A SAR multi-motion target imaging method, device and storage medium

Abstract

The application provides a SAR multi-motion target imaging method, device and storage medium, and belongs to the field of microwave remote sensing, and comprises the following steps: acquiring double-channel SAR data; pre-processing the double-channel SAR data to obtain a defocused motion target signal; constructing a multi-motion target sparse observation model through the defocused motion target signal; estimating the Doppler frequency modulation of the motion target in the multi-motion target sparse observation model by using an adaptive Chirplet decomposition method, and constructing an observation matrix by using the Doppler frequency modulation estimation value; and performing sparse reconstruction on the multi-motion target of the observation matrix in the sparse observation model by using an alternating direction multiplier method (ADMM), so as to obtain a multi-motion target image. The ADMM is used for performing sparse reconstruction on the multi-motion target, the ADMM decomposes a complex convex optimization problem into a plurality of sub-optimization problems for alternately searching for optimal solutions, so that the multi-motion target image is accurately and efficiently reconstructed, and the imaging quality and imaging efficiency are improved.

Description

Technical Field

[0001] This invention belongs to the field of microwave remote sensing technology, specifically relating to a SAR multi-moving target imaging method, device, and storage medium. Background Technology

[0002] Synthetic Aperture Radar (SAR) enables all-weather, all-day, high-resolution Earth observation and has been widely applied to imaging static scenes. However, radar observation scenarios often contain numerous moving targets. Due to the influence of target motion parameters, traditional SAR imaging algorithms cause defocusing in images of moving targets. Simultaneously, strong ground clutter and system noise interfere with the amplitude and phase of moving target signals, making focused imaging of moving targets increasingly difficult. Especially in multi-moving-target imaging scenarios, target geometric features and edge information become blurred, and multiple nearby moving targets are prone to aliasing and sidelobe interference, hindering subsequent target identification and classification tasks.

[0003] To achieve focused imaging of moving targets using SAR, JKJao et al. in the United States designed a Doppler frequency modulation filter bank by traversing the possible values ​​of target motion parameters. They then processed the defocused moving target signal separately and searched for the filter with the optimal focusing effect, thus achieving target parameter estimation and focused imaging. This method is simple in principle and easy to implement; however, its parameter estimation accuracy and imaging accuracy are limited by the traversal step size, and it cannot simultaneously focus on multiple moving targets. Considering that the defocused moving target signal can be characterized as a linear frequency modulation (LFM) signal along the azimuth, time-frequency analysis can be used to estimate the target's Doppler frequency modulation, and then a matched filter can be constructed to achieve secondary focusing of the moving target. S. Barbarossa et al. in Italy used the Wigner-Ville distribution (WVD) to achieve moving target frequency modulation estimation and focused imaging. WVD has the best estimation performance for a single moving target; however, when multiple moving targets exist, its WVD exhibits severe cross terms, affecting parameter estimation accuracy and imaging quality. Subsequently, a series of improved methods, such as smoothed pseudo-WVD and polynomial WVD, were proposed, achieving cross-term suppression by sacrificing the signal's time-frequency resolution. Furthermore, fractional Fourier transform and Lübeck transform methods have also been applied to multi-moving target focusing imaging, effectively avoiding cross-term interference. However, in multi-target scenarios, traditional matched filtering methods result in a low dynamic response range and high sidelobes. Simultaneously, in environments with strong background clutter, moving target signals are easily affected by background clutter and noise, leading to decreased parameter estimation accuracy and reduced target refocusing quality.

[0004] With the continuous improvement of sparse reconstruction theories such as compressed sensing, SAR moving target imaging methods based on sparse representation have been proposed. This method models the imaging problem as an inverse problem, using the sparse characteristics of the moving target to constrain the solution space, ensuring that the ill-conditioned inverse problem has a stable and unique solution. Accurate reconstruction of the moving target's scattering coefficients is then achieved through a sparse reconstruction algorithm. Compared to time-frequency analysis methods, sparse representation-based imaging methods improve imaging resolution while reducing response sidelobes. However, these methods require building an overcomplete target velocity dictionary, consuming significant memory and computation time, resulting in low imaging efficiency. Summary of the Invention

[0005] To overcome the shortcomings of the existing technology, the present invention provides a SAR multi-moving target imaging method based on the Alternating Direction Method of Multipliers (ADMM).

