Multi-channel radar foresight super-resolution imaging method based on structured sparseness

Abstract

The invention relates to a multi-channel radar foresight super-resolution imaging method based on structured sparseness, and relates to the technical field of radars, and the method comprises the steps: building an echo signal model in a multi-channel radar foresight imaging mode, processing a target echo signal obtained according to the echo signal model, and obtaining a corrected target echo signal; obtaining a structured sparse characteristic analysis result corresponding to the corrected target echo signal according to the structured sparse characteristic of the existing image; performing iterative convolution processing on the structured sparse characteristic analysis result to obtain a constraint optimization problem of multichannel radar structured sparse foresight imaging; and solving the constraint optimization problem of multichannel radar structured sparse foresight imaging through an alternating direction multiplier method to obtain a foresight high-resolution image of the target. According to the technical scheme, the structured sparse characteristic analysis result is obtained through iterative convolution processing, the anti-noise capability is improved through iterative convolution, and finally the foresight high-resolution image with the structured sparse characteristic is obtained.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and in particular to a multi-channel radar forward-looking super-resolution imaging method based on structured sparseness. Background Art

[0002] Radar forward imaging can provide detailed electromagnetic scattering characteristics of the target directly in front of the moving platform, which is crucial in applications such as terrain measurement, precision guidance and autonomous driving. At present, when radars using synthetic aperture systems image the forward-looking area, the Doppler resolution principle they rely on completely fails, forming a forward-looking "blind spot". For radar systems using real beam imaging, since the azimuth resolution is completely limited by the beam width, the imaging resolution cannot meet the actual needs of the moving platform.

[0003] Imaging methods based on compressed sensing take advantage of the sparse distribution of targets in the imaging scene and push the echo data of the short-aperture antenna to the echo data corresponding to the long-aperture antenna, which provides feasibility for realizing radar forward-looking super-resolution imaging. However, traditional imaging methods based on compressed sensing (CS) often do not consider the relationship between different scattering points. The image is composed of independent strong scattering points, which makes it difficult to identify targets based on forward-looking images. In addition, noise can easily affect the imaging method based on compressed sensing, resulting in a large number of false scattering points in the imaging results, thereby affecting the overall imaging performance. Summary of the invention

[0004] In order to solve the above problems existing in the prior art, the present invention provides a multi-channel radar forward-looking super-resolution imaging method based on structured sparse.

[0005] According to a first aspect of an embodiment of the present invention, a multi-channel radar forward-looking super-resolution imaging method based on structured sparseness is provided, the method comprising:

[0006] Establishing an echo signal model in a multi-channel radar forward-looking imaging mode, processing a target echo signal obtained according to the echo signal model, and obtaining a corrected target echo signal;

[0007] Obtaining a structured sparse characteristic analysis result corresponding to the corrected target echo signal according to the structured sparse characteristic of the existing image;

[0008] Performing iterative convolution processing on the structured sparse characteristic analysis result to obtain a constrained optimization problem of multi-channel radar structured sparse forward imaging;

[0009] The constrained optimization problem of the multi-channel radar structured sparse forward-looking imaging is solved by the alternating direction multiplier method to obtain a forward-looking high-resolution image of the target.

[0010] Optionally, establishing an echo signal model in a multi-channel radar forward-looking imaging mode, and processing a target echo signal obtained according to the echo signal model to obtain a corrected target echo signal includes:

[0011] Establish the echo signal model in the multi-channel radar forward imaging mode to obtain the target echo signal;

[0012] Performing pulse compression on the target echo signal to obtain a pulse-compressed target echo signal;

[0013] The target echo signal after pulse compression is corrected for range movement to obtain the corrected target echo signal.

[0014] Optionally, performing iterative convolution processing on the structured sparse characteristic analysis result to obtain a constrained optimization problem of multi-channel radar structured sparse forward imaging includes:

[0015] Performing motion compensation on the corrected target echo signal to obtain a two-dimensional echo matrix;

[0016] Performing iterative convolution processing on the structured sparse characteristic analysis result to obtain a convolution processing result;

[0017] A constrained optimization problem of the multi-channel radar structured sparse forward-looking imaging is established according to the convolution processing result and the two-dimensional echo matrix.

