Meshless azimuth super-resolution sparse aperture ISAR imaging method and system

Abstract

The invention relates to a meshless azimuth super-resolution sparse aperture ISAR (inverse synthetic aperture radar) imaging method and a meshless azimuth super-resolution sparse aperture ISAR imaging system, which are used for performing one-dimensional imaging processing on all effective distance units of received echo to obtain a super-resolution one-dimensional azimuth image of a target and further obtain a super-resolution ISAR image of the target. Sparse representation of missing azimuth echoes in a single distance unit is established based on a meshless compressed sensing framework, super-resolution one-dimensional azimuth imaging is modeled into an underdetermined inverse problem based on OANM and solved through a fast algorithm, and after a positive semidefinite Toeplitz matrix and an echo signal of the azimuth echoes of the distance unit are reconstructed, the sparse representation of the missing azimuth echoes in the distance unit is obtained. Vandermonde decomposition is carried out on the reconstructed Toeplitz matrix to obtain a super-resolution one-dimensional azimuth image, and a super-resolution ISAR image with a complete target is drawn, so that the technical effects of avoiding an off-grid error, being not constrained by a minimum atomic distance and improving the ISAR image quality under sparse aperture and short aperture radar observation conditions are achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of radar imaging, and relates to a gridless azimuth super-resolution sparse aperture ISAR imaging method and system. Background Art

[0002] Inverse synthetic aperture radar (ISAR) has the advantage of working all day and all weather, and has been widely used in many industries. The ISAR images obtained can characterize the backscatter distribution of the target, which is the basis for subsequent target characteristic diagnosis, three-dimensional reconstruction and automatic target recognition. However, in practical applications, due to factors such as limited radar resources, high-speed maneuvering of targets and noise interference, the received echo data usually has equivalent missing in the slow time dimension, and sparse aperture phenomenon occurs from time to time. In addition, the effective imaging period contained in the received echo data is usually short (or the radar exposure time is short due to limited radar resources, or it is difficult to effectively compensate for the long-term observation echo due to the limited performance of the existing motion compensation method), resulting in a small effective cumulative angle and short-aperture observation. At this time, the ISAR image obtained based on the traditional range-Doppler (RD) imaging method will face the challenges of defocusing and low resolution in the azimuth dimension, which is specifically manifested in the strong grating lobe, wide main lobe and high sidelobe problems in the ISAR image.

[0003] Most of the existing SA-ISAR imaging methods use gridded compressed sensing technology, which to a certain extent suppresses the strong grating lobes caused by sparse aperture and suppresses the side lobes. However, this type of existing method inherently has off-grid errors caused by the deviation of the scattering center from the preset grid, and there is still a lot of room for improvement in the quality of ISAR images. On this basis, the existing SA-ISAR imaging method based on gridless compressed sensing technology avoids off-grid errors and improves the quality of ISAR images, but it usually does not have the ability of super-Rayleigh resolution, and its application is constrained by the minimum atomic distance. When the minimum atomic distance constraint cannot be met, robust sparse recovery cannot be guaranteed, and low-quality ISAR images may be produced. Therefore, how to improve the quality of ISAR images under sparse aperture and short aperture radar observation conditions has become a technical problem to be solved, and solving this technical problem has important engineering application value. Summary of the invention

[0004] In view of the problems existing in the above-mentioned traditional technologies, the present invention proposes a gridless azimuthal super-resolution sparse aperture ISAR imaging method and a gridless azimuthal super-resolution sparse aperture ISAR imaging system, which can avoid off-grid errors under sparse aperture and short aperture radar observation conditions, are not constrained by the minimum atomic distance, and improve the ISAR image quality.

[0005] In order to achieve the above objectives, the embodiments of the present invention adopt the following technical solutions: On the one hand, a gridless azimuth super-resolution sparse aperture ISAR imaging method is provided, comprising the steps of: After receiving the broadband radar echo, demodulation and pulse compression are performed to obtain the echo model; Based on the echo model, the missing azimuth echo corresponding to a single range unit after motion compensation is sparsely represented; The super-resolution one-dimensional imaging of sparse aperture azimuth echoes is transformed into an orthogonal atomic norm minimization problem; The iterative Vandermonde shrinkage threshold algorithm is used to quickly solve the orthogonal atomic norm minimization problem and obtain the optimal solution; The optimal solution is decomposed by Vandermonde to obtain a super-resolution one-dimensional azimuth image of the target; According to the orthogonal atomic norm minimization problem, the missing azimuth echoes of all effective range units are quickly solved to obtain the super-resolution one-dimensional azimuth image of each effective range unit and draw the azimuth super-resolution ISAR image of the target.