[0006] First, a multi-target sparse observation model is established for the defocused moving target signal after clutter suppression and SAR imaging processing, transforming the imaging problem into a convex optimization problem. Considering that the observation matrix in the observation model contains unknown target motion parameters, the Doppler modulation frequency of the target is estimated based on the adaptive Chirplet decomposition method, thereby realizing the design of the observation matrix. To improve the dynamic response range and imaging efficiency, this invention uses ADMM to achieve sparse reconstruction of the scattering coefficients of moving targets. By introducing auxiliary variables, Lagrange multipliers, and penalty parameters, the originally complex convex optimization problem is transformed into a series of simple subproblems of alternating optimization, thereby achieving accurate and efficient reconstruction of multi-moving target images. Finally, the effectiveness and superiority of the proposed algorithm are verified through point target simulation experiments and airborne SAR measured data.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A SAR multi-moving target imaging method includes the following steps:

[0009] Acquire dual-channel SAR data;

[0010] The dual-channel SAR data is preprocessed to obtain the defocused moving target signal;

[0011] A sparse observation model for multiple moving targets is constructed using defocused moving target signals;

[0012] The adaptive Chirplet decomposition method is used to estimate the Doppler modulation frequency of the moving targets in the multi-moving-target sparse observation model, and then the observation matrix is ​​constructed using the estimated Doppler modulation frequency.

[0013] The Alternating Direction Multiplier Method (ADMM) is used to sparsely reconstruct the observation matrix of multiple moving targets in the sparse observation model to obtain images of multiple moving targets.

[0014] Preferably, before preprocessing the dual-channel SAR data to obtain the defocused moving target signal, a dual-channel SAR moving target imaging geometric model is constructed, wherein the moving target moves at a velocity v(t). m The object moves within the imaging scene, and its position vector is represented as...

[0015] Among them, t m For direction, slow time, The unit vector representing the Y-axis. Let v be the unit vector representing the X-axis, x0 and y0 be the initial positions of the moving target, and v be the unit vector representing the X-axis. x and v r =v y sinφ represents the tangential velocity and radial velocity of the moving target, respectively. y Let φ represent the ground range velocity of the moving target, and φ represent the radar's downward-facing angle. x and a r =a y sinφ represents the tangential acceleration and radial acceleration of the target, respectively, a y The acceleration of the moving target in the direction of distance from the ground;

[0016] The instantaneous slant range R between the i-th equivalent antenna and the moving target i (t m ) is represented as:

[0017]

[0018] q i Let t be the antenna velocity and p be the velocity of the moving target. Assume the radar antenna beam center is at t. ac The target is traversed at any time, and formula (1) is applied at t. m =t ac Expanding the Taylor series at this point yields:

[0019]

[0020] Among them, R B =R(t) ac ) represents the minimum slant distance between the antenna and the moving target, and V is the velocity.

[0021] Preferably, the dual-channel SAR data includes moving target signals, clutter signals, and system noise signals, which together constitute the total received signal.

[0022] The moving target signal is:

[0023]

[0024] in, Indicates the distance in fast time, A t Let w be the complex backscattering coefficient of the moving target. a (t m ) represents the azimuth envelope function, c is the speed of light, and B r λ represents the bandwidth of the transmitted signal, λ represents the wavelength, and j is a coefficient;

[0025] The total received signal is:

[0026]

[0027] Among them, t m Indicates direction in slow time, S c denoted as clutter signal generated by background ground clutter, and n as system noise.

[0028] Preferably, preprocessing the dual-channel SAR data to obtain the defocused moving target signal specifically includes:

[0029] Clutter suppression is achieved using dual-channel DPCA technology. Substituting equations (2)(2) into equations (4)(4) and (4)(2) into equations (4)(5), the signal after DPCA processing can be expressed as:

[0030]

[0031] in, The interference phase is represented as ψ = 4πv, where ψ represents the sum of residual clutter and noise. r d / (λV), f dt =-2v r / λ and γ dt =-[2(Vv x ) 2 +2a r R B ] / (λR B () represent the Doppler center frequency and modulation frequency of the moving target, respectively;

[0032] A matched filter is used to perform azimuth pulse compression on the echo signal after DPCA processing. The moving target image after azimuth matched filtering is represented as follows:

[0033]

[0034] Among them, A=A t [1-exp(jψ)]exp(-j4πR B / λ), after imaging processing, the image of the moving target shows defocusing, but it still remains an LFM signal along the azimuth direction, where ΔT=B a / γ is the LFM signal length, B a The Doppler bandwidth is represented by the Doppler modulation frequency γ of the signal, which is expressed as:

[0035]

[0036] In complex ground moving target imaging scenarios, multiple moving targets often exist in each range cell. Therefore, for each range cell, the multi-moving target signal can be represented as a multi-component LFM signal in the azimuth dimension. Assuming that there are K moving targets in a certain range cell, the moving target signal can be organized as follows:

[0037]

[0038] Among them, A k , ΔT k , and γ k This represents the parameter of the k-th moving target.

