Efficient multi-channel foresight SAR angular resolution space-variant enhanced imaging method

Abstract

The invention discloses a high-efficiency multichannel forward-looking SAR angular resolution space-variant enhanced imaging method, which comprises the following steps of: processing echo data of each snapshot by using a backward projection algorithm to obtain an imaging result of each snapshot, and performing coherent summation on the imaging result of each snapshot along a synthetic aperture dimension to obtain a multichannel forward-looking SAR pre-imaging result; establishing a linear equation between a pre-imaging result and a target scattering coefficient according to the angle dimension kernel function, decomposing the angle dimension space-variant kernel function into a linear combination of a plurality of non-space-variant kernel functions through singular value decomposition, and finally solving the linear equation by applying an alternating direction multiplier (ADMM) algorithm. And efficient multi-channel foresight SAR angular resolution space-variant enhanced imaging is realized. According to the method, the space-variant PSF is decomposed and approximated, the ADMM algorithm is used for solving in the frequency domain, efficient angular resolution space-variant enhancement is achieved, and the problems that foresight imaging of a multi-channel synthetic aperture radar is fuzzy, the imaging resolution is low and the super-resolution calculation efficiency is low are solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar imaging, and particularly relates to a high-efficiency multi-channel forward-looking SAR angle resolution space-variant enhancement imaging method. BACKGROUND

[0002] Forward-looking imaging has important research significance in the fields of autonomous landing, autonomous navigation, forward-looking reconnaissance and the like. Compared with optical and infrared imaging means, radar can penetrate clouds and fog, and can work all day and all weather, and has important development prospects. However, existing radar imaging systems, such as Doppler beam sharpening (DBS) or synthetic aperture radar (SAR), are limited by mechanism and can only perform high-resolution imaging on the side of the platform or in the squint direction, and have a typical forward-looking imaging blind area.

[0003] Multi-channel radar, by arranging multiple channels in the horizontal direction perpendicular to the platform's flight path, can overcome the Doppler ambiguity problem faced by conventional single-channel SAR forward-looking imaging, and has the potential for high-resolution imaging of the forward area. In recent years, it has been widely studied. For example, the document "G. Krieger, J. Mittermayer, M. Wendler, F. Witte, and A. Moreira, Sirev-sector imaging radar for enhanced vision. Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis. 2001" proposes to use the real aperture formed by multiple channels to realize forward-looking imaging, but there is a problem that the angular resolution is limited by the array length; the document "M. Jiang, G. Xu, Y. Chen, Z. Zhong, J. Chen and W. Hong, "High-Resolution Forward-Looking MIMO-SAR Imaging using Automotive Mmwave Radar," IGARSS 2024 - 2024 IEEE International Geoscience and Remote Sensing Symposium, Athens, Greece, 2024" uses multi-channel forward-looking SAR imaging, which improves the forward-looking imaging resolution through synthetic aperture processing, but the angular resolution along the flight line area depends on the real aperture length, which is still poor; the document "L. Ren, D. Wu, M. Liu and D. Zhu, "A Space-Time Iterative Adaptive Method for Forward-Looking Radar Imaging," 2021 CIE International Conference on Radar (Radar), Haikou, Hainan, China, 2021" further improves the forward-looking imaging resolution through spectral estimation super-resolution, but does not consider the angular resolution azimuth variable problem, resulting in poor algorithm performance; the document "Zou Jianwu, Zhu Mingbo, Li Wei, et al. L1 norm regularization and its constraint method for radar azimuth super-resolution. Optik, 2015" uses L1 regularization and ADMM method to improve the angular resolution of real beam image, which can be used to solve the variable problem in principle, but often faces a large computational complexity.In addition, another approach to solving the space-variable problem is to process it in blocks, that is, to approximate the space as invariant within each block. However, in practice, this often presents problems such as how to divide the blocks and performance degradation.

[0004] In summary, existing methods still have many shortcomings, and a new method needs to be studied to achieve efficient multi-channel forward-looking SAR angular resolution spatially variable enhancement imaging. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides an efficient multi-channel forward-looking SAR angular resolution spatial variation enhancement imaging method, which can achieve efficient multi-channel forward-looking SAR angular resolution spatial variation enhancement imaging.