[0006] On the other hand, a gridless azimuth super-resolution sparse aperture ISAR imaging system is also provided, comprising: The echo acquisition module is used to receive the broadband radar echo, perform demodulation and pulse compression, and obtain the echo model; An echo characterization module, used for sparsely characterizing the missing azimuth echo corresponding to a single range unit after motion compensation based on an echo model; A problem conversion module is used to convert the super-resolution one-dimensional imaging of sparse aperture azimuth echoes into an orthogonal atomic norm minimization problem; A fast solution module is used to quickly solve the orthogonal atomic norm minimization problem using an iterative Vandermonde shrinkage threshold algorithm to obtain the optimal solution; An azimuth image acquisition module is used to acquire a super-resolution one-dimensional azimuth image of the target by using Vandermonde decomposition on the optimal solution; The super-resolution imaging module is used to quickly solve the missing azimuth echoes of all effective range units according to the orthogonal atomic norm minimization problem, obtain the super-resolution one-dimensional azimuth image of each effective range unit and draw the azimuth super-resolution ISAR image of the target.

[0007] One of the above technical solutions has the following advantages and beneficial effects: The above-mentioned gridless azimuth super-resolution sparse aperture ISAR imaging method and system obtains a super-resolution one-dimensional azimuth image of the target by performing one-dimensional imaging processing on all effective range units of the received echo, and then obtains a super-resolution ISAR image of the target. First, a sparse representation of the missing azimuth echo in a single range unit is established based on the gridless compressed sensing framework, and then the super-resolution one-dimensional azimuth imaging is modeled as an underdetermined inverse problem based on the orthogonal atomic norm. Then, a fast algorithm of iterative Vandermonde decomposition shrinkage threshold is used to solve the semi-positive definite Toeplitz matrix and echo signal of the azimuth echo of the range unit. Then, the reconstructed semi-positive definite Toeplitz matrix is ​​subjected to Vandermonde decomposition, and the number, position and amplitude of the scattering centers in the range unit are estimated in turn. Finally, all effective range units are subjected to super-resolution one-dimensional azimuth imaging processing and a complete super-resolution ISAR image of the target is drawn. The problem of low image quality in existing ISAR imaging methods caused by strong grating lobes, wide main lobes, high side lobes, grid errors and failure to meet the minimum atomic constraint conditions is alleviated, and the technical effect of avoiding grid errors and not being constrained by the minimum atomic distance is achieved under sparse aperture and short aperture radar observation conditions, thereby improving the ISAR image quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the conventional technology, the drawings required for use in the embodiments or the conventional technology descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0009] Figure 1 A flowchart of a gridless azimuth super-resolution sparse aperture ISAR imaging method in one embodiment; Figure 2 It is a schematic diagram of a specific implementation flow of a gridless azimuthal super-resolution sparse aperture ISAR imaging method in one embodiment; Figure 3 A schematic diagram of a mid-point simulation aircraft target model in an embodiment; Figure 4 This is a schematic diagram of imaging a point-simulated aircraft target under full aperture conditions in one embodiment, wherein: Figure 4 (a) is a one-dimensional range image sequence, Figure 4 (b) is the ISAR image of the RD method; Figure 5 This is a schematic diagram of imaging of a point-simulated aircraft target under the condition of 50% sparsity in one embodiment, wherein: Figure 5 (a) is a one-dimensional range image sequence, Figure 5 (b) is the ISAR image of the RD method, Figure 5(c) is the ISAR image of the method of the present invention; Figure 6 It is a cross-sectional diagram (one-dimensional azimuth image) of the ISAR image obtained by different methods at the 171st distance unit of the point simulation aircraft target under the condition of 50% sparsity in one embodiment; Figure 7 FIG. 1 is a schematic diagram of imaging a cone combination target under full aperture conditions in an embodiment, wherein: Figure 7 (a) is a one-dimensional range image sequence, Figure 7 (b) is the ISAR image of the RD method; Figure 8 FIG. 1 is a schematic diagram of imaging of a cone combination target under the condition of 50% sparsity in one embodiment, wherein: Figure 8 (a) is a one-dimensional range image sequence, Figure 8 (b) is the ISAR image of the RD method, Figure 8 (c) is the ISAR image of the method of the present invention; Fig. 9 It is a cross-sectional diagram (one-dimensional azimuth image) of the ISAR image obtained by different methods at the 26th distance unit of the cone-combined target under the condition of 50% sparsity in an embodiment; Fig.10 The module block diagram of a gridless azimuthal super-resolution sparse aperture ISAR imaging system in one embodiment. DETAILED DESCRIPTION

[0010] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings and Examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art of the present invention. The terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0011] It should be noted that the reference to "embodiment" in this article means that the specific features, structures or characteristics described in conjunction with the embodiment may be included in at least one embodiment of the present invention. The presentation of this phrase at various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It will be appreciated by those skilled in the art that the embodiments described herein may be combined with other embodiments. The term "and / or" used in the specification and appended claims of the present invention refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations.