[0039] Preferably, the construction of a sparse observation model for multiple moving targets using defocused moving target signals specifically includes:

[0040] The moving target signal (8) is rearranged into a matrix form, and the sparse observation model of multiple moving targets is expressed as:

[0041]

[0042] in,

[0043]

[0044] Where, N a The number of azimuth sampling points is given, and PRF represents the pulse repetition frequency. The observation vector is the complex image of the defocused moving target. For additive perturbation vectors, The total observation matrix is ​​composed of K sub-observation matrices corresponding to the target frequency modulation frequency. This represents the complex scattering coefficient vector of K moving targets. A multi-moving-target image is obtained by linearly superimposing the complex scattering coefficients of the K targets.

[0045] Preferably, the process of constructing the observation matrix is ​​as follows:

[0046] Using the Chirplet basis as the basis function set, the multi-moving target signal s(t) to be decomposed is... mIt can be decomposed into a linear combination of several Chirplet basis functions:

[0047]

[0048] Among them, a k Here are the coefficients of the k-th Chirplet basis function. The Chirplet basis function is expressed as:

[0049]

[0050] Where, σ k t k f k and γ k Let the time width, time center, center frequency, and frequency modulation of the basis functions be represented respectively. The best-fitting Chirplet basis functions can be calculated as follows:

[0051]

[0052] Among them, s k (t m Let be the residual signal, and let a be the coefficient of the k-th Chirplet basis function. k = k (t m ),g k (t m The residual signal is updated by separating the signal component from the signal. k+1 (t m ) = s k (t m )-a k g k (t m Repeat the above decomposition until the predetermined number of iterations is reached or the residual signal energy is less than a threshold. This enables adaptive Chirplet decomposition, ultimately yielding the frequency modulation estimate.

[0053] Obtain the estimated frequency modulation value of the moving target based on the frequency modulation estimate. Construct the observation matrix

[0054] Preferably, the alternating direction multiplier method (ADMM) is used to sparsely reconstruct the multiple moving targets in the constructed observation matrix to obtain a multi-moving target image, specifically including:

[0055] As can be seen from formula (9), the moving target focusing imaging process utilizes S Na×1 Solving for Φ ​By leveraging the sparse features of the moving target in the imaging scene, this problem can be transformed into a minimum L1 norm convex optimization problem:

[0056]

[0057] Where λ represents the regularization factor, which determines the sparsity of the reconstructed moving target image;

[0058] The ADMM method is used to solve the above convex optimization problem. By introducing auxiliary variables, Lagrange multipliers and penalty parameters, the convex optimization problem is transformed into a series of simple sub-optimization problems of alternating optimization.

[0059] ADMM is used to sparsely reconstruct the scattering coefficients of multiple moving targets for each range cell, ultimately achieving focused imaging of all moving targets in the imaging scene.

[0060] Preferably, the step of transforming the convex optimization problem into a series of simpler sub-optimization problems through the introduction of auxiliary variables, Lagrange multipliers, and penalty parameters specifically includes:

[0061] First, we introduce an auxiliary variable μ, and formula (14) can be equivalent to:

[0062]

[0063] The augmented Lagrangian function of formula (15) can be expressed as:

[0064]

[0065] Where α and ρ represent the Lagrange multipliers and the penalty parameter, respectively, the above convex optimization problem can be decomposed into three subproblems that are solved iteratively in alternating ways:

[0066]

[0067] Where i represents the i-th iteration, obtained by solving L ρ The solution to the first two subproblems can be obtained by having zero first-order partial derivatives of (A,μ,α) with respect to A and μ:

[0068]

[0069] Where S(x,a)=(x / |x|)max(|x|-a,0) represents the augmented complex field soft thresholding function; repeat the above iterative optimization process until the predetermined number of iterations is reached or the residual signal energy is less than the threshold.

[0070] The present invention also provides a SAR multi-moving target imaging device based on ADMM, comprising:

[0071] The data acquisition module is used to acquire dual-channel SAR data;

[0072] The data preprocessing module is used to preprocess the dual-channel SAR data to obtain defocused moving target signals;

[0073] The sparse observation model construction module is used to construct a sparse observation model of multiple moving targets using defocused moving target signals.

[0074] The observation matrix construction module is used to estimate the Doppler modulation frequency of moving targets in the multi-moving-target sparse observation model using the adaptive Chirplet decomposition method, and then construct the observation matrix using the estimated Doppler modulation frequency.

