

[0009] The original echo data includes echo signals received by multiple receiving antennas, and the multiple receiving antennas are arranged at equal intervals;

[0010] Step 2: The original echo data is sequentially subjected to beamforming, data rearrangement, Fourier transform, and static clutter suppression to obtain a data matrix after static clutter filtering;

[0011] Step 3: constructing an optimization problem for suppressing micro-Doppler based on the data matrix after static clutter filtering, the range image sequence of the target body scattering point to be solved, and the range image sequence of the rapidly rotating scattering point;

[0012] Step 4: introduce the Schatten-p norm and the graph Laplace regularization term, and use the alternating direction multiplier method to solve the optimization problem of suppressing micro-Doppler, and obtain the range image sequence of the target body scattering point.

[0013] Beneficial effects of the present invention:

[0014] The present invention provides a micro-Doppler suppression method for millimeter-wave ISAR vehicle target imaging. The method constructs an optimization problem for suppressing micro-Doppler by acquiring raw echo data. Based on the original RPCA model, a more generalized Schatten-p norm is used to perform a non-convex approximation on the rank function. At the same time, a graph Laplace regularization term based on a custom graph adjacency weight matrix is ​​introduced into the optimization function to better distinguish the local features of the subject and micro-motion range image between different pulses. While retaining the target subject scattering points as complete as possible, the micro-Doppler effect can be better suppressed to obtain a more ideal ISAR image.

[0015] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart of a method for suppressing micro-Doppler in millimeter-wave ISAR vehicle target imaging provided by the present invention;

[0017] Figure 2 is the target scatter plot provided by the present invention;

[0018] Figure 3 It is a graph of a total one-dimensional range image sequence provided by the present invention;

[0019] Figure 4 This is the curve of the pulse change in the distance unit of the RPCA method

[0020] Figure 5 It is a curve diagram of the pulse variation in the distance unit of the algorithm of the present invention;

[0021] Figure 6 is an ISAR image that has not been processed by the algorithm of the present invention;

[0022] Figure 7 is the ISAR image processed by the algorithm of the present invention;

[0023] Figure 8 is a graph showing the average mD suppression rate changing with SNR;

[0024] Figure 9 is a graph showing the average subject target recovery rate versus SNR;

[0025] Figure 10 is a graph showing the average image contrast changing with SNR;

[0026] Figure 11 It is a curve of average image entropy changing with SNR. DETAILED DESCRIPTION

[0027] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0028] like Figure 1 As shown, the present invention provides a millimeter wave ISAR vehicle target imaging micro-Doppler suppression method comprising:

[0029] Step 1: Collect raw echo data from the millimeter-wave radar device when the radar wave illuminates the vehicle target;

[0030] The original echo data includes echo signals received by multiple receiving antennas, and the multiple receiving antennas are arranged at equal intervals;

[0031] The present invention can use an industrial-grade millimeter-wave radar placed beside the road to perform oblique detection on target vehicles. The radar transmits a linear frequency-modulated continuous wave and uses a one-transmit-multiple-receive working system to transmit and receive signals.

[0032] Step 2: The original echo data is sequentially subjected to beamforming, data rearrangement, Fourier transform, and static clutter suppression to obtain a data matrix after static clutter filtering;

[0033] In a specific embodiment, step 2 includes:

[0034] Step 21: beamforming the echo signals received by all receiving antennas to weightedly combine the echo signals of all receiving antennas to obtain a combined received signal;

[0035] Multiple receiving antennas can be used to obtain multi-path received signals. The echo signals of a single or multiple receiving antennas can be selected for beamforming. Assuming that an equidistant linear array of r receiving antennas is used to receive signals, the received data of the r antennas are first weighted and combined through beamforming. The combined received signal is:

[0036] y(t)=w H x(t)

[0037] where w=[w1,w2,…,w r ] T represents the array weight vector of the equidistant linear array, x(t) is the r×1 array data vector, x(t)=[x1(t),x2(t),…,x r (t)] T , [·] T Indicates the matrix transpose, x in the data vector r(t) represents the complex-sampled echo data from the rth receiving element, consisting of one row and (Nr × Na) columns of complex data, where Nr represents the number of range sampling points per pulse, and Na represents the number of pulses selected for imaging. The output signal after beamforming weighting has a significantly improved signal-to-noise ratio compared to the echo signal from a single receiving antenna.

