A sparse imaging and autofocusing method for synthetic aperture radar

Abstract

The present invention discloses a synthetic aperture radar (SAR) sparse imaging and autofocusing method, comprising the following steps: S1: assuming that a SAR transmits a continuous wave signal from an ideal array element position and receives an echo, and that the SAR's moving platform has no motion error, an ideal observation matrix and an ideal echo can be obtained; S2: in actual situations, the SAR's moving platform may experience random three-dimensional jitter, and an actual SAR echo containing motion error is obtained, and a mapping relationship between the actual echo and the ideal echo is established; S3: constructing a sparse imaging and autofocusing model; and S4: solving the sparse imaging and autofocusing model using an augmented Lagrangian function and an alternating direction multiplier method to achieve SAR sparse imaging and autofocusing. The present invention introduces an ADMM algorithm within the augmented Lagrangian multiplier, utilizing the structured sparsity of the target and significantly improving image reconstruction quality in weakly sparse scenarios.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and in particular to a synthetic aperture radar sparse imaging and self-focusing method. Background Art

[0002] Synthetic aperture radar (SAR), an active imaging tool in modern microwave remote sensing, has been widely used in various fields, including environmental monitoring, building mapping, and target detection, thanks to its unique advantages, including all-weather, all-day, and high-resolution imaging. In a SAR system, a radar platform moves along a predetermined trajectory and continuously emits electromagnetic waves at a fixed pulse repetition interval. By recording coherent information from different observation positions, the system synthesizes a virtual long aperture, achieving high-resolution imaging in azimuth. Simultaneously, the transmission of broadband radar signals enables high resolution in range. Ultimately, by processing multiple sets of received pulse signals, high-resolution radar imaging of the target area is achieved. In practical applications, radar platforms are often affected by atmospheric interference, platform vibration, and terrain, making it difficult to accurately track the predetermined trajectory. Consequently, significant uncertainty in platform position and measurement errors can occur. These deviations cause phase distortion in the echo signal, which is equivalent to the convolution of the image with a blur kernel, resulting in image blurring and significantly degrading image quality. Although modern navigation systems, such as inertial navigation systems, global positioning systems, or BeiDou navigation systems, can partially compensate for platform motion, their measurement capabilities remain limited due to hardware precision limitations, and they cannot completely eliminate all errors. Residual phase errors can severely impact the quality of the final reconstructed image. Therefore, accurately correcting these residual errors is essential to reduce artifacts introduced during the image generation process and thus improve the quality of SAR images.

[0003] With the development of compressed sensing (CS) theory, significant breakthroughs have been achieved in the fields of compressed SAR imaging and autofocusing. Many studies have explored CS-based SAR autofocusing methods. One study proposed a sparsity-based autofocusing imaging method in which the phase error is separated into 1D and 2D phase errors and corrected using regularization. However, since this method only considers the sparsity prior and fails to account for the target's structural features, the target's structural outline in the reconstructed image is incomplete. Another study introduced an imaging algorithm based on orthogonal matching pursuit and motion error compensation for multiple-input, multiple-output (MIMO) array radars. This method employs a cyclic iterative framework, alternating between target reconstruction and MIMO array motion error estimation and compensation. However, the orthogonal matching pursuit (OMP) algorithm is a greedy algorithm that requires a stepwise search for the support set of the signal to be recovered. As sparsity increases, the number of iterations also increases. The computational complexity of this technique increases dramatically when processing extended targets, limiting its feasibility in certain practical applications. Summary of the Invention

[0004] To address these issues, this paper proposes a synthetic aperture radar (SAR) sparse imaging and autofocusing method. This method incorporates the ADMM algorithm within the augmented Lagrangian multiplier (ALM) framework, decomposing the optimization problem into multiple, easily solvable subproblems. The Lagrangian term is then introduced to accelerate convergence. Unlike traditional point scattering sparse priors, this method exploits the underlying structured sparsity of targets in the image domain, significantly improving image reconstruction quality in weakly sparse scenarios.

[0005] The present invention proposes a synthetic aperture radar sparse imaging and self-focusing method, comprising:

[0006] S1: The synthetic aperture radar transmits a broadband linear frequency modulated continuous wave signal from an ideal array element position and receives the echo. Assuming that the synthetic aperture radar moving platform has no motion error, an ideal observation matrix and ideal echo are obtained.

[0007] S2: In practice, the SAR platform experiences random three-dimensional jitter, and the actual SAR echo containing motion errors is obtained. The phase error between the actual echo and the ideal echo is calculated, and a mapping relationship between the actual echo and the ideal echo is constructed.