[0006] The technical solution adopted in this invention is: a high-efficiency multi-channel forward-looking SAR angular resolution spatially variable enhancement imaging method, the specific steps of which are as follows:

[0007] S1. Multi-channel forward-looking SAR echo modeling;

[0008] The multi-channel radar employs a single-transmitter, multiple-receiver channel configuration, transmitting signals using linear frequency modulated (LFM) signals. The radar platform transmits signals at a pre-set pulse repetition frequency (PRF), and its time-domain form... The expression is as follows:

[0009] ;

[0010] in, Indicates a fast time. Indicates the carrier frequency. Indicates frequency modulation.

[0011] The scene contains point targets. , These represent the distance and angle of the point target, respectively. The platform receives echoes from multiple snapshots, and their echoes... The expression is as follows:

[0012] ;

[0013] in, Indicates the first The slow time of a quick shot, the time interval between quick shots , Indicates the first Azimuth coordinates of each receiving antenna, channel spacing , Indicates the wavelength of the transmitted signal. The scattering coefficient of a point target, speed of light This represents the distance to the envelope. The expression for two-way distance is as follows:

[0014] ;

[0015] in, Indicates the platform's movement speed. This indicates the distance from the transmitting antenna to the target. This represents the distance from the k-th receiving antenna to the target.

[0016] S2. Based on step S1, perform range pulse compression on the received echo signal;

[0017] Set the matching function for pulse compression as follows: The signal after pulse compression The expression is as follows:

[0018] ;

[0019] in, Indicates the bandwidth of the transmitted signal. , These represent the Fast Fourier Transform (FFT) and Fast Inverse Fourier Transform (FAST) operators, respectively.

[0020] S3. Based on step S2, process the multi-shot synthetic aperture BP imaging;

[0021] Draw a grid of the imaging area in polar coordinates, with equal intervals set in the distance direction. Each grid corresponds to a distance. azimuth direction equally spaced Set up N grids, each corresponding to an azimuth angle. At point target Distance Above, the distance pulse compression data The back projection algorithm is used to accumulate the real aperture dimension and the synthetic aperture dimension, as shown in the following expression:

[0022] ;

[0023] in, Indicates the azimuth angle of the imaging grid. Indicates the number of channels. Indicates the number of snapshots. Indicates the two-way delay of a point target. Indicates azimuth angle The point target imaging result, i.e., the point spread function (PSF).

[0024] The imaging result of a single range cell is then obtained, expressed as follows:

[0025] ;

[0026] in, This indicates the amplitude of the synthetic aperture pattern; a 3dB width is approximately... , This represents the amplitude of the actual aperture radiation pattern; a 3dB width is approximately... .

[0027] S4. Based on step S3, obtain the angle spatially variable kernel function or point spread function (PSF) of the multi-channel forward-looking SAR according to BP imaging.

[0028] For multi-target scenarios, the expression for multi-channel forward-looking SAR imaging results in a given range cell is as follows:

[0029] ;

[0030] in, Indicates the first Azimuth Imaging response at that location, Indicates the first distance unit. Azimuth The scattering coefficient at that location, .

[0031] Assuming additive noise exists When expressed in matrix-vector form, the radar imaging results... The expression is as follows:

[0032] ;

[0033] in, This represents the scattering coefficient vector on this range cell. The degradation matrix representing forward-looking imaging by multi-channel radar is expressed as follows:

[0034] ;

[0035] S5. Based on step S4, decompose the PSF using Singular Value Decomposition (SVD);

[0036] S6. Based on step S5, establish the least squares equation and solve the equation using the alternating direction multiplier method (ADMM) to obtain the enhanced imaging results.

[0037] Furthermore, step S5 is specifically as follows:

[0038] First, transform matrix H into matrix A, and then the first... The column is composed of the first column of matrix H. The column is obtained by performing a cyclic shift, as shown in the following expression:

[0039] ;

[0040] in, express right The result after taking the modulus, .