[0012] The following will describe the implementation of the present invention in detail with reference to the accompanying drawings in the embodiment diagram of the present invention.

[0013] In view of the problem of low imaging quality of existing ISAR imaging methods, this specification proposes an azimuth super-resolution sparse aperture inverse synthetic aperture radar (SA-ISAR) imaging method based on orthonormal atomic norm minimization (OANM)-iterative Vandermonde decomposition and shrinkage-Thresholding (IVDST), hereinafter referred to as a gridless azimuth super-resolution sparse aperture ISAR imaging method.

[0014] In one embodiment, Figure 1 As shown, a gridless azimuth super-resolution sparse aperture ISAR imaging method is provided, which may include the following steps S10 to S20: S10, receiving the broadband radar echo, performing demodulation and pulse compression to obtain an echo model; S12, sparsely representing the missing azimuth echo corresponding to a single range unit after motion compensation based on the echo model; S14, super-resolution one-dimensional imaging of sparse aperture azimuth echoes is transformed into an orthogonal atomic norm minimization problem; S16, using the iterative Vandermonde shrinkage threshold algorithm to quickly solve the orthogonal atomic norm minimization problem and obtain the optimal solution; S18, using Vandermonde decomposition on the optimal solution to obtain a super-resolution one-dimensional azimuth image of the target; S20, according to the orthogonal atomic norm minimization problem, the missing azimuth echoes of all effective range units are quickly solved to obtain a super-resolution one-dimensional azimuth image of each effective range unit and draw an azimuth super-resolution ISAR image of the target.

[0015] The above-mentioned gridless azimuth super-resolution sparse aperture ISAR imaging method obtains a super-resolution one-dimensional azimuth image of the target by performing one-dimensional imaging processing on all effective range units of the received echo, and then obtains a super-resolution ISAR image of the target. First, a sparse representation of the missing azimuth echo in a single range unit is established based on the gridless compressed sensing framework, and then the super-resolution one-dimensional azimuth imaging is modeled as an underdetermined inverse problem based on the orthogonal atomic norm (OANM). Then, a fast algorithm of iterative Vandermonde decomposition shrinkage threshold (IVDST) is used to solve the semi-positive definite Toeplitz matrix and echo signal of the azimuth echo in the range unit. Then, the reconstructed Toeplitz matrix is ​​subjected to Vandermonde decomposition, and the number, position and amplitude of the scattering center in the range unit are estimated in turn. Finally, all effective distance units are processed with super-resolution one-dimensional azimuth imaging and a complete super-resolution ISAR image of the target is drawn, which alleviates the problem of low image quality caused by strong grating lobes, wide main lobes, high side lobes, grid errors and failure to meet the minimum atomic constraint conditions in existing ISAR imaging methods. This achieves the technical effect of avoiding grid errors and improving ISAR image quality under sparse aperture and short aperture radar observation conditions without being constrained by the minimum atomic distance.

[0016] Among them Figure 2 As shown, regarding the above step S10, after receiving the broadband radar echo, demodulation and pulse compression are performed to obtain an echo model.

[0017] Specifically, taking a linear frequency modulation ISAR radar system as an example (other ISAR radar systems can be implemented in the same way as the design concept given in this specification), the echo model obtained after demodulation and pulse compression of the received broadband radar echo can be expressed as: (1) In formula (1), Indicates fast time, Indicates slow time, , and They represent the carrier frequency, bandwidth and electromagnetic propagation speed of the radar system respectively. For the q The intensity of the scattering center, For the q The scattering centers are The radial distance along the radar line of sight at any moment, is the number of scattering centers.

[0018] Regarding the above step S12, a sparse representation is performed on the missing azimuth echo corresponding to the single range unit after motion compensation.

[0019] Specifically, the coherent processing interval (CPI) time of ISAR imaging Usually shorter. After translation compensation, the target's motion during this time period can be approximated by an angular velocity of The effective imaging accumulation angle Also usually smaller, ( ) can be expanded by its first-order Taylor expansion (due to and Smaller, and )approximate: (2) In formula (2), The rotation center of the radar to the target The distance and Respectively q Scattering center to rotation center The horizontal and vertical coordinates of represents the angular velocity, T Represents the coherent processing interval. Substituting equation (2) into equation (1), the motion-compensated echo model corresponding to the received broadband radar echo can be expressed as: (3) In formula (3), represents the wavelength, the first phase term is a constant term, and the second phase term is the Doppler phase term, where the Doppler phase term is used to obtain the target azimuth coordinates. The key.