[0008] S3: Based on the mapping relationship between actual echo and ideal echo, a sparse imaging and autofocus model is constructed;

[0009] S4: Solve the sparse imaging and self-focusing model through augmented Lagrangian function and alternating direction multiplier method to realize sparse imaging and self-focusing of synthetic aperture radar.

[0010] Furthermore, the S1 includes:

[0011] Assume the spatial position of the target is , the position of the ideal array element is , then the ideal echo S is:

[0012] ;

[0013] in, is the ideal echo at fast time t, is the triple integral operator symbol, is the target scattering function, σ is the target scattering coefficient, j is the imaginary unit, exp() is the exponential function, K is the frequency modulation slope, B is the sweep bandwidth, T is the pulse duration, and π is the circumference. yes The instantaneous frequency within the range, is the carrier frequency, t is the fast time, and c is the speed of light.

[0014] Furthermore, the S1 includes:

[0015] If both the ideal echo and the target scattering function are expressed as vectors, the ideal echo is:

[0016] ;

[0017] Where ω is the additive noise vector and P is the ideal measurement matrix.

[0018] Furthermore, the S2 includes:

[0019] S21: Assuming that the antennas transmitting and receiving SAR signals are located at the same position, calculate the ideal distance R between the ideal SAR array element and the scattering point of the target:

[0020] ;

[0021] S22: Calculate the actual distance R between the actual array element of the synthetic aperture radar and the scattering point of the target, including motion errors e :

[0022] ;

[0023] in, It represents the actual position of the actual array element of the synthetic aperture radar, which is specifically expressed as:

[0024] ;

[0025] in, are the offset errors of the actual array element of the synthetic aperture radar along the x, y and z directions respectively;

[0026] S23: Calculate the actual echo of synthetic aperture radar including motion error:

[0027] ;

[0028] in, represents the actual echo including motion errors, represents the actual echo at fast time t; Indicates the error between the actual distance between the actual array element and the target and the ideal distance, Indicates the phase error between the actual echo and the ideal echo, is the observation matrix containing the motion error;

[0029] The mapping relationship between the actual echo and the ideal echo is expressed as:

[0030] ;

[0031] in, represents the Hadamard product, Indicates phase.

[0032] Furthermore, the S3 includes:

[0033] According to the mapping relationship between the actual echo and the ideal echo, the initial objective function is constructed, which is:

[0034] ;

[0035] Among them, argmin means taking the minimum value of the initial objective function. is the Frobenius norm, Represents the phase error calibration matrix between the actual echo and the ideal echo;

[0036] By utilizing the structured sparsity prior of the image and combining it with the echo phase error estimation, the initial objective function is optimized to construct a sparse imaging and autofocus model:

[0037] ;

[0038] in, is the convolution operation, represents an arbitrarily small positive number, It is in k In the iteration, the update of the reconstruction operation represents the k The radar image obtained in the iteration; is the regularization parameter, Represents the convolution kernel.

[0039] Furthermore, the S4 includes:

[0040] Solve the sparse imaging and self-focusing models using the alternating direction multiplier method:

[0041] First, introduce auxiliary variables , the sparse imaging and self-focusing models are replaced by:

[0042] ;

[0043] Among them, st means that the satisfaction is subject to certain specific conditions;

[0044] Define the augmented Lagrangian function ;

[0045] ;

[0046] in, represents the Lagrange multiplier, is the penalty factor;

[0047] The sparse imaging and self-focusing models are transformed into alternating solutions to multiple sub-problems:

[0048] ;

[0049] in, Represents the growth factor, used to control the penalty factor The growth trend of In the iteration, update The process of represents the reconstruction operation process, which means the Radar images obtained in iterations; update The process is represented as a denoising process, and the update The process is expressed as the echo phase error update operation process, update The process is expressed as a Lagrange multiplier update process;

[0050] By taking partial derivatives of the augmented Lagrangian function, , and set the derivative to zero to solve the sparse imaging and self-focusing model, specifically:

[0051] ;

[0052] in, represents the conjugate transpose, represents the inverse of the matrix, Indicates the iterations, It means to find the phase of a complex number; Indicates that in the kth iteration, the denoising process and the Lagrange multiplier are updated respectively; is the k-th penalty factor, represents the soft threshold operator, represents the conjugate transpose of the actual echo;

[0053] when When , the iteration ends and the output ; Otherwise, let k=k+1 and repeat the update .