[0041] Then, SVD decomposition was performed on A to obtain... , This indicates the conjugate transpose. Representing a unitary matrix, by The eigenvectors are composed of, Represent a diagonal matrix, by The singular values ​​constitute the composition. Representing a unitary matrix, by The eigenvectors of A are used to form a low-rank approximation. The first L largest singular values ​​of A are taken as a set of length L. basis vectors That is, the non-empty variable PSF, in which It is U's The PSF at each orientation is decomposed into a linear combination of these basis vectors, where the coefficients of the linear combination are a set of lengths... row vectors { },Depend on The sum of the first L diagonal elements The first L rows are calculated to obtain: .

[0042] According to the Eckart-Young theorem, among all matrices of rank L, the matrix formed by the L largest singular values ​​and their corresponding singular vectors of matrix A is the best approximation of matrix A. The low-rank approximation of matrix A using its L largest singular values ​​is expressed as follows:

[0043] ;

[0044] Then according to equation (10) and The mapping relationship, and the approximate expression of matrix H are as follows:

[0045] ;

[0046] The simplified expression of equation (12) is as follows:

[0047] ;

[0048] Among them, matrix Indicates that the first column is The constructed Toplitz matrix; matrix Indicates the diagonal is The diagonal matrix is ​​expressed as follows:

[0049] ;

[0050] ;

[0051] The simplified expression of equation (13) is as follows:

[0052] ;

[0053] Among them, matrix ,matrix = .

[0054] Finally, combining equation (8), we obtain the following expression:

[0055] .

[0056] Furthermore, step S6 is specifically as follows:

[0057] The linear computation is transformed into solving a regularized least squares problem, as shown in the following expression:

[0058] ;

[0059] in, This represents the regularization coefficient.

[0060] Then perform variable splitting, let Equation (18) can be rewritten as the following expression:

[0061] ;

[0062] Then, by using the augmented Lagrange method (ALM), the constrained minimization problem is transformed into an unconstrained minimization problem, resulting in the alternating minimization problem, as expressed below:

[0063] ;

[0064] in, This represents the auxiliary variables introduced by ALM. Indicates parameters, This represents the augmented Lagrange function. and Representing the constrained residuals respectively and The penalty term is applied, and the variable is updated sequentially in each iteration. Then the first The calculation steps for this iteration are as follows:

[0065] 1) Update :fixed Minimize and The relevant part, the expression is as follows:

[0066] ;

[0067] Differentiate and set to zero, the expression is as follows:

[0068] ;

[0069] in, express The conjugate transpose of .

[0070] Finally obtained The expression is as follows:

[0071] ;

[0072] in, , Represents the identity matrix.

[0073] 2) Update :fixed Minimize and The relevant part, the expression is as follows:

[0074] ;

[0075] Differentiate and set to zero, the expression is as follows:

[0076] ;

[0077] in, express The conjugate transpose of .

[0078] Finally obtained The expression is as follows:

[0079] ;

[0080] 3) Update :fixed Minimize and The relevant part, the expression is as follows:

[0081] ;

[0082] Since the squares of the l1 norm and the l2 norm are separable, equation (27) is equivalent to the following expression:

[0083] ;

[0084] in, The first in For each element, equation (28) is equivalent to solving for the following expression:

[0085] ;

[0086] Taking the derivative again, we obtain the closed-form solution for the soft threshold, as shown in the following expression:

[0087] ;

[0088] Finally obtained The expression is as follows:

[0089] ;

[0090] in, It is the Hadama product, which means multiplying each term.

[0091] 4) According to formula (20), the augmented Lagrangian function with penalty term right and The gradients are respectively and And update the dual variable based on the gradient ascent method. The expression is as follows:

[0092] ;

[0093] ;

[0094] During the initial iteration, All values ​​are set to zero. As the number of iterations increases, Gradually approaching the original scene until reaching the termination condition, that is... It is less than a pre-set minimum value. Finally, iterate through all distance cells and solve for each distance cell. Ultimately, enhanced imaging results are obtained.