[0020] To facilitate writing descriptions, you can use The discretization of equation (3) can be further written as: (4) In formula (4), n ( ) indicates the n The index of the distance unit, m ( ) indicates the m The index of the pulse, PRF represents the pulse repetition frequency of the radar system. In the case of no defect in the echo (i.e. full aperture), the equation (3) is related to t m The ISAR image of the target can be obtained by performing Fourier transform.

[0021] However, limited by the effective imaging accumulation angle The azimuth resolution of the ISAR image obtained based on the range-Doppler (RD) method is , it is difficult to meet the demand for high-quality ISAR images in practical applications.

[0022] Under the sparse aperture radar observation conditions, the azimuth pulse equivalent is missing. n Taking a range unit as an example, the missing azimuth echo data of the range unit can be modeled as: (5) in, represents the sparse aperture azimuth echo, represents the azimuth downsampling index, the number of pulses is ; Represents the observation matrix, whose row vector has only one element that is 1 and the rest are 0. Depend on Q column vectors, where and denote the steering vector and normalized Doppler frequency (hereinafter referred to as Doppler frequency), respectively; represents the intensity of the scattering center, Represents system noise. When there is no fuzzy observation condition When it is established, the Doppler frequency and the azimuth coordinates of the scattering center There is a one-to-one correspondence (obtaining the target's azimuth Doppler by default is equivalent to obtaining the target's azimuth coordinates).

[0023] Regarding the above-mentioned step S14, the super-resolution one-dimensional imaging of sparse aperture azimuth echoes is transformed into an orthogonal atomic norm minimization problem.

[0024] Specifically, from equation (4), we can see that the essence of azimuth range compression in ISAR imaging is to obtain the Doppler frequency .

[0025] Existing compressed sensing imaging methods based on the idea of ​​grid division usually require the establishment of an explicit gridded complete dictionary matrix and assume that all scattering centers are located on a preset grid. Different from the above existing methods, this embodiment defines a set of Doppler frequency atoms that characterize any position as: (6) In formula (6) Without considering the system noise, the minimum number of scattering centers can be directly used to characterize , that is, orthorhombic atoms Minimize the norm: (7) In formula (7), the atoms are mutually orthogonal. However, formula (7) is an NP-hard problem. Therefore, we perform convex relaxation on formula (7) and define orthogonal atoms Norm minimization (orthogonal atomic norm for short): (8) In formula (8), the atoms are orthogonal to each other. It is worth noting that the use of the orthogonal atomic norm is not subject to the constraint of the minimum atomic distance (the distance between any two atoms must satisfy certain constraints, such as ,in and ), with super-resolution performance. Considering the system noise, equation (8) can be further transformed into the following optimization problem: (9) In formula (9), the atoms are mutually orthogonal. is a constant related to the noise level. Equation (9) is an infinite-dimensional optimization problem and is difficult to solve directly. Therefore, we further transform Equation (9) into an SDP (Semidefinite Programming) constrained optimization problem (i.e., orthogonal atomic norm minimization problem): (10) In formula (10), is a low-rank, semi-positive definite, and Hermitian symmetric Toeplitz matrix, is an auxiliary variable, represents the inner product operation of vectors, and . It should be noted that due to It has a semi-positive Toeplitz structure and a unique Vandermonde decomposition, that is, once can be reconstructed, and the number, position and amplitude of the scattering centers can be uniquely estimated.

[0026] Regarding the above-mentioned step S16, the iterative Vandermonde shrinkage threshold algorithm is used to quickly solve the orthogonal atomic norm minimization problem to obtain the optimal solution; specifically, the steps may include: The orthogonal atomic norm minimization problem is transformed into an optimization problem without explicit constraints; The neighboring gradient framework is used to solve the optimization problem without explicit constraints. The matrix T and the matrix Z are updated in sequence by alternating iterative projection to obtain the optimal solution. The alternating iterative projection includes low-rank constraint projection, semi-positive definite constraint projection and Toeplitz structure projection.

[0027] Specifically, in order to achieve a fast solution, equation (10) is further transformed into an optimization problem without explicit constraints: (11) in is the composite variable to be optimized, is a constant coefficient related to the noise level, about the variable to be optimized The matrix is And there is . Note that equation (11) is a convex function, where Can be guided It is not differentiable and is solved using the neighboring gradient framework.

[0028] Smoothing the variables to be optimized: (12) In formula (12), .

[0029] On this basis The negative gradient direction update, the accelerated composite variable for: (13) In formula (13), is a step size related to the Lipschitz constant, is the gradient operator. Since Only with related, Formula (13) can be further clarified as: (14) In theory, the neighbor projection operation is: (15) Since Equation (15) has no analytical solution, inspired by the low rank, semi-positive definiteness and Toeplitz structure of T in the orthogonal atomic norm, alternating iterative projection is used to update the matrix T and the matrix Z in turn to approximate Equation (15).