[0054] The beneficial effects brought about by the technical solution provided by the present invention include at least:

[0055] This paper introduces the ADMM algorithm within the augmented Lagrangian multiplier (ALM) framework, decomposing the optimization problem into multiple easily solvable subproblems and accelerating convergence by introducing Lagrangian terms. This method effectively compensates for phase errors and produces well-focused images. Unlike traditional point scattering sparse priors, this method exploits the underlying structured sparsity of objects in the image domain, significantly improving image reconstruction quality in weakly sparse scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A flowchart of a synthetic aperture radar sparse imaging and autofocusing method provided by an embodiment of the present invention;

[0057] Figure 2 It is a flowchart of the sparse imaging and autofocusing model in the present invention;

[0058] Figure 3 It is a simulated experimental scenario;

[0059] Figure 4 This is the imaging result obtained using the BP method;

[0060] Figure 5 This is the imaging result obtained using the FISTA-PGA method;

[0061] Figure 6 This is an imaging result diagram obtained using the synthetic aperture radar sparse imaging and self-focusing method provided by the present invention. DETAILED DESCRIPTION

[0062] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0063] Example 1:

[0064] This embodiment will describe a synthetic aperture radar sparse imaging and autofocusing method of the present invention in more detail with reference to the accompanying drawings. Figure 1 As shown, the following steps are included:

[0065] S1: The synthetic aperture radar transmits a broadband linear frequency modulated continuous wave signal from an ideal array element position and receives the echo. Assuming that the synthetic aperture radar moving platform has no motion error, an ideal observation matrix and ideal echo are obtained.

[0066] Assume the spatial position of the target is , the position of the ideal array element is , then the ideal echo S is:

[0067] ;

[0068] in, is the ideal echo at fast time t, is the triple integral operator symbol, is the target scattering function, σ is the target scattering coefficient, j is the imaginary unit, exp() is the exponential function, K is the frequency modulation slope, B is the sweep bandwidth, T is the pulse duration, and π is the circumference. yes The instantaneous frequency within the range, is the carrier frequency, t is the fast time, and c is the speed of light;

[0069] If both the ideal echo and the target scattering function are expressed as vectors, the ideal echo is:

[0070] ;

[0071] Where ω is the additive noise vector, P is the ideal observation matrix;

[0072] S2: In practice, the SAR platform experiences random three-dimensional jitter, and the actual SAR echo containing motion errors is obtained. The phase error between the actual echo and the ideal echo is calculated, and a mapping relationship between the actual echo and the ideal echo is constructed.

[0073] S21: Assuming that the antennas transmitting and receiving SAR signals are located at the same position, calculate the ideal distance R between the ideal SAR array element and the scattering point of the target:

[0074] ;

[0075] S22: Calculate the actual distance R between the actual array element of the synthetic aperture radar and the scattering point of the target, including motion errors e :

[0076] ;

[0077] in, It represents the actual position of the actual array element of the synthetic aperture radar, which is specifically expressed as:

[0078] ;

[0079] in, are the offset errors of the actual array element of the synthetic aperture radar along the x, y and z directions respectively;

[0080] It's important to note that in practical Synthetic Aperture Radar (SAR) applications, the SAR platform's motion is often affected by external environmental factors, causing jitter and making it difficult to precisely follow the ideal trajectory. When the actual path deviates from the ideal path, the position of the measurement elements often cannot be perfectly aligned with the ideal position, introducing motion errors and ultimately causing defocus in the radar image. Therefore, the three-dimensional jitter of the motion platform must be accounted for when calculating the actual distance between the radar element and the target scattering point.

[0081] S23: Calculate the actual echo of synthetic aperture radar including motion error:

[0082] ;

[0083] in, represents the actual echo including motion errors, represents the actual echo at fast time t; Indicates the error between the actual distance between the actual array element and the target and the ideal distance, Indicates the phase error between the actual echo and the ideal echo, is the observation matrix containing the motion error;

[0084] The mapping relationship between the actual echo and the ideal echo is expressed as:

[0085] ;

[0086] in, represents the Hadamard product, Indicates phase.

[0087] It should be noted that when the synthetic aperture radar motion platform is affected by external factors and cannot move along the ideal trajectory, the ideal observation matrix Will be offset to the actual observation matrix , thereby introducing a phase error between the ideal echo and the actual echo. By defining the phase , we can get the mapping relationship between the actual echo and the ideal echo.