[0038] Step 22, rearrange the combined received signal from one row (Nr×Na) of complex data to Nr rows and Na columns of complex data, to obtain a rearranged data matrix;

[0039] Among them, the dimension along the Nr direction is the distance dimension, and the dimension along the Na direction is the orientation dimension;

[0040] After step 22, a two-dimensional data matrix of Nr×Na is obtained, where the distance dimension is along the Nr direction and the orientation dimension is along the Na direction.

[0041] Step 23, performing a one-dimensional Fourier transform on the data matrix along the distance dimension to obtain a data matrix in the frequency domain;

[0042] The data matrix after rearrangement is subjected to a one-dimensional Fourier transform along the range dimension. Each pulse in 1, 2, …Na has an Nr×1 column vector, which is called a one-dimensional range image. The range image reflects the distribution of target scattering points in different range units. The peak value in a certain range unit in the range image indicates that there are one or more target scattering points in the current range unit.

[0043] Step 24 : using a two-pulse clutter cancellation method to suppress static clutter in the frequency domain data matrix, and obtaining a data matrix after static clutter is filtered out.

[0044] Clutter suppression filters are used to suppress static ground clutter, improving the radar signal's signal-to-clutter ratio and facilitating moving target detection. Static clutter is typically concentrated near zero frequency, so two-pulse cancellation can effectively suppress it. After static clutter removal, the data matrix is ​​X, of size Nr × Na. X contains all information about the target's main scattering points and rapidly rotating scattering points.

[0045] Step 3: constructing an optimization problem for suppressing micro-Doppler based on the data matrix after static clutter filtering, the range image sequence of the target body scattering point to be solved, and the range image sequence of the rapidly rotating scattering point;

[0046] The matrix X obtained in step 2 is decomposed using the following method model. X is the input matrix, T is the range image sequence of the target body scattering point, and R is the range image sequence of the rapidly rotating scattering point. The model for suppressing micro-Doppler is constructed as follows:

[0047]

[0048] stT=Z

[0049] X=T+R

[0050] Where X is the data matrix after static clutter is filtered out, T is the range image sequence of the target scattering point to be solved, R is the range image sequence of the rapidly rotating scattering point, and Z and T have the same meaning. The purpose is to separately solve the Schatten-p norm and the graph Laplace regularization term in the subsequent optimization problem. Represents the Schatten-p norm, which is specifically defined as: Let Is a low-rank matrix and rank(A)=r<<min(m,n), there is

[0051]

[0052] σ i (A) represents the i-th largest singular value of matrix A.

[0053] In addition, L=DW in the model represents the graph Laplacian matrix. Each column of data in the matrix, that is, the one-dimensional distance image of each pulse, is regarded as a node of the graph. W is represented as the graph adjacency matrix, which is used to represent the weight relationship between different pulse distance images. D represents the degree matrix. diag(·) represents the diagonalization operation. Considering the similarity between different pulse range images, W is defined as:

[0054] W ij =e -|i-j|

[0055] When i=j, there is W ij =1.

[0056] The above optimization problem can be solved using the Alternating Direction Method of Multipliers (ADMM).

[0057] Step 4: Use the alternating direction multiplier method to solve the optimization problem of suppressing micro-Doppler, and obtain a range image sequence of the target body scattering points.

[0058] In a specific embodiment, the solution process, i.e., step 4, includes:

[0059] Step 41: Let k = k + 1, and use the alternating direction multiplier method in the k + 1 outer loop to iteratively solve the optimization problem of suppressing micro-Doppler. In the t-th inner loop iteration process of the k + 1 outer loop, the norm problem of the optimization problem is solved to update the range image sequence of the target body scattering point to T. t+1 ,

[0060] Step 42, determining whether the inner loop termination condition is met after the t-th iteration is completed. If the inner loop termination condition is not met, set t=t+1 and return to step 41;

[0061] Step 43: If the inner loop termination condition is reached after the tth iteration, the updated T is output. t+1 ;

[0062] Among them, the inner loop termination condition is (t <t max )or ε=10 -4 ;

[0063] Step 44, in the k+1th outer loop iteration process, the range image sequence of the rapidly rotating scattering point is updated to R k+1 and Z k+1 ;

[0064] Step 45, determining whether the outer loop termination condition is met after the k+1th outer loop iteration is completed, if not, setting k=k+2 and returning to step 41;

[0065] Step 46: If the inner loop termination condition is reached after the k+1th iteration, the updated T is output. k+1 ;

[0066] Among them, the outer loop termination condition is (k <k max )or ε=10 -4 .