[0030] (1) Low-rank constrained projection.

[0031] Specifically, yes Perform Vandermonde decomposition: (16) In formula (16), It is a is the Vandermonde matrix of eigenvectors, and the column vectors are mutually orthogonal; It is the characteristic diagonal matrix formed by the corresponding eigenvalues. The columns in are mutually orthogonal, ensuring the orthogonality of atoms in iterative optimization.

[0032] The low-rank constraint of is determined by shrinking the threshold. The diagonal is smaller than the preset threshold The value is set to 0: (17) use Substitute (16) , and then complete the low-rank projection operation: (18) After the low-rank projection operation, the matrix Updated to: (19) (2) Semidefinite Constrained Projection.

[0033] Specifically, in theory, The semi-positive definite projection of can be achieved by retaining the eigencomponents with eigenvalues ​​greater than 0. To impose a more compact semi-positive definite constraint, the matrix The rank of To this end, partial eigendecomposition is used to calculate of s The main characteristic components: (20) In the formula and After the semi-positive definite constraint projection operation, Updated to: (twenty one) (3) Toeplitz structure projection.

[0034] Specifically, to ensure It has a Toeplitz structure, and the Toeplitz structure operator is defined as follows: (twenty two) In formula (22), is the conjugate operator, Determined by the following formula: (twenty three) It can be seen that after the Toeplitz structure projection operation, Updated to: (twenty four) Therefore, after the i After iterations The variables in are determined according to the following formula: (25) Before the algorithm iteration, let and In order to ensure the orthogonality of the initial atoms, Perform a Vandermonde decomposition to determine and On this basis, the SORTE (Second Order Statistic of Eigenvalues) algorithm is used to determine Rank (number of atoms). and , Determined by least squares estimation, that is . Therefore, the algorithm initializes the composite variable for: (26) when or When and As the optimal solution.

[0035] Regarding the above-mentioned step S18, Vandermonde decomposition is used for the optimal solution to obtain a super-resolution one-dimensional azimuth image of the target.

[0036] It can be understood that in obtaining the optimal solution of formula (10) and Then, the Vandermonde decomposition is used to embed The scattering components in are solved. Among them, the number of scattering centers Determined by the SORTE algorithm; Doppler frequency Determined by MPM (Matrix Pencil Method); based on The matrix formed and reconstruct the signal , the scattering intensity is estimated by the least squares method At this point, a super-resolution one-dimensional azimuth image of the missing echo in the azimuth of a single range unit can be obtained.

[0037] Regarding the above step S20, the missing azimuth echoes of all effective range units are quickly solved according to the orthogonal atomic norm minimization problem to obtain a super-resolution one-dimensional azimuth image of each effective range unit and draw an azimuth super-resolution ISAR image of the target.

[0038] It can be understood that the effective scattering components of radar targets are usually distributed only within a certain range of distance units. . The super-resolution one-dimensional azimuth image of the corresponding range unit is obtained by repeatedly solving equation (10) for each range unit. Then, the super-resolution one-dimensional azimuth image of a single range unit is drawn in sequence on the two-dimensional plane, thereby obtaining a complete azimuth super-resolution ISAR image of the target. Specifically, when drawing the ISAR image, the intensity position of the scattering center is jointly determined by the index of the range unit (or the distance after calibration) and the Doppler frequency (or the coordinate after azimuth calibration), and the intensity of the scattering center is jointly reflected by solid circles of different sizes and different colors.

[0039] The above-mentioned gridless azimuth super-resolution sparse aperture ISAR imaging method avoids off-grid errors and is not constrained by the minimum atomic distance. It can improve the quality of ISAR images under sparse aperture and short aperture radar observation conditions. Specifically, it adopts orthogonal atomic norm minimization to model azimuth missing echoes and uses the Iterative Vandermonde Decomposition Shrinkage Threshold (IVDST) algorithm to quickly solve, without the need to establish a dictionary matrix, avoiding off-grid errors, effectively suppressing strong grating lobe artifacts caused by sparse apertures, and distinguishing neighboring scattering centers below the Rayleigh resolution distance caused by short apertures, with super-Rayleigh resolution capabilities. The obtained ISAR image has no main lobe broadening and side lobes in the azimuth dimension, and has the advantage of characterizing the number, position and intensity of scattering centers in a single distance unit. The ISAR image has a clear physical meaning and has great engineering application value.