[0095] The beneficial effects of this invention are as follows: The method of this invention first uses the back-projection (BP) algorithm to process the echo data of each snapshot, obtaining the imaging results of each snapshot. Then, the imaging results of each snapshot are coherently summed along the synthetic aperture dimension to obtain the multi-channel forward-looking SAR pre-imaging results. Next, a linear equation is established between the pre-imaging results and the target scattering coefficient based on the angular dimension kernel function. The angular dimension spatially variable kernel function is decomposed into a linear combination of multiple non-spatially variable kernel functions using singular value decomposition (SVD). Finally, the alternating direction multiplier (ADMM) algorithm is applied to solve the linear equation, achieving efficient multi-channel forward-looking SAR angular resolution spatially variable enhancement imaging. This method, through the decomposition and approximation of the spatially variable PSF (point spread function), allows the ADMM algorithm to be solved quickly in the frequency domain, thereby achieving efficient angular resolution spatially variable enhancement. This helps solve the problems of blurred forward-looking imaging, low imaging resolution, and low super-resolution computational efficiency in multi-channel synthetic aperture radar. Attached Figure Description

[0096] Figure 1 This is a flowchart of a high-efficiency multi-channel forward-looking SAR angular resolution spatially variable enhancement imaging method according to the present invention.

[0097] Figure 2 This is a geometric model diagram of multi-channel radar forward-looking SAR imaging in an embodiment of the present invention.

[0098] Figure 3 This is a schematic diagram of the observation scene in an embodiment of the present invention.

[0099] Figure 4 This is a schematic diagram of the multi-channel forward-looking SAR BP imaging results in an embodiment of the present invention.

[0100] Figure 5 The degradation matrix in the embodiment of the present invention Schematic diagram.

[0101] Figure 6 This is a schematic diagram of matrix A in an embodiment of the present invention.

[0102] Figure 7 This is a schematic diagram of the enhanced imaging results obtained by the original ADMM method in an embodiment of the present invention.

[0103] Figure 8 This is a schematic diagram of the enhanced imaging results in an embodiment of the present invention. Detailed Implementation

[0104] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0105] like Figure 1The flowchart of a high-efficiency multi-channel forward-looking SAR angular resolution spatially variable enhancement imaging method of the present invention is shown below, and the specific steps are as follows:

[0106] S1. Multi-channel forward-looking SAR echo modeling;

[0107] In this embodiment, the multi-channel radar adopts a single-transmitter, multi-receiver channel configuration, and the geometric configuration of the forward-looking multi-channel radar is as follows: Figure 2 As shown, the transmitting antenna is located at the center position in this embodiment. The receiving antennas are evenly distributed along the Y-axis, with a spacing of [missing information]. The height is The radar platform along the X-axis The forward-looking multi-channel radar parameters are shown in Table 1.

[0108] Table 1

[0109]

[0110] To achieve a large time width and bandwidth product in the transmitted signal, LFM is used. The radar platform transmits the signal at the designed pulse repetition frequency (PRF), with a snapshot interval of [missing information]. Its time-domain form The expression is as follows:

[0111] ;

[0112] in, Indicates a fast time. Indicates the carrier frequency. Indicates frequency modulation.

[0113] The scene contains point targets. , These represent the distance and angle of the point target, respectively. The platform receives echoes from multiple snapshots, and their echoes... The expression is as follows:

[0114] ;

[0115] in, Indicates the first The slow time of a quick shot, the time interval between quick shots , Indicates the first Azimuth coordinates of each receiving antenna, channel spacing , Indicates the wavelength of the transmitted signal. The scattering coefficient of a point target, speed of light This represents the distance to the envelope. The expression for two-way distance is as follows:

[0116] ;

[0117] in, Indicates the platform's movement speed. This indicates the distance from the transmitting antenna to the target. This represents the distance from the k-th receiving antenna to the target.

[0118] like Figure 3 As shown, in this embodiment, the azimuth of the area to be imaged is -10° to 10°, and the range is 6200m to 6800m. The time domain form of the transmitted signal can be calculated using equation (1), and then the echo signal of the target area can be obtained using equations (2) and (3). Gaussian white noise is added to the echo, with a signal-to-noise ratio of 20dB.

[0119] S2. Based on step S1, perform range pulse compression on the received echo signal;

[0120] Set the matching function for pulse compression as follows: The signal after pulse compression The expression is as follows:

[0121] ;

[0122] in, Indicates the bandwidth of the transmitted signal. , These represent the Fast Fourier Transform (FFT) and Fast Inverse Fourier Transform (FAST) operators, respectively.