[0075] The multi-moving target image generation module uses the Alternating Direction Multiplier Method (ADMM) to sparsely reconstruct the multi-moving targets in the constructed observation matrix to obtain multi-moving target images.

[0076] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements any step in the SAR multi-moving target imaging method.

[0077] The SAR multi-moving target imaging method provided by this invention has the following beneficial effects:

[0078] This invention employs Active Dynamic Modeling (ADMM) for sparse reconstruction of multiple moving targets. ADMM decomposes a complex convex optimization problem into multiple sub-optimization problems that alternately seek optimal solutions, thereby achieving accurate and efficient reconstruction of images of multiple moving targets, improving imaging quality and efficiency. Finally, simulation experiments and airborne SAR measurement data verify that the proposed algorithm outperforms other imaging methods in terms of focusing imaging quality and efficiency. Attached Figure Description

[0079] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0080] Figure 1 A geometric model for imaging moving targets using dual-channel SAR;

[0081] Figure 2 Schematic diagram of a sparse observation model for multiple moving targets;

[0082] Figure 3 Here is a flowchart of ADMM-based SAR multi-moving target imaging;

[0083] Figure 4 Simulated imaging results for moving targets: a) Imaging scene, b) RD imaging result, c) MF imaging result, d) L1 imaging result, e) BCS imaging result, f) ADMM imaging result;

[0084] Figure 5 Here are the azimuth cross-sections of moving targets 2-4; a) azimuth cross-section of target 2, b) azimuth cross-sections of targets 3 and 4. Detailed Implementation

[0085] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0086] Example 1

[0087] This invention provides a SAR multi-moving target imaging method. To improve the simultaneous focusing performance (imaging quality) and imaging efficiency of SAR multi-moving targets, this invention utilizes the multi-component linear frequency modulated (LFM) signal form and sparse prior knowledge of multi-moving target signals to propose a SAR multi-moving target imaging method based on the Alternating Direction Method of Multipliers (ADMM). Specifically, as follows... Figure 3 As shown, it includes the following steps:

[0088] Step 1: Acquire dual-channel SAR data.

[0089] Dual-channel SAR moving target imaging geometric model as follows Figure 1 As shown, assuming the airborne SAR system operates in front-looking-side mode, the radar platform is at an altitude H above the ground and flies along the X-axis at a constant speed V. A phased array antenna is placed along the flight path, and the entire antenna is used to transmit LFM signals. The antenna is divided into two channels to simultaneously receive echo signals. According to the principle of antenna phase center equivalence, the antenna transmit / receive split mode can be equivalent to the antenna self-transmitting and self-receiving mode. The phase center of the i-th (i=1,2) equivalent antenna is located at the midpoint between the transmitting and receiving antennas. At t m At time i, the position vector of the i-th equivalent antenna is represented as Among them, t m Let d be the azimuth time slow, and d be the distance between the two equivalent antennas. and These are unit vectors along the X and Z axes, respectively. The moving target moves at a velocity v(t). m The object moves within the imaging scene, and its position vector is represented as... Among them, S cThe clutter signal generated by background ground clutter, n is the system noise, x0 and y0 are the initial positions of the moving target, and v x and v r =v y sinφ represents the tangential velocity and radial velocity of the moving target, respectively. y Let φ represent the ground range velocity of the moving target, and φ represent the radar's downward-facing angle. x and a r =a y sinφ represents the tangential acceleration and radial acceleration of the target, respectively, a y The acceleration of the moving target in the direction of distance from the ground.

[0090] The instantaneous slant range R between the i-th equivalent antenna and the moving target i (t m ) is represented as:

[0091]

[0092] q i Let t be the antenna velocity and p be the velocity of the moving target. Assume the radar antenna beam center is at t. ac The target is traversed at any time, and formula (1) is applied at t. m =t ac Expanding the Taylor series at this point yields:

[0093]

[0094] Among them, R B =R(t) ac ) represents the minimum slant distance between the antenna and the moving target, and V is the velocity.

[0095] After range pulse compression and range migration correction, the moving target signal can be expressed as:

[0096]

[0097] in, Indicates the distance in fast time, A t Let w be the complex backscattering coefficient of the moving target. a (t m ) represents the azimuth envelope function, c is the speed of light, and B r Let λ represent the bandwidth of the transmitted signal, λ represent the wavelength, and j be a coefficient. In actual imaging scenarios, in addition to the moving target signal, the received echo also includes clutter signals generated by background objects and system noise. Therefore, the total received signal can be expressed as:

[0098]

[0099] Among them, tm Indicates direction in slow time, S c denoted as clutter signal generated by background ground clutter, and n as system noise.