[0067] Refer to the algorithm in Table 1, which shows the algorithm process of the Sp-LRSGL-ADMM algorithm of the present invention for solving the optimization problem.

[0068] Table 1 Sp-LRSGL-ADMM algorithm

[0069]

[0070]

[0071] The above optimization problem is initially solved using the alternating direction multiplier method, and its augmented Lagrangian function is

[0072]

[0073] where ||·|| F represents the Frobenius norm, Y1 and Y2 represent Lagrange multipliers, μ1 and μ2 represent penalty coefficients, and the alternating direction multiplication method updates each variable alternately at each alternation. The updated variable in the k+1th iteration is:

[0074]

[0075] Update variable T in the k+1th outer loop k+1 for

[0076]

[0077] Among them, let the Schatten-p norm The Schatten-p norm problem is solved by using the factor group-sparse regularizer (FGSR) instead of the rank function proposed in the paper "Jicong Fan, Lijun Ding, Yudong Chen, and Madeleine Udell. Factor group-sparse regularization for efficient low-rank matrix recovery. Proceedings of the 33rd International Conference on Neural Information Processing Systems. Curran Associates Inc., Red Hook, NY, USA, Article 459, 5104–5114.2019."

[0078]

[0079]

[0080] in, rank(T)=r≤d≤min(Nr,Na),α>0, let the singular value decomposition (SVD) of T be Then the A and B matrices are

[0081] So update the variable T k+1 This is equivalent to solving the optimization subproblem:

[0082]

[0083] stT=AB

[0084] The above optimization subproblem is solved using the ADMM method, and its augmented Lagrangian function is

[0085]

[0086] Where Y3 represents the Lagrange multiplier. At the t+1th iteration, the variables A, B, T, and Y3 are updated alternately. A is updated first. t+1 ,have

[0087]

[0088] Formula A t+1 In A t The first-order Taylor expansion or linearization is

[0089]

[0090] Where,

[0091] Formula A t+1 The closed form solution is

[0092]

[0093] Among them, Φ τ (·) is the column vector soft threshold operator

[0094]

[0095] Then update B t+1 ,as follows

[0096]

[0097] Next, update T t+1 :

[0098]

[0099] Last updated Y 3(t+1) :

[0100] Y 3(t+1) =Y 3(t) +μ3(T t+1 -A t+1 B t+1 )

[0101] After the iterative inner loop ends, T can be obtained k+1 =A t+1 B t+1 ;

[0102] In step 44, update the variable R k+1 for

[0103]

[0104] The solution is

[0105]

[0106] in

[0107] Update variable Z k+1 for

[0108]

[0109] Finally update the variable Y 1(k+1) ,Y 2(k+1) for

[0110] Y 1(k+1) =Y 1(k) +μ1(Z k+1 -T k+1 )

[0111] Y 2(k+1) =Y 2(k) +μ2(XT k+1 -R k+1 )

[0112] When the outer loop cutoff condition is reached for k+1 times, output T k+1 .

[0113] The effects of the present invention can be further illustrated by the following simulation experiments.

[0114] The present invention is simulated on an Intel(R) Core(TM) i7-10700 CPU@2.90GHz 2.90GHz, 64-bit operating system using MATLAB R2021b developed by technicians.

[0115] The methods compared in the experiment are as follows:

[0116] The robust principal component analysis method is denoted as RPCA in the experiment. The reference is W. Zhou, C. Yeh, R. Jin, Z. Li, S. Song, J. Yang. ISAR imaging of targets with rotating parts based on robust principal component analysis, IET Radar Sonar Navigation, vol. 11, no. 4, pp. 563–569, April 2017.

[0117] Experiment 1:

[0118] Select 5 target body scattering points with coordinates (x p ,y p), respectively (0m, 0m), (2m, 7m), (5m, -1m), (0m, -8m), (-5m, -5m), and the coordinates of the three rotating scattering points are (4m, 0m), (0m, 7m), (-3m, -5m), the rotation radius is 1m, 2m and 1m respectively, the rotation angular velocity is 20πrad / s, 60πrad / s and 50πrad / s respectively, the real position of the target scattering point is as follows Figure 2 As shown in the figure, the radar transmits a linear frequency modulation signal with a carrier frequency of 15 GHz, a signal bandwidth of 400 MHz, a pulse number of 256, a sampling point number of 1024 in each pulse, and a signal-to-noise ratio of 20 dB.