[0123] In this embodiment, according to equation (4), the echo signal is pulse-compressed using a pulse compression matching function to obtain the signal. Range imaging was achieved by pulse compression in the synthetic aperture dimension of a single channel. The echoes after range pulse compression of the first snapshot of each channel were obtained.

[0124] S3. Based on step S2, process the multi-shot synthetic aperture BP imaging;

[0125] Draw a grid of the imaging area in polar coordinates, with equal intervals set in the distance direction. Each grid corresponds to a distance. azimuth direction equally spaced Set up N grids, each corresponding to an azimuth angle. At point target Distance Above, the distance pulse compression data The back projection algorithm is used to accumulate the real aperture dimension (channel) and the synthetic aperture (snapshot) dimension, as shown in the following expression:

[0126] ;

[0127] in, Indicates the azimuth angle of the imaging grid. Indicates the number of channels. Indicates the number of snapshots. Indicates the two-way delay of a point target.

[0128] The imaging result of a single range cell is then obtained, expressed as follows:

[0129] ;

[0130] in, This indicates the amplitude of the synthetic aperture pattern; a 3dB width is approximately... , This represents the amplitude of the actual aperture radiation pattern; a 3dB width is approximately... .

[0131] It can be seen that the forward-looking imaging results The imaging results of the midpoint target vary with the angular position of the point target. The resolution changes, with higher resolution on both sides of the route but lower resolution near the center of the route, indicating that the point spread function exhibits significant azimuth spatial variation.

[0132] In this embodiment, a grid is drawn over the area to be imaged. The azimuth direction is divided into 500 equally spaced grids, and the range direction is divided into 200 equally spaced grids. The pixel grid is used for imaging. Then, equation (3) is used to calculate the distance from each channel to the imaging grid in the synthetic aperture dimension of a snapshot. Using the back projection (BP) algorithm, the pulse compression results are coherently accumulated according to equation (5) based on the distance, to achieve multi-channel synthetic aperture BP imaging, such as... Figure 4 As shown, the resolution at the center of the scene in the imaging results is still low. Furthermore, there is spatial blurring, with the resolution in the azimuth-oriented central region being significantly lower than that on either side.

[0133] S4. Based on step S3, obtain the angle spatially variable kernel function or point spread function (PSF) of the multi-channel forward-looking SAR according to BP imaging.

[0134] For multi-target scenarios, the expression for multi-channel forward-looking SAR imaging results in a given range cell is as follows:

[0135] ;

[0136] in, Indicates the first Azimuth Imaging response at that location, Indicates the first distance unit. Azimuth The scattering coefficient at that location, .

[0137] Assuming additive noise exists When expressed in matrix-vector form, the radar imaging results... The expression is as follows:

[0138] ;

[0139] in, This represents the scattering coefficient vector on this range cell. The degradation matrix representing forward-looking imaging by multi-channel radar is expressed as follows:

[0140] ;

[0141] The PSF of different range cells is approximately the same, therefore one range cell of the imaging range is taken. Get PSF. Select an azimuth angle. Grid setting point target Afterwards, the pulse-compressed echo is obtained according to steps S1 and S2, and then BP imaging is performed according to equation (5) to obtain the range cell. superior azimuth PSF at that location, i.e. By traversing all the meshes in the azimuth direction, the degradation matrix H in the degradation model is obtained, such as... Figure 5 As shown.

[0142] S5. Based on step S4, decompose the PSF using Singular Value Decomposition (SVD);

[0143] because Composed of spatially variable PSFs, it is not a standard convolution matrix, which greatly increases the computational cost during solution. Here, the spatially variable PSF is decomposed into a linear combination of multiple non-spatially variable PSFs.

[0144] First, transform matrix H into matrix A, and then the first... The column is composed of the first column of matrix H. The column is obtained by performing a cyclic shift, as shown in the following expression:

[0145] ;

[0146] in, express right The result after taking the modulus, .