[0040] In some embodiments, Figure 3 The aircraft target model is simulated as a point and rotated at a constant speed of 2° / s. The radar system simulation parameters can be as follows: center frequency 10GHz, bandwidth 300MHz, pulse repetition frequency 200Hz, pulse accumulation time 0.6s. The full aperture echo contains 121 pulses, each pulse contains 201 frequency sampling points, and the corresponding range Rayleigh resolution is , the azimuth Rayleigh resolution is . Figure 3 The scattering center shown in is the closest scattering center in the azimuth direction of the simulated target. The azimuth distance between the two is 0.5m, which is lower than the azimuth Rayleigh resolution distance. .

[0041] Figure 4 (a) Figure 4 (b) are the one-dimensional range image sequence and ISAR image of the point simulation target under full aperture conditions. Figure 4 (b) It can be seen that the ISAR image obtained by the traditional RD method has high sidelobe phenomenon.

[0042] from Figure 460 pulses are randomly selected from the full-aperture data shown in (a) to simulate the sparse aperture radar observation condition with a sparsity of 50%. Figure 5 (a) shows a missing one-dimensional range image sequence of point simulation targets with a sparsity of 50%. Figure 5 (b) Figure 5 (c) The imaging results of the RD method and the method of the present invention are respectively. Figure 5 (b) It can be seen that the ISAR image obtained by the RD method is severely defocused and seriously interfered by the strong grating lobes. The scattering center is almost completely submerged in the grating lobes, making it difficult to reflect the scattering distribution of the target. Figure 5 (c) It can be seen that the above method of the present invention eliminates grating lobe artifacts and azimuth side lobes, and the obtained ISAR image can clearly reflect the scattering distribution of the target.

[0043] For further analysis, Figure 6 Given Figure 5 (b) and Figure 5 (c) is a cross-sectional view (one-dimensional azimuth image) of the 171th distance unit RD method and the above method of the present invention, wherein the normalized scattering amplitude is a relative value with the value "1" as the unit. Figure 6 It can be seen that under full aperture conditions, the azimuth image obtained by the RD method has a main lobe broadening and cannot distinguish adjacent scattering centers. When sparse aperture occurs, the one-dimensional azimuth image obtained by the RD method also has strong grating lobe artifacts. In contrast, the above method of the present invention eliminates grating lobe and side lobe artifacts, has no main lobe broadening, can distinguish adjacent scattering centers below the Rayleigh resolution, and is consistent with the true value, further verifying the effectiveness of the above method of the present invention.

[0044] When taking the cone combination target darkroom measurement model as an example, the model has a height of 1.2m, a bottom radius of 0.26m, and a uniform rotation of 4° / s. The radar system measurement parameters are as follows: center frequency 9GHz, bandwidth 1GHz, pulse repetition frequency 20Hz, and pulse accumulation time 1.55s. The full aperture data contains 32 pulses, each of which contains 51 frequency sampling points, and the corresponding range Rayleigh resolution is , the azimuth Rayleigh resolution is .

[0045] Figure 7 (a) Figure 7 (b) are the one-dimensional range image sequence and ISAR image of the cone-combined target under full aperture conditions. Figure 7 (b) It can be seen that the ISAR image obtained by the traditional RD method can distinguish six strong scattering centers, but each scattering center has a widened main lobe and high side lobes.

[0046] Sixteen pulses are randomly selected from the full-aperture data of the cone-combined target to simulate the sparse aperture radar observation condition with a sparsity of 50%. Figure 8 (a) shows the missing one-dimensional range image sequence of the cone combination target with a sparsity of 50%. Figure 8 (b) Figure 8 (c) are the imaging results of the RD method and the above method of the present invention. Figure 8 (b) It can be seen that the ISAR image obtained by the RD method is defocused and interfered by strong grating lobes, making it difficult to distinguish the cone-shaped target structure. Figure 8 (c) It can be seen that the above method of the present invention eliminates grating lobe artifacts and azimuth side lobes, successfully extracts 6 strong scattering centers, and the obtained ISAR image can clearly reflect the target structure.

[0047] For further analysis, Fig. 9 Given Figure 8 (b) and Figure 8 (c) is a cross-sectional view (one-dimensional azimuth image) of the 26th distance unit of the RD method and the method of the present invention. Fig. 9 It can be seen that under full aperture conditions, the azimuth image obtained by the RD imaging method has a widened main lobe and high side lobes. When sparse aperture occurs, the one-dimensional azimuth image obtained by the RD method still has strong grating lobe artifacts, making it difficult to distinguish the scattering center of the target. In contrast, the above method of the present invention can still effectively extract the strong scattering center of the cone combination target, further verifying the effectiveness of the above method of the present invention.

[0048] In summary, the method of the present invention can work under sparse aperture and short aperture radar observation conditions, avoids off-grid errors, has no main lobe broadening, and can effectively suppress grating lobes and side lobe artifacts; is not constrained by the minimum atomic distance, can resolve adjacent scattering centers under super-Rayleigh resolution conditions, and improves ISAR image quality; has the ability to characterize the number, position and intensity of scattering centers in a single distance unit, has clear physical meaning, and has high engineering application value.