[0100] Step 2: Preprocess the dual-channel SAR data to obtain the defocused moving target signal.

[0101] As can be seen from equation (4), the moving target is submerged in clutter signals and noise, making it impossible to directly extract the moving target signal for imaging processing. Therefore, clutter suppression processing is required to improve the signal-to-clutter-noise ratio (SCNR). This invention uses dual-channel DPCA (Displaced Phase Center Antenna) technology to achieve clutter suppression, and substitutes equations (2)(2) into equations (4)(4), and simultaneously substitutes equations (4)(2) into equations (4)(5). The signal after DPCA processing can be expressed as:

[0102]

[0103] in, This represents the additive disturbance caused by factors such as inconsistent antenna patterns across channels and non-ideal device components; it is the sum of residual clutter and noise. The interference phase is expressed as ψ = 4πv r d / (λV), f dt =-2v r / λ and γ dt =-[2(Vv x ) 2 +2a r R B ] / (λR B ) represent the Doppler center frequency and modulation frequency of the moving target, respectively.

[0104] Since the target motion parameters are unknown, a matched filter corresponding to the stationary target parameters is used to perform azimuth pulse compression processing on the echo signal after DPCA processing. The moving target image after azimuth matched filtering can be represented as:

[0105]

[0106] Among them, A=A t [1-exp(jψ)]exp(-j4πR B / λ). After imaging processing, the image of the moving target shows defocusing, but it still remains an LFM signal along the azimuth direction, where ΔT = B a / γ is the LFM signal length, B a The Doppler bandwidth is represented by the Doppler modulation frequency γ of the signal, which is expressed as:

[0107]

[0108] In complex ground moving target imaging scenarios, multiple moving targets often exist within each range cell. Therefore, for each range cell, the multi-moving target signal can be represented as a multi-component LFM signal in the azimuth dimension. Assuming there are K moving targets within a certain range cell, the moving target signal can be organized as follows:

[0109]

[0110] Among them, A k , ΔT k , and γ k This represents the parameter of the k-th moving target.

[0111] Step 3: Construct a sparse observation model of multiple moving targets using defocused moving target signals.

[0112] A schematic diagram of the sparse observation model is shown below. Figure 2 As shown, the moving target signal (8) is organized into a matrix form, and the sparse observation model of multiple moving targets is expressed as follows:

[0113]

[0114] in,

[0115]

[0116] Where, N a The number of azimuth sampling points is given, and PRF represents the pulse repetition frequency. The observation vector is the complex image of the defocused moving target. This is an additive perturbation vector. The total observation matrix is ​​composed of K sub-observation matrices corresponding to the target frequency modulation frequency. This represents the complex scattering coefficient vector of K moving targets. A multi-moving-target image is obtained by linearly superimposing the complex scattering coefficients of the K targets.

[0117] Step 4: Construct the observation matrix based on adaptive Chirplet decomposition.

[0118] In a sparse observation model with multiple moving targets, the observation matrix contains unknown Doppler modulation frequency information γ of the moving targets. k Considering that multiple moving target signals can be represented as multi-component LFM signals, this invention employs an adaptive Chirplet decomposition method to estimate the frequency modulation (FM) of the moving targets, and then uses the FM estimate to construct an observation matrix.

[0119] Adaptive Chirplet decomposition uses the Chirplet basis as the basis function set to adaptively decompose the signal into multiple moving target signals s(t). m It can be decomposed into a linear combination of several Chirplet basis functions:

[0120]

[0121] Among them, a k Let be the coefficients of the k-th Chirplet basis function. The Chirplet basis function is expressed as:

[0122]

[0123] Where, σ k t k f k and γ k Let represent the time width, time center, center frequency, and modulation frequency of the basis function, respectively. Because this basis function has a modulation frequency parameter, it is suitable for decomposing multi-component LFM signals. The best-fitting Chirplet basis function can be calculated as:

[0124]

[0125] Among them, s k (t m () represents the residual signal. The coefficient of the k-th Chirplet basis function is calculated as a. k = k (t m ),g k (t m The residual signal is updated by separating the signal component from the signal. k+1 (t m ) = s k (t m )-a k g k (t m Repeat the above decomposition until the predetermined number of iterations is reached or the residual signal energy is less than a threshold. This enables adaptive Chirplet decomposition, ultimately yielding the frequency modulation estimate.