[0147] Then, SVD decomposition was performed on A to obtain... , This indicates the conjugate transpose. Representing a unitary matrix, by The eigenvectors are composed of, Represent a diagonal matrix, by The singular values ​​constitute the composition. Representing a unitary matrix, by The eigenvectors of A are used to form a low-rank approximation. The first L largest singular values ​​of A are taken as a set of length L. basis vectors That is, the non-empty variable PSF, in which It is U's The PSF at each orientation is decomposed into a linear combination of these basis vectors, where the coefficients of the linear combination are a set of lengths... row vectors { },Depend on The sum of the first L diagonal elements The first L rows are calculated to obtain: .

[0148] According to the Eckart-Young theorem, among all matrices of rank L, the matrix formed by the L largest singular values ​​and their corresponding singular vectors of matrix A is the best approximation of matrix A. The low-rank approximation of matrix A using its L largest singular values ​​is expressed as follows:

[0149] ;

[0150] Then according to equation (10) and The mapping relationship, and the approximate expression of matrix H are as follows:

[0151] ;

[0152] The simplified expression of equation (12) is as follows:

[0153] ;

[0154] Among them, matrix Indicates that the first column is The constructed Toplitz matrix; matrix Indicates the diagonal is The diagonal matrix is ​​expressed as follows:

[0155] ;

[0156] ;

[0157] The simplified expression of equation (13) is as follows:

[0158] ;

[0159] Among them, matrix ,matrix = .

[0160] Finally, combining equation (8), we obtain the following expression:

[0161] ;

[0162] In this embodiment, matrix A is calculated according to equation (10) for the decomposition of H. Matrix A is as follows: Figure 6 As shown. The matrix is ​​obtained by performing SVD decomposition. Take the first L=10 eigenvalues ​​for low-rank approximation. Construct the block convolution matrix B and the block diagonal matrix M according to equations (13)-(14).

[0163] S6. Based on step S5, establish the least squares equation and solve the equation using the alternating direction multiplier method (ADMM) to obtain the enhanced imaging results;

[0164] To solve equation (17), the linear computation is transformed into solving a regularized least squares problem, as shown in the following expression:

[0165] ;

[0166] in, This represents the regularization coefficient.

[0167] Then perform variable splitting, let Equation (18) can be rewritten as the following expression:

[0168] ;

[0169] Then, using ALM (Augmented Lagrange Multiplication), the constrained minimization problem is transformed into an unconstrained minimization problem, resulting in the alternating minimization problem, expressed as follows:

[0170] ;

[0171] in, This represents the auxiliary variables introduced by ALM. Indicates parameters, This represents the augmented Lagrange function. and Representing the constrained residuals respectively and The penalty term is applied, and the variable is updated sequentially in each iteration. Then the first The calculation steps for this iteration are as follows:

[0172] 1) Update :fixed Minimize and The relevant part, the expression is as follows:

[0173] ;

[0174] Differentiate and set to zero, the expression is as follows:

[0175] ;

[0176] in, express The conjugate transpose of .

[0177] Finally obtained The expression is as follows:

[0178] ;

[0179] in, , This represents the identity matrix. The multiplication of convolution matrices can be transformed into the frequency domain for fast computation; this property is utilized to complete... The calculation.

[0180] 2) Update :fixed Minimize and The relevant part, the expression is as follows:

[0181] ;

[0182] Differentiate and set to zero, the expression is as follows:

[0183] ;

[0184] in, express The conjugate transpose of .

[0185] Finally obtained The expression is as follows:

[0186] ;

[0187] 3) Update :fixed Minimize and The relevant part, the expression is as follows:

[0188] ;

[0189] Since the squares of the l1 norm and the l2 norm are separable, equation (27) is equivalent to the following expression:

[0190] ;

[0191] in, The first in For each element, equation (28) is equivalent to solving for the following expression:

[0192] ;

[0193] Taking the derivative again, we obtain the closed-form solution for the soft threshold, as shown in the following expression:

[0194] ;

[0195] Finally obtained The expression is as follows:

[0196] ;

[0197] in, It is the Hadama product, which means multiplying each term.