[0018] Optionally, solving the constrained optimization problem of the multi-channel radar structured sparse forward-looking imaging by an alternating direction multiplier method to obtain a forward-looking high-resolution image of the target includes:

[0019] Converting the constrained optimization problem of the multi-channel radar structured sparse forward-looking imaging into a convex optimization problem;

[0020] The convex optimization problem is solved by the alternating direction multiplier method to obtain a forward-looking high-resolution image of the target.

[0021] Optionally, solving the convex optimization problem by the alternating direction multiplier method to obtain a forward-looking high-resolution image of the target includes:

[0022] Converting the convex optimization problem into an expression of an augmented Lagrangian function to obtain a converted convex optimization problem;

[0023] The transformed convex optimization problem is iteratively solved by the alternating direction multiplier method to obtain a forward-looking high-resolution image of the target.

[0024] Optionally, the corrected target echo signal is expressed as follows:

[0025]

[0026] Among them, S rc (τ, t) represents the corrected target echo signal, τ represents fast time, t represents slow time, A represents the complex scattering coefficient of the target, c represents the speed of light, B represents the bandwidth, R 0 is the slant distance from the center of the array antenna of the multi-channel radar to the target, exp(·) represents an exponential function, j represents an imaginary unit, R(t) represents the distance from the nth antenna array element of the multi-channel radar to the target P, λ represents the wavelength of the multi-channel radar, and v a represents the switching speed of the array element transmitting signal of the multi-channel radar, x 0 represents the horizontal coordinate of the target, y 0 represents the ordinate of the target, and v represents the flight speed of the radar platform of the multi-channel radar.

[0027] Optionally, the two-dimensional echo matrix is ​​expressed as follows:

[0028] S rc =Y+E=FX+E;

[0029] Among them, S rc represents the two-dimensional echo matrix, Y represents the signal matrix, E represents the noise matrix, F is the dictionary matrix, and X is the two-dimensional image matrix of the radar image.

[0030] Optionally, the constrained optimization problem of the multi-channel radar structured sparse forward imaging is expressed as follows:

[0031]

[0032] Among them, ω represents the convolution kernel matrix, ||·|| 1 Indicates l 1 norm,||·|| F represents the Frobenius norm, represents a two-dimensional convolution operation, ⊙ represents a matrix Hadamard product operation, ε represents an arbitrary minimum value, λ' represents a regularization parameter, represents the optimization objective of the constrained optimization problem of multi-channel radar structured sparse forward imaging, stS rc =FX+E represents the constraint conditions of the constrained optimization problem of the multi-channel radar structured sparse forward imaging.

[0033] The technical solution provided by the present invention may include the following beneficial effects:

[0034] Through the above technical scheme, the present invention proposes a forward-looking super-resolution imaging method based on structured sparseness, obtains a forward-looking image of the target with structured characteristics, improves the anti-noise ability of the imaging through iterative convolution, and obtains a high-quality forward-looking high-resolution image.

[0035] Other features and advantages of the present invention will be described in detail in the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the following specific embodiments, they are used to explain the present invention but do not constitute a limitation of the present invention. In the accompanying drawings:

[0037] Figure 1 The present invention is a flowchart of a multi-channel radar forward-looking super-resolution imaging method based on structured sparse according to an exemplary embodiment.

[0038] Figure 2 The diagram is a schematic diagram of observation geometry of a multi-channel radar forward-looking imaging according to an exemplary embodiment.

[0039] Figure 3a FIG. 4 is an imaging result of a long aperture data according to an exemplary embodiment.

[0040] Figure 3b FIG. 4 is an imaging result of a short aperture data according to an exemplary embodiment.

[0041] Figure 4 It is a schematic diagram of a measured experimental scenario according to an exemplary embodiment.

[0042] Figure 5 It is a schematic diagram of key parameters of a radar system in a measured experiment according to an exemplary embodiment.

[0043] Figure 6a is a schematic diagram of an imaging result of the present invention according to an exemplary embodiment.

[0044] Figure 6b It is a schematic diagram of imaging results of a real beam imaging method according to an exemplary embodiment.

[0045] Figure 6c It is a schematic diagram of imaging results of a traditional compressed sensing imaging method according to an exemplary embodiment.

[0046] Figure 6d It is a schematic diagram of imaging results of a weighted compressed sensing imaging method according to an exemplary embodiment.

[0047] Figure 7ais another schematic diagram of an imaging result of the present invention shown according to an exemplary embodiment.