[0126] Obtain the estimated frequency modulation value of the moving target based on the frequency modulation estimate. Construct the observation matrix

[0127] Step 5: Use the Alternating Direction Multiplier Method (ADMM) to sparsely reconstruct the multiple moving targets in the constructed observation matrix to obtain a multi-moving target image. Specifically, this includes:​

[0128] From the formula It can be seen that the moving target focusing imaging process utilizes Solving for Φ Utilizing the sparse features of moving targets in the imaging scene, Solving for Φ The problem can be transformed into a minimum L1 norm convex optimization problem:

[0129]

[0130] Where λ represents the regularization factor, which determines the sparsity of the reconstructed moving target image. To improve computational efficiency, ADMM is used to solve the above convex optimization problem. By introducing auxiliary variables, Lagrange multipliers, and penalty parameters, the originally complex convex optimization problem is transformed into a series of simpler sub-optimization problems of alternating optimization. First, an auxiliary variable μ is introduced, and formula (14) can be equivalent to:

[0131]

[0132] The augmented Lagrangian function of formula (15) can be expressed as:

[0133]

[0134] Here, α and ρ represent the Lagrange multipliers and the penalty parameter, respectively. The above convex optimization problem can be decomposed into three subproblems that are solved iteratively in alternating ways:

[0135]

[0136] Where i represents the i-th iteration. By solving L... ρ The solution to the first two subproblems can be obtained by setting the first-order partial derivatives of (A,μ,α) with respect to A and μ to zero:

[0137]

[0138] Where S(x,a)=(x / |x|)max(|x|-a,0) represents the augmented complex domain soft thresholding function. Repeat the above iterative optimization process until the predetermined number of iterations is reached or the residual signal energy is less than the threshold.

[0139] ADMM is used to sparsely reconstruct the scattering coefficients of multiple moving targets for each range cell, ultimately achieving focused imaging of all moving targets in the imaging scene.

[0140] Experimental Results and Analysis

[0141] In the SAR point target imaging simulation experiment, the system simulation parameters are shown in Table 1. Four moving point targets 1-4 are set in the imaging scene. Among them, targets 2-4 are in the same distance cell, and targets 3 and 4 are relatively close in the azimuth dimension. The point target distribution model is as follows: Figure 4 As shown in a), an additive perturbation consisting of residual clutter and additive noise is added to the point target model. The probability density function of the additive perturbation is expressed as:

[0142]

[0143] The settings include: number of views n = 1, texture parameter ν = 3, and input signal-to-noise ratio (SCNR) = 10 dB.

[0144] Table 1 SAR System Simulation Parameters

[0145]

[0146] Imaging results of moving targets after traditional RD processing, as shown Figure 4 As shown in b), the moving target exhibits defocusing along the azimuth direction, with multiple moving target images within the same range cell overlapping, making it difficult to directly distinguish each target's image. Simultaneously, background clutter and noise negatively impact the focused imaging of the moving target. An adaptive Chirplet decomposition method is used to estimate the target's Doppler modulation frequency. Based on the modulation frequency estimation results, an azimuth matched filter and observation matrix are designed. The imaging results based on matched filtering (MF), L1 norm regularization, Bayesian compressed sensing (BCS), and ADMM are shown below. Figure 4 As shown in c)-f), it can be seen that background clutter is effectively suppressed and the image focusing ability is improved. Among them, only the ADMM algorithm can effectively distinguish the images of targets 3 and 4, and ADMM has the best focusing imaging effect.

[0147] To illustrate the dynamic response range and sidelobes of the algorithm's imaging results, Figure 5 Azimuth profiles of point targets 2-4 are presented. Compared to other methods, the ADMM-processed image exhibits the largest dynamic response range, the smallest azimuth main lobe width, and the best side lobe suppression effect. Figure 5(b) It can be seen that the notch between the two peaks is less than -12dB, which can clearly distinguish targets 3 and 4. The focusing ability of the proposed algorithm is quantitatively analyzed by calculating the point target azimuth resolution, peak-to-sidelobe ratio (PSLR), and integrated-sidelobe ratio (ISLR). Table 2 shows that ADMM has the smallest main lobe width, PSLR, and ISLR, therefore ADMM has the best azimuth resolution and sidelobe suppression ability, and the strongest focusing imaging capability. Meanwhile, the computation time of the proposed algorithm is shown in Table 2. It can be seen that ADMM is slightly better than BCS in imaging efficiency, but has the longest L1 imaging time.

[0148] Table 2. Imaging quality and efficiency analysis of simulated moving target 2

[0149]

[0150] This invention first establishes a sparse observation model for multiple moving target signals after clutter suppression and SAR imaging processing, modeling the multi-moving target imaging problem as an inverse problem under sparse feature constraints. Based on the adaptive Chirplet decomposition method, the Doppler modulation frequency of the target is estimated, thereby enabling the design of the observation matrix. To obtain a high dynamic response range and low sidelobe response, this invention employs ADMM for sparse reconstruction of multiple moving targets. ADMM decomposes the complex convex optimization problem into multiple sub-optimization problems that alternately seek optimal solutions, thus achieving accurate and efficient reconstruction of multi-moving target images. Finally, simulation experiments and airborne SAR measured data verify that the proposed algorithm outperforms other imaging methods in terms of focusing imaging quality and efficiency.