[0198] 4) According to formula (20), the augmented Lagrangian function with penalty term right and The gradients are respectively and And update the dual variable based on the gradient ascent method. The expression is as follows:

[0199] ;

[0200] ;

[0201] During the initial iteration, All values ​​are set to zero. As the number of iterations increases, Gradually approaching the original scene until reaching the termination condition, that is... It is less than a pre-set minimum value. Finally, iterate through all distance cells and solve for each distance cell. Ultimately, enhanced imaging results are obtained.

[0202] This embodiment sets parameters. Using the ADMM method, iterative solutions are performed on each distance cell according to equations (23), (26), (31), (32), and (33), with the iteration termination condition being... . The initial value is set to 0. Let the imaging result at this range cell be the super-resolution result obtained after iteration. Setting parameters Equation (8) can be solved directly using ADMM, with a computation time complexity of O(n) for each iteration. Each distance unit is calculated sequentially, and the total running time is... The result is as follows Figure 7 As shown. This embodiment uses the method of the present invention, and the time complexity of each iteration is O(n). The total running time is 90.90 seconds. Figure 8 As shown.

[0203] In summary, the multi-channel forward-looking synthetic aperture radar angular resolution spatial variation enhancement imaging method in this embodiment helps to solve the problems of blurred forward-looking imaging, low imaging resolution, and low super-resolution computational efficiency of multi-channel synthetic aperture radar.

[0204] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A highly efficient multi-channel forward-looking SAR angular resolution spatially variable enhancement imaging method, the specific steps of which are as follows: S1. Multi-channel forward-looking SAR echo modeling; The multi-channel radar employs a single-transmitter, multiple-receiver channel configuration, transmitting signals using linear frequency modulated (LFM) signals. The radar platform transmits signals at a pre-set pulse repetition frequency (PRF), and its time-domain form... The expression is as follows: ； in, Indicates a fast time. Indicates the carrier frequency. Indicates frequency modulation; The scene contains point targets. , These represent the distance and angle of the point target, respectively; the platform receives echoes from multiple snapshots, and their echoes... The expression is as follows: ； in, Indicates the first The slow time of a quick shot, the time interval between quick shots , Indicates the first Azimuth coordinates of each receiving antenna, channel spacing , Indicates the wavelength of the transmitted signal. The scattering coefficient of a point target, speed of light Indicates distance to the envelope; The expression for two-way distance is as follows: ； in, Indicates the platform's movement speed. This indicates the distance from the transmitting antenna to the target. This represents the distance from the k-th receiving antenna to the target; S2. Based on step S1, perform range pulse compression on the received echo signal; Set the matching function for pulse compression as follows: The signal after pulse compression The expression is as follows: ； in, Indicates the bandwidth of the transmitted signal. , These represent the Fast Fourier Transform and Fast Inverse Fourier Transform operators, respectively. S3. Based on step S2, process the multi-shot synthetic aperture BP imaging; Draw a grid of the imaging area in polar coordinates, with equal intervals set in the distance direction. Each grid corresponds to a distance. azimuth direction equally spaced Set up N grids, each corresponding to an azimuth angle. ; at point target Distance Above, the distance pulse compression data The back projection algorithm is used to accumulate the real aperture dimension and the synthetic aperture dimension, as shown in the following expression: ； in, Indicates the azimuth angle of the imaging grid. Indicates the number of channels. Indicates the number of snapshots. Indicates the two-way delay of a point target. Indicates azimuth angle The point target imaging result at that location, i.e., the point spread function (PSF); The imaging result of a single range cell is then obtained, expressed as follows: ； in, This indicates the amplitude of the synthetic aperture pattern; a 3dB width is approximately... , This represents the amplitude of the actual aperture radiation pattern; a 3dB width is approximately... ; S4. Based on step S3, obtain the angle spatially variable kernel function or point spread function (PSF) of the multi-channel forward-looking SAR according to BP imaging. For multi-target scenarios, the expression for multi-channel forward-looking SAR imaging results in a given range cell is as follows: ； in, Indicates the first Azimuth Imaging response at that location, Indicates the first distance unit. Azimuth The scattering coefficient at that location, ; Assuming additive noise exists When expressed in matrix-vector form, the radar imaging results... The expression is as follows: ； in, This represents the scattering coefficient vector on this range cell. The degradation matrix representing forward-looking imaging by multi-channel radar is expressed as follows: ； S5. Based on step S4, decompose the PSF using Singular Value Decomposition (SVD); S6. Based on step S5, establish the least squares equation and solve the equation using the alternating direction multiplier method (ADMM) to obtain the enhanced imaging results.