[0088] S3: Based on the mapping relationship between actual echo and ideal echo, a sparse imaging and autofocus model is constructed;

[0089] According to the mapping relationship between the actual echo and the ideal echo, the initial objective function is constructed, which is:

[0090] ;

[0091] Among them, argmin means taking the minimum value of the initial objective function. is the Frobenius norm, Represents the phase error calibration matrix between the actual echo and the ideal echo;

[0092] Without considering the noise factor, the structured sparsity prior of the image is used, combined with the echo phase error estimation, to optimize the initial objective function and construct a sparse imaging and autofocus model:

[0093] ;

[0094] in, is the convolution operation, represents an arbitrarily small positive number, It is in k In the iteration, the update of the reconstruction operation represents the k The radar image obtained in the iteration; is the regularization parameter, Represents the convolution kernel.

[0095] It should be noted that in the sparse imaging and self-focusing models, the correlation between scatterers is introduced into the traditional norm and re-weights the values ​​of the previous iteration through convolution. This re-weighting method effectively captures the clustered sparsity in the image, thereby improving image quality.

[0096] S4: Solve the sparse imaging and self-focusing model by augmented Lagrangian function and alternating direction multiplier method to achieve sparse imaging and self-focusing of synthetic aperture radar;

[0097] Solve the sparse imaging and self-focusing models using the alternating direction multiplier method:

[0098] First, introduce auxiliary variables , the sparse imaging and self-focusing models are replaced by:

[0099] ;

[0100] Among them, st means that the satisfaction is subject to certain specific conditions;

[0101] Define the augmented Lagrangian function :

[0102] ;

[0103] in, represents the Lagrange multiplier, is the penalty factor;

[0104] The sparse imaging and self-focusing models are transformed into alternating solutions to multiple sub-problems:

[0105] ;

[0106] in, Represents the growth factor, used to control the penalty factor The growth trend of In the iteration, update The process represents the reconstruction operation process, indicating the Radar images obtained in iterations; update The process is represented as a denoising process, and the update The process is expressed as the echo phase error update operation process, update The process is expressed as a Lagrange multiplier update process;

[0107] By taking partial derivatives of the augmented Lagrangian function, , and set the derivative to zero to solve the sparse imaging and self-focusing model, specifically:

[0108] ;

[0109] in, represents the conjugate transpose, represents the inverse of the matrix, Indicates the iterations, It means to find the phase of a complex number; Indicates that in the kth iteration, the reconstruction operation, denoising process, and Lagrange multiplier are updated respectively; is the k-th penalty factor, represents the soft threshold operator, represents the conjugate transpose of the actual echo;

[0110] when When , the iteration ends and the output ; Otherwise, let k=k+1 and repeat the update .

[0111] It should be noted that the multivariable optimization problem of sparse imaging and autofocus model can be solved by alternating direction multiplier method (ADMM) to update The process represents the reconstruction operation process, updating The process is represented as a denoising process, and the update The process is expressed as phase error update operation, update The process is expressed as a Lagrange multiplier update process.

[0112] Simulation test

[0113] The effectiveness of the proposed method is evaluated in a simulation scenario. First, an equivalent scaled SAR imaging scenario is simulated. The target is located 0.4m from the radar, and a complex satellite point cloud consisting of 13,580 scatterers is used. The radar carrier frequency is 110GHz, the bandwidth is 4GHz, the number of sampling points is 101, the virtual aperture is 0.2m×0.2m, and the number of sampling points in both the horizontal and vertical directions is 150. Assuming that the platform experiences random jitter in three-dimensional space, the phase error range is , the sparse sampling rate is 0.5. In addition, Gaussian white noise is added to the echo, and the signal-to-noise ratio is set to 10dB.

[0114] like Figure 3-Figure 5 Imaging results obtained using BP, FISTA-PGA, and the proposed method are shown. As can be seen, in the presence of phase error, the images generated by the traditional BP algorithm exhibit significant defocus and artifacts. While FISTA-PGA partially suppresses background clutter and improves image quality, the target is still not fully focused. In contrast, the proposed method effectively compensates for phase error, produces a well-focused image, and effectively suppresses background clutter.

[0115] It should be noted that the serial numbers of the above-mentioned embodiments of the present invention are for descriptive purposes only and do not represent the advantages or disadvantages of the embodiments. In addition, the terms "including", "comprising" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, device, article or method comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, device, article or method. In the absence of further restrictions, an element defined by the sentence "including a ..." does not exclude the presence of other identical elements in the process, device, article or method comprising the element.