[0119] According to the specific embodiment of the present invention, in order to facilitate the comparison of algorithm performance, four indicators are used: micro-Doppler suppression rate (hereinafter referred to as mD suppression rate), subject target recovery rate, maximum contrast of the reconstructed image, and image entropy. The mD suppression rate and subject target recovery rate are specifically defined as:

[0120]

[0121]

[0122] in Indicates the energy at some coordinates containing micro-Doppler effect in the original ISAR image. It represents the residual energy of micro-Doppler at the corresponding position in the ISAR image after the proposed algorithm suppresses micro-Doppler. Represents the energy of the original one-dimensional range image sequence of the target body scattering points without the rotation scattering points, Represents the energy of the one-dimensional range image sequence of the target subject's scattering points after reconstructing the image. Image contrast and image entropy are defined as:

[0123]

[0124] Where Avg{·} represents the averaging operator, and E(m,n) represents the amplitude of the (m,n)th pixel in the image matrix.

[0125]

[0126] in

[0127] The results are shown in Table 2.

[0128] Table 2 Algorithm performance analysis (SNR 20dB)

[0129] mD inhibition rate Subject recovery rate Image contrast Image entropy RPCA 0.647 0.868 2.776 2.450 The present invention 0.806 0.935 10.136 1.950

[0130] As can be seen from Table 2, compared with RPCA, the present invention has the characteristics of high mD suppression rate, high main body recovery rate, large image contrast and smaller image entropy, which verifies the effectiveness of the present invention. Figures 3 to 7 In order to more intuitively illustrate the advantages of the present invention in terms of subject recovery rate.

[0131] Figure 3 represents the total one-dimensional range image sequence of the target body and the rapidly rotating scattering points, where Figure 4 Represents the one-dimensional range image sequence of the target's rapidly rotating scattering points restored using RPCA, Figure 5 The algorithm of the present invention is used. Figure 4 The straight line part in the RPCA method indicates that the RPCA method will suppress more main components and suppress some useful signals as clutter. Figure 5 This indicates that the present invention suppresses the micro-Doppler without suppressing the main component, thus ensuring the integrity of the main signal. Figure 6 It indicates that the ISAR image that has not been processed by the algorithm of the present invention contains the micro-Doppler effect caused by rapidly rotating scattering points, which needs to be suppressed. Figure 7 It shows that after the ISAR image is processed by the algorithm of the present invention, the micro-Doppler effect caused by the rapidly rotating scattering points has been well suppressed.

[0132] Experiment 2:

[0133] On the basis of Experiment 1, the same simulation parameters were selected and Monte Carlo experiments were used to compare the performance of the algorithm of the present invention under different signal-to-noise ratio conditions. The signal-to-noise ratio was selected in the range of [-5, 25] dB, with a signal-to-noise ratio step of 5 dB. 100 Monte Carlo experiments were performed for each signal-to-noise ratio to solve the average mD suppression rate, average subject target recovery rate, average image contrast after reconstruction, and average image entropy. The numerical results were plotted as the signal-to-noise ratio changed. The results are shown in the figure. Figure 8-11 As shown, the results show that the performance of the algorithm of the present invention is better under different signal-to-noise ratio conditions.

[0134] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature identified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0135] Although the present application is described herein with reference to various embodiments, those skilled in the art will be able to understand and implement other variations of the disclosed embodiments in practicing the claimed application by reviewing the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0136] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A millimeter wave ISAR vehicle target imaging micro-Doppler suppression method, characterized in that: include: Step 1: Collect raw echo data from the millimeter-wave radar device when the radar wave illuminates the vehicle target; The original echo data includes echo signals received by multiple receiving antennas, and the multiple receiving antennas are arranged at equal intervals; Step 2: The original echo data is sequentially subjected to beamforming, data rearrangement, Fourier transform, and static clutter suppression to obtain a data matrix after static clutter filtering; Step 3: constructing an optimization problem for suppressing micro-Doppler based on the data matrix after static clutter filtering, the range image sequence of the target body scattering point to be solved, and the range image sequence of the rapidly rotating scattering point; Step 4, introduce Schatten- norm and graph Laplace regularization term, and the optimization problem of suppressing micro-Doppler is solved using the alternating direction multiplier method to obtain a range image sequence of the target body scattering point.