[0151] The above-described embodiments are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited thereto. Any simple changes or equivalent substitutions of the technical solutions that can be obviously obtained by those skilled in the art within the scope of the technology disclosed in the present invention shall fall within the scope of protection of the present invention.

Claims

1. A SAR multi-motivated target imaging method, characterized in that, The method comprises the following steps: acquiring dual-channel SAR data; preprocessing the dual-channel SAR data to obtain a defocused moving target signal; constructing a multi-moving target sparse observation model through the defocused moving target signal; adopting an adaptive Chirplet decomposition method to estimate a moving target Doppler frequency rate in the multi-moving target sparse observation model, and then constructing an observation matrix by using the Doppler frequency rate estimate value; adopting an alternating direction multiplier method (ADMM) to sparsely reconstruct the multi-moving target in the observation matrix to obtain a multi-moving target image; specifically comprising: The moving target focused imaging process is to solve K moving target complex scattering coefficient vectors and total observation matrix Φ using a multi-moving target sparse observation model Using the sparse feature of moving targets in the imaging scene, the problem can be converted into a minimum L1 norm convex optimization problem: wherein, λ represents a regularization factor, and the parameter determines the sparsity of the reconstructed moving target image; solving the above convex optimization problem by using the ADMM, converting the convex optimization problem into an alternating optimization sub-optimization problem for solving by introducing an auxiliary variable, a Lagrange multiplier and a penalty parameter; sparsely reconstructing the multi-moving target scattering coefficients by using the ADMM for each distance unit, and finally realizing focused imaging of all moving targets in the imaging scene.

2. The SAR multi-moving target imaging method of claim 1, wherein, Before the defocus motion target signal is obtained by preprocessing the dual-channel SAR data, a dual-channel SAR motion target imaging geometry model is constructed, a motion target moves in an imaging scene at a speed v(t m ) and a position vector is represented as where t m is the azimuthal slow time, is the unit vector along the Y-axis, is the unit vector along the X-axis, x0and y0are the initial position of the moving target, v x is the tangential velocity of the moving target, v y is the ground range velocity of the moving target; a x is the tangential acceleration of the target, a y is the ground range acceleration of the moving target; the instantaneous slant range R between the ith equivalent antenna and the moving target i (t m ) is expressed as: q i Let t be the antenna velocity and p be the velocity of the moving target. Assume the radar antenna beam center is at t. ac The target is crossed at any time, and the formula (1) is applied at t. m =t ac Expanding the Taylor series at this point yields: where R B = R(t ac ) represents the minimum slant range between the antenna and the moving target, V is the velocity, a r = a y sinφ is the radial acceleration of the target, v r = v y sinφ represents the radial velocity of the moving target, and φ represents the radar depression angle.

3. The SAR multi-moving target imaging method of claim 2, wherein, The dual-channel SAR data comprises a moving target signal, a clutter signal and a system noise signal, and the moving target signal, the clutter signal and the system noise signal constitute a total received signal; The moving target signal is: wherein represents the range migration in fast time, A t is the complex backscattering coefficient of the moving target, w a (t m ) represents the azimuth envelope function, c is the speed of light, B r represents the transmitted signal bandwidth, λ' represents the wavelength, and j is a coefficient; The total received signal is: where t m denotes the azimuthal slow time, S c is the clutter signal due to the background terrain clutter, and n is the system noise.

4. The SAR multi-moving target imaging method of claim 3, wherein, The dual-channel SAR data is preprocessed to obtain a defocused moving target signal, specifically comprising: The clutter is suppressed by adopting a dual-channel DPCA technology, and formula (2) is substituted into formula (4), and the signal after DPCA processing is represented as: where represents the sum of residual clutter and noise, the interference phase is represented as ψ = 4πv r d / (λV), f dt = -2v r / λ and γ dt = -[2(V-v x ) 2 + 2a r R B ] / (λR B ) respectively represent the Doppler center frequency and the frequency modulation of the moving target; The echo signal after DPCA processing is processed by adopting a matched filter for azimuth direction pulse compression, and the moving target image after azimuth direction matched filter processing is represented as: where A = A t [1 - exp(jψ)]exp(-j4πR B / λ), after imaging processing, the moving target image appears defocus phenomenon, and is still in the form of LFM signal along the azimuth direction, where ΔT = B a / γ is the length of LFM signal, B a represents the Doppler bandwidth, and the Doppler frequency γ of the signal is represented as: For each distance unit, the multi-moving target signal can be represented in the form of a multi-component LFM signal in the azimuth dimension, and assuming that there are K moving targets in a certain distance unit, the moving target signal is: where A k , ΔT k , and γ k denotes the kth motion target parameter.