Claims

1. A synthetic aperture radar sparse imaging and self-focusing method, characterized in that: include: S1: The synthetic aperture radar transmits a broadband linear frequency modulated continuous wave signal from an ideal array element position and receives the echo. Assuming that the synthetic aperture radar moving platform has no motion error, an ideal observation matrix and ideal echo are obtained. S2: In practice, the SAR platform experiences random three-dimensional jitter, and the actual SAR echo containing motion errors is obtained. The phase error between the actual echo and the ideal echo is calculated, and a mapping relationship between the actual echo and the ideal echo is constructed. S3: Based on the mapping relationship between actual echo and ideal echo, a sparse imaging and autofocusing model is constructed; S4: Solve the sparse imaging and self-focusing model by augmented Lagrangian function and alternating direction multiplier method to realize sparse imaging and self-focusing of synthetic aperture radar.

2. The synthetic aperture radar sparse imaging and autofocusing method according to claim 1, wherein: Said S1 comprises: Assume the spatial position of the target is , the position of the ideal array element is , then the ideal echo S is: ; in, For fast time t The ideal echo, is the triple integral operator symbol, is the target scattering function, σ is the target scattering coefficient, j is the imaginary unit, exp() is the exponential function, K is the frequency modulation slope, B is the sweep bandwidth, T is the pulse duration, and π is the circumference. yes The instantaneous frequency within the range, is the carrier frequency, t is the fast time, and c is the speed of light.

3. The synthetic aperture radar sparse imaging and autofocusing method according to claim 2, wherein: Said S1 comprises: If both the ideal echo and the target scattering function are expressed as vectors, the ideal echo is: ； Where ω is the additive noise vector, P is the ideal observation matrix.

4. The synthetic aperture radar sparse imaging and autofocusing method according to claim 3, wherein: The S2 includes: S21: Assuming that the antennas transmitting and receiving SAR signals are located at the same position, calculate the ideal distance R between the ideal SAR array element and the scattering point of the target: ； S22: Calculate the actual distance R between the actual array element of the synthetic aperture radar and the scattering point of the target, including motion errors e : ; in, It represents the actual position of the actual array element of the synthetic aperture radar, which is specifically expressed as: ； in, are the offset errors of the actual array element of the synthetic aperture radar along the x, y and z directions respectively; S23: Calculate the actual echo of synthetic aperture radar including motion error: ； in, represents the actual echo including motion errors, represents the actual echo at fast time t; Indicates the error between the actual distance between the actual array element and the target and the ideal distance, Indicates the phase error between the actual echo and the ideal echo, is the observation matrix containing the motion error; The mapping relationship between the actual echo and the ideal echo is expressed as: ； in, represents the Hadamard product, Indicates phase.

5. The synthetic aperture radar sparse imaging and autofocusing method according to claim 4, wherein: The step S3 includes: constructing an initial objective function according to the mapping relationship between the actual echo and the ideal echo, specifically: ； Among them, argmin means taking the minimum value of the initial objective function. is the Frobenius norm, Represents the phase error calibration matrix between the actual echo and the ideal echo; By utilizing the structured sparsity prior of the image and combining it with the echo phase error estimation, the initial objective function is optimized to construct a sparse imaging and autofocus model: ； in, is the convolution operation, represents an arbitrarily small positive number, It is in k In the iteration, the update of the reconstruction operation represents the k The radar image obtained in the iteration; is the regularization parameter, Represents the convolution kernel.

6. The synthetic aperture radar sparse imaging and autofocusing method according to claim 5, characterized in that: The S4 includes: Solve the sparse imaging and self-focusing models using the alternating direction multiplier method: First, introduce auxiliary variables , the sparse imaging and self-focusing models are replaced by: ； Among them, st means that the satisfaction is subject to certain specific conditions; Define the augmented Lagrangian function : ； in, represents the Lagrange multiplier, is the penalty factor; The sparse imaging and self-focusing models are transformed into alternating solutions to multiple sub-problems: ； in, Represents the growth factor, used to control the penalty factor The growth trend of In the iteration, update The process represents the reconstruction operation process, indicating the Radar images obtained in iterations; update The process is represented as a denoising process, and the update The process is expressed as the echo phase error update operation process, update The process is expressed as a Lagrange multiplier update process; By taking partial derivatives of the augmented Lagrangian function, , and set the derivative to zero to solve the sparse imaging and self-focusing model, specifically: ； in, represents the conjugate transpose, represents the inverse of the matrix, Indicates the iterations, It means to find the phase of a complex number; Indicates that in the kth iteration, the denoising process and the Lagrange multiplier are updated respectively; For the k The penalty factor, represents the soft threshold operator, represents the conjugate transpose of the actual echo; when When , the iteration ends and the output Otherwise, let k=k+ 1. Repeated updates .

Images