[0048] Figure 7b It is a schematic diagram of imaging results of another real beam imaging method according to an exemplary embodiment.

[0049] Figure 7c It is a schematic diagram of another conventional imaging result based on a compressed sensing imaging method according to an exemplary embodiment.

[0050] Figure 7d It is a schematic diagram of imaging results of another weighted compressed sensing imaging method according to an exemplary embodiment. DETAILED DESCRIPTION

[0051] Figure 1 is a flowchart of a multi-channel radar forward-looking super-resolution imaging method based on structured sparse according to an exemplary embodiment, such as Figure 1 As shown, the method includes the following steps.

[0052] S101, establishing an echo signal model in a multi-channel radar forward-looking imaging mode, and processing a target echo signal obtained according to the echo signal model to obtain a corrected target echo signal.

[0053] Optionally, S101 may include:

[0054] Establish the echo signal model in the multi-channel radar forward imaging mode to obtain the target echo signal;

[0055] Performing pulse compression on the target echo signal to obtain a pulse compressed target echo signal;

[0056] The target echo signal after pulse compression is corrected for range movement to obtain a corrected target echo signal.

[0057] Understandably, Figure 2 is a schematic diagram of observation geometry of a multi-channel radar forward imaging according to an exemplary embodiment. Figure 2 The multi-channel radar shown in the figure works in the "single-transmit single-receive" mode, that is, the N array elements on the array antenna transmit signals and receive echoes in turn at a pulse repetition interval (PRI). Assume that there is a target P (x 0 ,y 0 ,0), the distance from the nth antenna array element to the point target P is:

[0058]

[0059] Among them, t represents slow time, H and v are the height and flight speed of the radar platform respectively, and x 0 and 0 They represent the horizontal and vertical coordinates of the target P. Assuming d represents the array element spacing, then v a =d / PRI is the switching speed of the array element transmitting signal, which is also the equivalent azimuth movement speed.

[0060] In the forward imaging of small moving platforms such as drones, the distance between the target and the radar platform is usually large relative to the length of the array antenna, so the above formula can be approximated as:

[0061]

[0062] in, is the slant distance from the center of the multi-channel radar array antenna to the target P.

[0063] Assume that the linear frequency modulation signal s(τ) emitted by the radar is:

[0064]

[0065] Among them, τ represents fast time, G represents the distance window function, and f c is the carrier frequency, and γ is the frequency modulation slope. If the complex scattering coefficient of the target P is A, then after coherent demodulation, the target echo signal s(τ,t) is:

[0066]

[0067] Where λ is the wavelength and c is the speed of light.

[0068] The target echo signal s(τ,t) is pulse compressed, and the target echo signal S after range pulse compression is rc (τ,t) can be expressed as:

[0069]

[0070] Where B is the bandwidth and sinc(·) represents the Sinque function.

[0071] Optionally, the corrected target echo signal is expressed as follows:

[0072]

[0073] Among them, S rc (τ, t) represents the corrected target echo signal, τ represents the fast time, t represents the slow time, A represents the complex scattering coefficient of the target, c represents the speed of light, B represents the bandwidth, and R 0is the slant distance from the center of the multi-channel radar array antenna to the target, exp(·) represents the exponential function, j represents the imaginary unit, R(t) represents the distance from the nth antenna array element of the multi-channel radar to the target P, λ represents the wavelength of the multi-channel radar, and v a Indicates the switching speed of the array element transmission signal of the multi-channel radar, x 0 Indicates the horizontal coordinate of the target, y 0 represents the ordinate of the target, and v represents the flight speed of the radar platform of the multi-channel radar.

[0074] S102: Obtain a structured sparse characteristic analysis result corresponding to the corrected target echo signal according to the structured sparse characteristic of the existing image.

[0075] S103, performing iterative convolution processing on the structured sparse characteristic analysis result to obtain a constrained optimization problem of multi-channel radar structured sparse forward imaging.

[0076] Optionally, S103 may include:

[0077] Performing motion compensation on the corrected target echo signal to obtain a two-dimensional echo matrix;

[0078] Performing iterative convolution processing on the structured sparse characteristic analysis result to obtain a convolution processing result;

[0079] The constrained optimization problem of multi-channel radar structured sparse forward-looking imaging is established based on the convolution processing results and the two-dimensional echo matrix.