5. The SAR multi-motion target imaging method of claim 4, wherein, The multi-moving target sparse observation model is constructed through the defocused moving target signal, specifically comprising: The moving target signal (8) is arranged in a matrix form, and the multi-moving target sparse observation model is represented as: wherein, where N a is the number of azimuth samples, PRF represents the pulse repetition frequency, is the observation vector, i.e., the defocused moving target complex image, is the additive disturbance vector, represents the total observation matrix, which is composed of K sub-observation matrices corresponding to the target Doppler frequency, represents K moving target complex scattering coefficient vectors, and the multiple moving target image is obtained by linearly superimposing the complex scattering coefficients of the K targets 6. The SAR multi-moving target imaging method of claim 5, wherein, The construction process of the observation matrix is: The multi-motion target signal s(t) to be decomposed is decomposed into a linear combination of several Chirplet basis functions using Chirplet bases as the basis function set: m ) where a k is the coefficient of the kth Chirplet basis function, which is expressed as: where σ k , t k , f k and γ k denote the time width, time center, center frequency and chirp rate of the basis function, respectively, and the best matching Chirplet basis function can be computed as where s k (t m ) is the residual signal, the kth Chirplet basis function coefficient is calculated as a k k = arg max k (t m ),g k (t m )>, the signal component is separated from the signal to update the residual signal s k+1 (t m ) = s k (t m )-a k g k (t m ); repeat the above decomposition until a predetermined number of iterations is reached or the residual signal energy is less than a threshold , thereby realizing adaptive Chirplet decomposition and ultimately obtaining the frequency modulation rate estimate Obtaining a motion target frequency estimate from a frequency modulation estimate Constructing an observation matrix 7. The SAR multi-moving target imaging method of claim 6, wherein, The convex optimization problem is converted into an alternating optimization sub-optimization problem for solving by introducing an auxiliary variable, a Lagrange multiplier and a penalty parameter, specifically comprising: First, an auxiliary variable μ is introduced, and formula (14) can be equivalent to formula (14): The augmented Lagrange function of formula (15) can be represented as: wherein, α and ρ respectively represent a Lagrange multiplier and a penalty parameter, and the above convex optimization problem can be decomposed into three sub-problems for alternating iteration solving: where i denotes the ith iteration, by solving L ρ The solution of the first two sub-problems can be obtained by setting the first-order partial derivatives of (A, μ, α) with respect to A and μ to zero: where S denotes the augmented complex-valued soft threshold function; and the above iterative optimization process is repeated until a predetermined number of iterations is reached or the residual signal energy is less than a threshold value 8. An ADMM-based SAR multi-moving target imaging device, characterized in that, comprising: a data acquisition module, configured to acquire dual-channel SAR data; a data preprocessing module, configured to preprocess the dual-channel SAR data to obtain a defocused moving target signal; a sparse observation model construction module, configured to construct a multi-moving target sparse observation model through the defocused moving target signal; an observation matrix construction module, configured to adopt an adaptive Chirplet decomposition method to estimate a moving target Doppler frequency rate in the multi-moving target sparse observation model, and then construct an observation matrix by using the Doppler frequency rate estimate value; The multi-motion target image generation module is configured to perform sparse reconstruction on the multi-motion targets in the observation matrix by using an alternating direction multiplier method (ADMM) to obtain a multi-motion target image. Specifically, the multi-motion target image generation module includes the following steps: The moving target focused imaging process is to solve K moving target complex scattering coefficient vectors and total observation matrix Φ Using the sparse feature of moving targets in the imaging scene, the problem can be converted into a minimum L1 norm convex optimization problem: where λ represents a regularization factor, which determines the sparsity of the reconstructed motion target image; The ADMM is used to solve the above convex optimization problem, and the convex optimization problem is converted into an alternating optimization sub-optimization problem for solving by introducing an auxiliary variable, a Lagrange multiplier and a penalty parameter. The ADMM is used to perform sparse reconstruction on the multi-motion target scattering coefficients of each distance unit, so that the focused imaging of all motion targets in the imaging scene is finally realized.

9. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 8. The computer program is executed by the processor to implement the SAR multi-motion target imaging method according to any one of claims 1-7.

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