2. The efficient multi-channel forward-looking SAR angular resolution spatially variable enhancement imaging method according to claim 1, characterized in that, Step S5 is as follows: First, transform matrix H into matrix A, and then the first... The column is composed of the first column of matrix H. The column is obtained by performing a cyclic shift, as shown in the following expression: ； in, express right The result after taking the modulus, ; Then, SVD decomposition was performed on A to obtain... , This indicates the conjugate transpose. Representing a unitary matrix, by The eigenvectors are composed of, Represent a diagonal matrix, by The singular values ​​constitute the composition. Representing a unitary matrix, by The eigenvectors are composed of A; the first L largest singular values ​​of A are used for low-rank approximation; the first L columns of U are used as a set of lengths... basis vectors That is, the non-empty variable PSF, in which It is U's The PSF at each orientation is decomposed into a linear combination of these basis vectors, where the coefficients of the linear combination are a set of lengths... row vectors { },Depend on The sum of the first L diagonal elements The first L rows are calculated to obtain: ; According to the Eckart-Young theorem, among all matrices of rank L, the matrix formed by the L largest singular values ​​and their corresponding singular vectors of matrix A is the best approximation of matrix A. A low-rank approximation is performed using the L largest singular values ​​of matrix A, and the approximation result is expressed as follows: ； Then according to equation (10) and The mapping relationship, and the approximate expression of matrix H are as follows: ； The simplified expression of equation (12) is as follows: ； Among them, matrix Indicates that the first column is The constructed Toplitz matrix; matrix Indicates the diagonal is The diagonal matrix is ​​expressed as follows: ； ； The simplified expression of equation (13) is as follows: ； Among them, matrix ,matrix = ; Finally, combining equation (8), we obtain the following expression: 。 3. The efficient multi-channel forward-looking SAR angular resolution spatially variable enhancement imaging method according to claim 2, characterized in that, Step S6 is as follows: The linear computation is transformed into solving a regularized least squares problem, as shown in the following expression: ； in, Represents the regularization coefficient; Then perform variable splitting, let Equation (18) can be rewritten as the following expression: ； Then, by using the augmented Lagrange method (ALM), the constrained minimization problem is transformed into an unconstrained minimization problem, resulting in the alternating minimization problem, as expressed below: ； in, This represents the auxiliary variables introduced by ALM. Indicates parameters, This represents the augmented Lagrange function. and Representing the constrained residuals respectively and The penalty term is applied, and the variable is updated sequentially in each iteration. Then the first The calculation steps for this iteration are as follows: 1) Update :fixed Minimize and The relevant part, the expression is as follows: ； Differentiate and set to zero, the expression is as follows: ； in, express The conjugate transpose of; Finally obtained The expression is as follows: ； in, , Represents the identity matrix; 2) Update :fixed Minimize and The relevant part, the expression is as follows: ； Differentiate and set to zero, the expression is as follows: ； in, express The conjugate transpose of; Finally obtained The expression is as follows: ； 3) Update :fixed Minimize and The relevant part, the expression is as follows: ； And since the squares of the l1 norm and the l2 norm are separable, equation (27) is equivalent to the following expression: ； in, The first in For each element, equation (28) is equivalent to solving for the following expression: ； Taking the derivative again, we obtain the closed-form solution for the soft threshold, as shown in the following expression: ； Finally obtained The expression is as follows: ； in, It is the Hadamardi product, which means multiplying each term. 4) According to formula (20), the augmented Lagrangian function with penalty term right and The gradients are respectively and And update the dual variable based on the gradient ascent method. The expression is as follows: ； ； During the initial iteration, All values ​​are set to zero. As the number of iterations increases, Gradually approaching the original scene until reaching the termination condition, that is... It is less than a pre-set minimum value; finally, iterate through all distance cells and solve for each distance cell. Ultimately, enhanced imaging results are obtained.

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