2. The micro-Doppler suppression method for millimeter wave ISAR vehicle target imaging according to claim 1, characterized in that: Step 2 includes: Step 21: beamforming the echo signals received by all receiving antennas to weightedly combine the echo signals of all receiving antennas to obtain a combined received signal; Step 22, the combined received signal is processed from 1 line The complex data of the column is rearranged as OK Column complex data, obtain the rearranged data matrix; Among them, along The direction is the distance dimension, along Direction is the azimuth dimension; Step 23, performing a one-dimensional Fourier transform on the data matrix along the distance dimension to obtain a data matrix in the frequency domain; Step 24 : using a two-pulse clutter cancellation method to suppress static clutter in the frequency domain data matrix, and obtaining a data matrix after static clutter is filtered out.

3. The micro-Doppler suppression method for millimeter wave ISAR vehicle target imaging according to claim 1, characterized in that: The optimization problem for suppressing micro-Doppler in step 3 is: in, is the data matrix after static clutter filtering, is the range image sequence of the target body scattering point to be solved, is the range image sequence of the rapidly rotating scattering point, and The meaning is the same, and the purpose is to solve the Schatten- norm and graph Laplace regularization term; Indicates Schatten- norm, Schatten- The norm is specifically defined as: is a low-rank matrix and ,have , express Matrix Large singular values; express of norm, represents the matrix trace operation, express The conjugate transpose of the matrix, and is the penalty parameter, Represents the graph Laplacian matrix. Each column of data in the graph Laplacian matrix represents the one-dimensional distance image of each pulse. Each column of data is regarded as a node of the graph. Represented as a graph adjacency matrix, it is used to represent the weight relationship between different pulse range images. represents the degree matrix, , represents the diagonalization operation, ,when Sometimes, there are .

4. The method for suppressing micro-Doppler in millimeter-wave ISAR vehicle target imaging according to claim 3, characterized in that: Step 4 includes: Step 41: Let k = k + 1, and use the alternating direction multiplier method in the k + 1 outer loop to iteratively solve the optimization problem of suppressing micro-Doppler. In the t-th inner loop iteration process of the k + 1 outer loop, the norm problem of the optimization problem is solved to update the range image sequence of the target body scattering point to be: , Step 42: determine whether the inner loop termination condition is met after the tth iteration is completed. If the inner loop termination condition is not met, another , return to step 41; Step 43: If the inner loop termination condition is reached after the tth iteration, the updated value after the tth iteration is output. ; The inner loop termination condition is or , ; Step 44, in the k+1th outer loop iteration process, the range image sequence of the fast rotating scattering point is updated to as well as ; Step 45, determining whether the outer loop termination condition is met after the k+1th outer loop iteration is completed, if not, setting k=k+2 and returning to step 41; Step 46: If the inner loop termination condition is met after the k+1th iteration, the range image sequence of the target body scattering point after the k+1th update is output. ; Among them, the outer loop termination condition is or , .

5. The method for suppressing micro-Doppler in millimeter-wave ISAR vehicle target imaging according to claim 4, characterized in that: The augmented Lagrangian function of the alternating direction multiplier method is in represents the Frobenius norm, and represents the Lagrange multiplier, and Represents the penalty coefficient, the alternating direction multiplier method updates each variable alternately at each alternation, The updated variables for the iteration are: Update the variable in the k+1th outer loop for Among them, let Schatten- Norm , using the factor group sparse regularization operator instead of the rank function to solve the Schatten- Norm problem, there is in, , , ,set up The singular value decomposition of ,but The matrices are , ; So update the variable This is equivalent to solving the optimization subproblem: The above optimization subproblem is solved using the ADMM method, and its augmented Lagrangian function is in represents the Lagrange multiplier, in the iteration Update variables alternately , update first ,have The above formula exist The first-order Taylor expansion or linearization is Where, , ; The above formula The closed form solution is in, is the column vector soft threshold operator Then update ,as follows Next update : Last Updated : After the iterative inner loop is terminated, we can get ; Update the variables in step 44 for The solution is in ; Update variables for Last updated variable for When the outer loop termination condition is reached for k+1 times, the output .

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