[0080] Optionally, the two-dimensional echo matrix is ​​represented as follows:

[0081] S rc =Y+E=FX+E;

[0082] Among them, S rc represents the two-dimensional echo matrix, Y represents the signal matrix, E represents the noise matrix, F is the dictionary matrix, and X is the two-dimensional image matrix of the radar image.

[0083] It is understandable that in the front-view super-resolution imaging technology based on compressed sensing, short-aperture data is used to derive long-aperture data, which requires the introduction of prior information to ensure the accuracy of image reconstruction. Sparse prior is a common method that uses l 0 or 1 Norm constraints are used to exploit the sparse distribution of targets in the imaging scene to reconstruct high-resolution images. Nevertheless, existing sparse imaging algorithms can usually only reconstruct isolated strong scatterers, but cannot reflect the relationship between scatterers or identify weak scatterers. For example, Figure 3a is an imaging result of a long aperture data according to an exemplary embodiment. Figure 3bis an imaging result of a short aperture data according to an exemplary embodiment, such as Figure 3a and Figure 3b As shown, by comparing the imaging results of long aperture and short aperture data, it can be seen that real beam imaging technology can display a continuous distribution of scattering points and show structured sparse features.

[0084] Optionally, by introducing a continuity of scattering points 1 Minimization, that is, the convolution of the neighborhood values ​​obtained in the previous iteration is reweighted. The constrained optimization problem of multi-channel radar structured sparse forward imaging is expressed as follows:

[0085]

[0086] Among them, ω represents the convolution kernel matrix, ||·|| 1 Indicates l 1 norm,||·|| F represents the Frobenius norm, represents a two-dimensional convolution operation, ⊙ represents a matrix Hadamard product operation, ε represents an arbitrary minimum value, λ' represents a regularization parameter, represents the optimization objective of the constrained optimization problem of multi-channel radar structured sparse forward imaging, stS rc =FX+E represents the constraint conditions of the constrained optimization problem of multi-channel radar structured sparse forward imaging.

[0087] S104. Solve the constrained optimization problem of multi-channel radar structured sparse forward-looking imaging by using an alternating direction multiplier method to obtain a forward-looking high-resolution image of the target.

[0088] Optionally, S104 may include:

[0089] The constrained optimization problem of multi-channel radar structured sparse forward imaging is converted into a convex optimization problem;

[0090] The convex optimization problem is solved by the alternating direction multiplier method to obtain the forward-looking high-resolution image of the target.

[0091] Optionally, the convex optimization problem is solved by an alternating direction multiplier method to obtain a forward-looking high-resolution image of the target, including:

[0092] The convex optimization problem is converted into the expression form of augmented Lagrangian function to obtain the converted convex optimization problem;

[0093] The transformed convex optimization problem is iteratively solved by the alternating direction multiplier method to obtain the forward-looking high-resolution image of the target.

[0094] In one embodiment, the convex optimization problem can be expressed as:

[0095]

[0096] The convex optimization problem is transformed into the expression of augmented Lagrangian function. Let J = X. Then the optimization problem is expressed in the form of augmented Lagrangian function:

[0097]

[0098] Among them, Q 1 , Q 2 is the Lagrange multiplier matrix, u 1 、u 2 is the penalty term coefficient. The alternating direction multiplier method is used to alternately estimate the variables J, X, and E, that is, to estimate one variable while keeping other variables unchanged.

[0099] Then update the iteration to solve the value of each variable, the k-th iteration solution of variable J is:

[0100] J k+1 =max(0,R 1 k )+min(0,R 2 k );

[0101] in, η is an arbitrary minimum value to avoid singular values ​​during the calculation process.

[0102] The k-th iteration solution of variable X is:

[0103]

[0104] Where I is the identity matrix.

[0105] The k-th iteration solution of variable E is:

[0106]

[0107] By continuously iterating to solve J, X, E, until the termination condition || S is met rc -FX k || F / ||S rc || F ≤10 -6 Or the maximum number of iterations is reached, and finally a forward-looking high-resolution image that retains the structured sparse characteristics is obtained.