[0049] In one embodiment, Fig.10As shown, a gridless azimuth super-resolution sparse aperture ISAR imaging system 100 is provided, including an echo acquisition module 11, an echo characterization module 13, a problem conversion module 15, a fast solution module 17, an azimuth image acquisition module 19 and a super-resolution imaging module 21. Among them, the echo acquisition module 11 is used to receive the broadband radar echo and then demodulate and pulse compress it to obtain an echo model. The echo characterization module 13 is used to sparsely characterize the missing azimuth echo corresponding to a single distance unit after motion compensation based on the echo model. The problem conversion module 15 is used to convert the super-resolution one-dimensional imaging of the sparse aperture azimuth echo into an orthogonal atomic norm minimization problem. The fast solution module 17 is used to use an iterative Vandermonde shrinkage threshold algorithm to quickly solve the orthogonal atomic norm minimization problem to obtain an optimal solution. The azimuth image acquisition module 19 is used to use Vandermonde decomposition to obtain a super-resolution one-dimensional azimuth image of the target for the optimal solution. The super-resolution imaging module 21 is used to quickly solve the missing azimuth echoes of all effective range units according to the orthogonal atomic norm minimization problem, obtain the super-resolution one-dimensional azimuth image of each effective range unit and draw the azimuth super-resolution ISAR image of the target.

[0050] The above-mentioned gridless azimuth super-resolution sparse aperture ISAR imaging system 100 performs one-dimensional imaging processing on all effective distance units of the received echo to obtain a super-resolution one-dimensional azimuth image of the target, and then obtains a super-resolution ISAR image of the target. First, a sparse representation of the missing azimuth echo in a single distance unit is established based on the gridless compressed sensing framework, and then the super-resolution one-dimensional azimuth imaging is modeled as an underdetermined inverse problem based on OANM. Then, a fast IVDST algorithm is used to solve the semi-positive definite Toeplitz matrix and echo signal of the azimuth echo of the distance unit. Then, the reconstructed Toeplitz matrix is ​​subjected to Vandermonde decomposition, and the number, position and amplitude of the scattering centers in the distance unit are estimated in turn. Finally, all effective distance units are subjected to super-resolution one-dimensional azimuth imaging processing and a complete super-resolution ISAR image of the target is drawn. The problem of low image quality in existing ISAR imaging methods caused by strong grating lobes, wide main lobes, high side lobes, grid errors and failure to meet the minimum atomic constraint conditions is alleviated, and the technical effect of avoiding grid errors and not being constrained by the minimum atomic distance is achieved under sparse aperture and short aperture radar observation conditions, thereby improving the ISAR image quality.

[0051] In one embodiment, the orthogonal atomic norm minimization problem is: ; in, is a low-rank, semi-positive definite, and Hermitian symmetric Toeplitz matrix, Indicates Full aperture azimuth echo of range cells, The upper right subscript H indicates the conjugate transpose, is an auxiliary variable, M represents the number of full-aperture pulses, represents the trace of the matrix, represents the observation matrix, Indicates Sparse aperture azimuth echo of range cells, is a constant related to the noise level, and denote the steering vector and normalized Doppler frequency respectively, represents the inner product operation of vectors, , and , is the number of scattering centers.

[0052] In one embodiment, the fast solution module 17 uses an iterative Vandermonde shrinkage threshold algorithm to quickly solve the orthogonal atomic norm minimization problem. In the process of obtaining the optimal solution, the orthogonal atomic norm minimization problem is converted into an optimization problem without explicit constraints, and the neighboring gradient framework is used to solve the optimization problem without explicit constraints; wherein, alternating iterative projection is used to update the matrix T and the matrix Z in turn to obtain the optimal solution, and the alternating iterative projection includes low-rank constraint projection, semi-positive definite constraint projection and Toeplitz structure projection.

[0053] For specific limitations of the gridless azimuthal super-resolution sparse aperture ISAR imaging system 100 , reference may be made to the corresponding limitations of the gridless azimuthal super-resolution sparse aperture ISAR imaging method described above, which will not be repeated here.

[0054] It should be understood that, although the various steps in the above flowchart are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless there is a clear description in this article, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps in the above flowchart may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the sub-steps or stages of other steps.

[0055] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus dynamic random access memory (RambusDRAM, referred to as RDRAM) and interface dynamic random access memory (DRDRAM).

[0056] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0057] The above embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of protection of the invention. It should be pointed out that, for those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the attached claims.