[0108] In one embodiment, the present invention is verified based on the actual measured data experiment. The actual measured conditions are as follows:

[0109] Figure 4is a schematic diagram of a measured experimental scenario according to an exemplary embodiment. Figure 4 As shown, the experimental data is obtained from the AWR2243 cascade radar. The experimental scene is located in a parking lot and the experimental targets are two cars. Figure 5 It is a schematic diagram of key parameters of a radar system in a measured experiment according to an exemplary embodiment.

[0110] Test content 1: Verify the super-resolution imaging capability of the method of the present invention. Figure 6a is a schematic diagram of an imaging result of the present invention according to an exemplary embodiment. Figure 6b is a schematic diagram of imaging results of a real beam imaging method according to an exemplary embodiment. Figure 6c is a schematic diagram of imaging results based on a traditional compressed sensing imaging method according to an exemplary embodiment. Figure 6d The present invention is a schematic diagram of imaging results of a weighted compressed sensing imaging method according to an exemplary embodiment. Taking 8 times super-resolution of foresight imaging as a benchmark, the imaging results of the method of the present invention are compared with those of a real beam imaging method, a traditional compressed sensing imaging method and a weighted compressed sensing imaging method.

[0111] From a visual perspective, the imaging method proposed by the present invention can distinguish the two cars, and the outlines are more obvious, the structural information of the target is preserved, and a satisfactory imaging result can be produced. Figure 6a It can be seen that the present invention has a higher super-resolution imaging capability and can retain more information of the target; Figure 6b It can be seen that the two cars are fused together in the real beam method imaging results and cannot be distinguished at all; Figure 6c and Figure 6d It can be seen that the traditional compressed sensing method and the weighted compressed sensing method are also difficult to distinguish between the two vehicles, and many false scattering points appear in the imaging results, which seriously affects the detection of subsequent targets.

[0112] Test content 2: Verify the noise robustness of the method of the present invention. Figure 7a is another schematic diagram of imaging results of the present invention according to an exemplary embodiment. Figure 7b is a schematic diagram of imaging results of another real beam imaging method according to an exemplary embodiment. Figure 7c is a schematic diagram of another conventional imaging result based on a compressed sensing imaging method according to an exemplary embodiment. Figure 7dIt is a schematic diagram of imaging results of another weighted compressed sensing imaging method according to an exemplary embodiment. Taking the signal-to-noise ratio of 5dB as a benchmark, the imaging results of the method of the present invention are compared with those of a real beam imaging method, a traditional compressed sensing imaging method and a weighted compressed sensing imaging method.

[0113] The target of the method of the present invention is still clear and distinguishable, and has strong anti-dry noise ability, such as Figure 7a shown; from Figure 7b It can be seen that although the real beam imaging method is not sensitive to noise, the two cars are completely fused together in the imaging results and cannot be distinguished. Figure 7c and Figure 7d It can be seen that when the signal-to-noise ratio is low, the imaging target based on compressed sensing and weighted compressed sensing methods is submerged by noise, and more false scattering points appear.

[0114] Aiming at the problem that the existing forward-looking imaging method based on compressed sensing does not consider the connection between the target scattering points, the present invention proposes a multi-channel radar forward-looking super-resolution imaging method based on structured sparseness, which improves the imaging resolution while retaining the structural characteristics of the target and has strong noise robustness. The weight of each pixel in the next iteration is calculated by convolution of its neighbor values ​​in the current solution during the solution process of the alternating direction multiplier method to obtain the structured sparse characteristics of the target, and a multi-channel radar structured sparse forward-looking super-resolution imaging model based on convolution weighting is established to improve the imaging performance.

[0115] The preferred embodiments of the present invention are described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, a variety of simple modifications can be made to the technical solution of the present invention, and these simple modifications all belong to the protection scope of the present invention.

[0116] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not further describe various possible combinations.

[0117] In addition, various embodiments of the present invention may be arbitrarily combined, and as long as they do not violate the concept of the present invention, they should also be regarded as the contents disclosed by the present invention.

Claims

1. A multi-channel radar forward-looking super-resolution imaging method based on structured sparseness, characterized in that: The method comprises: Establishing an echo signal model in a multi-channel radar forward-looking imaging mode, processing a target echo signal obtained according to the echo signal model, and obtaining a corrected target echo signal; Obtaining a structured sparse characteristic analysis result corresponding to the corrected target echo signal according to the structured sparse characteristic of the existing image; Performing iterative convolution processing on the structured sparse characteristic analysis result to obtain a constrained optimization problem of multi-channel radar structured sparse forward imaging; The constrained optimization problem of the multi-channel radar structured sparse forward-looking imaging is solved by the alternating direction multiplier method to obtain a forward-looking high-resolution image of the target.