Claims

1. A gridless azimuth super-resolution sparse aperture ISAR imaging method, characterized in that: Includes steps: After receiving the broadband radar echo, demodulation and pulse compression are performed to obtain the echo model; Based on the echo model, a sparse representation is performed on the missing azimuth echo corresponding to the single range unit after motion compensation; The super-resolution one-dimensional imaging of sparse aperture azimuth echoes is transformed into an orthogonal atomic norm minimization problem; An iterative Vandermonde shrinkage threshold algorithm is used to quickly solve the orthogonal atomic norm minimization problem to obtain an optimal solution; the optimal solution includes a semi-positive definite Toeplitz matrix of a sparse aperture azimuth echo of a range unit and a reconstructed signal; Using Vandermonde decomposition on the optimal solution to obtain a super-resolution one-dimensional azimuth image of the target; According to the orthogonal atomic norm minimization problem, the missing azimuth echoes of all effective range units are quickly solved to obtain the super-resolution one-dimensional azimuth image of each effective range unit and draw the azimuth super-resolution ISAR image of the target.

2. The gridless azimuth super-resolution sparse aperture ISAR imaging method according to claim 1, characterized in that: The orthogonal atomic norm minimization problem is: in, is a low-rank, semi-positive definite, and Hermitian symmetric Toeplitz matrix, Indicates Full aperture azimuth echo of range cells, The upper right subscript H indicates the conjugate transpose, is an auxiliary variable, M represents the number of full-aperture pulses, represents the trace of the matrix, represents the observation matrix, Indicates Sparse aperture azimuth echo of range cells, is a constant related to the noise level, and denote the steering vector and normalized Doppler frequency respectively, represents the inner product operation of vectors, , and , is the number of scattering centers.

3. A gridless azimuth super-resolution sparse aperture ISAR imaging method according to claim 1 or 2, characterized in that: The iterative Vandermonde shrinkage threshold algorithm is used to quickly solve the orthogonal atomic norm minimization problem. The steps to obtain the optimal solution include: Converting the orthogonal atomic norm minimization problem into an optimization problem without explicit constraints; The neighboring gradient framework is used to solve the optimization problem without explicit constraints. The matrix T and the matrix Z are updated in sequence by alternating iterative projection to obtain the optimal solution. The alternating iterative projection includes low-rank constraint projection, semi-positive definite constraint projection and Toeplitz structure projection.

4. A gridless azimuth super-resolution sparse aperture ISAR imaging system, characterized in that: include: The echo acquisition module is used to receive the broadband radar echo, perform demodulation and pulse compression, and obtain the echo model; An echo characterization module, used for sparsely characterizing the missing azimuth echo corresponding to the single range unit after motion compensation based on the echo model; A problem conversion module is used to convert the super-resolution one-dimensional imaging of sparse aperture azimuth echoes into an orthogonal atomic norm minimization problem; A fast solution module, used for quickly solving the orthogonal atomic norm minimization problem by using an iterative Vandermonde shrinkage threshold algorithm to obtain an optimal solution; the optimal solution includes a semi-positive definite Toeplitz matrix of a sparse aperture azimuth echo of a range unit and a reconstructed signal; An azimuth image acquisition module, used for acquiring a super-resolution one-dimensional azimuth image of the target by using Vandermonde decomposition on the optimal solution; The super-resolution imaging module is used to quickly solve the missing azimuth echoes of all effective range units according to the orthogonal atomic norm minimization problem, obtain the super-resolution one-dimensional azimuth image of each effective range unit and draw the azimuth super-resolution ISAR image of the target.

5. The gridless azimuth super-resolution sparse aperture ISAR imaging system according to claim 4, characterized in that: The orthogonal atomic norm minimization problem is: in, is a low-rank, semi-positive definite, and Hermitian symmetric Toeplitz matrix, Indicates Full aperture azimuth echo of range cells, The upper right subscript H indicates the conjugate transpose, is an auxiliary variable, M represents the number of full-aperture pulses, represents the trace of the matrix, represents the observation matrix, Indicates Sparse aperture azimuth echo of range cells, is a constant related to the noise level, and denote the steering vector and normalized Doppler frequency respectively, represents the inner product operation of vectors, , and , is the number of scattering centers.

6. A gridless azimuth super-resolution sparse aperture ISAR imaging system according to claim 4 or 5, characterized in that: The fast solution module uses an iterative Vandermonde shrinkage threshold algorithm to quickly solve the orthogonal atomic norm minimization problem. In the process of obtaining the optimal solution, the orthogonal atomic norm minimization problem is converted into an optimization problem without explicit constraints, and the neighboring gradient framework is used to solve the optimization problem without explicit constraints; wherein, alternating iterative projection is used to sequentially update the matrix T and the matrix Z to obtain the optimal solution, and the alternating iterative projection includes low-rank constraint projection, semi-positive definite constraint projection and Toeplitz structure projection.

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