2. The multi-channel radar forward-looking super-resolution imaging method based on structured sparse according to claim 1 is characterized in that: The step of establishing an echo signal model in a multi-channel radar forward-looking imaging mode and processing a target echo signal obtained according to the echo signal model to obtain a corrected target echo signal includes: Establish the echo signal model in the multi-channel radar forward imaging mode to obtain the target echo signal; Performing pulse compression on the target echo signal to obtain a pulse-compressed target echo signal; The target echo signal after pulse compression is corrected for range movement to obtain the corrected target echo signal.

3. The multi-channel radar forward-looking super-resolution imaging method based on structured sparse according to claim 1 is characterized in that: The iterative convolution processing is performed on the structured sparse characteristic analysis result to obtain the constrained optimization problem of multi-channel radar structured sparse forward imaging, including: Performing motion compensation on the corrected target echo signal to obtain a two-dimensional echo matrix; Performing iterative convolution processing on the structured sparse characteristic analysis result to obtain a convolution processing result; A constrained optimization problem of the multi-channel radar structured sparse forward-looking imaging is established according to the convolution processing result and the two-dimensional echo matrix.

4. The multi-channel radar forward-looking super-resolution imaging method based on structured sparse according to claim 3 is characterized in that: The method of solving the constrained optimization problem of the multi-channel radar structured sparse forward-looking imaging by an alternating direction multiplier method to obtain a forward-looking high-resolution image of the target includes: Converting the constrained optimization problem of the multi-channel radar structured sparse forward-looking imaging into a convex optimization problem; The convex optimization problem is solved by the alternating direction multiplier method to obtain a forward-looking high-resolution image of the target.

5. The multi-channel radar forward-looking super-resolution imaging method based on structured sparse according to claim 4 is characterized in that: The method of solving the convex optimization problem by the alternating direction multiplier method to obtain a forward-looking high-resolution image of the target includes: Converting the convex optimization problem into an expression of an augmented Lagrangian function to obtain a converted convex optimization problem; The transformed convex optimization problem is iteratively solved by the alternating direction multiplier method to obtain a forward-looking high-resolution image of the target.

6. The multi-channel radar forward-looking super-resolution imaging method based on structured sparse according to claim 2 is characterized in that: The corrected target echo signal is expressed as follows: Among them, S rc (τ, t) represents the corrected target echo signal, τ represents fast time, t represents slow time, A represents the complex scattering coefficient of the target, c represents the speed of light, B represents the bandwidth, R0 is the slant distance from the center of the array antenna of the multi-channel radar to the target, exp(·) represents the exponential function, j represents the imaginary unit, R(t) represents the distance from the nth antenna array element of the multi-channel radar to the target P, λ represents the wavelength of the multi-channel radar, and v a represents the switching speed of the array element transmitting signal of the multi-channel radar, x0 represents the horizontal coordinate of the target, y0 represents the vertical coordinate of the target, and v represents the flight speed of the radar platform of the multi-channel radar.

7. The multi-channel radar forward-looking super-resolution imaging method based on structured sparse according to claim 3 is characterized in that: The two-dimensional echo matrix is ​​expressed as follows: S rc =Y+E=FX+E; Among them, S rc represents the two-dimensional echo matrix, Y represents the signal matrix, E represents the noise matrix, F is the dictionary matrix, and X is the two-dimensional image matrix of the radar image.

8. The multi-channel radar forward-looking super-resolution imaging method based on structured sparse according to claim 7 is characterized in that: The constrained optimization problem of multi-channel radar structured sparse forward imaging is expressed as follows: s.t.S rc =FX+E Among them, ω represents the convolution kernel matrix, ·1 represents the l1 norm, · F represents the Frobenius norm, represents a two-dimensional convolution operation, ⊙ represents a matrix Hadamard product operation, ε represents an arbitrary minimum value, λ' represents a regularization parameter, represents the optimization objective of the constrained optimization problem of multi-channel radar structured sparse forward imaging, stS rc =FX+E represents the constraint conditions of the constrained optimization problem of the multi-channel radar structured sparse forward imaging.

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