A Meshless Azimuth Super-Resolution Sparse Aperture ISAR Imaging Method and System

Abstract

The present invention relates to a meshless azimuth super-resolution sparse aperture ISAR imaging method and system, which performs one-dimensional imaging processing on all effective range cells of the received echo to obtain the super-resolution one-dimensional azimuth image of the target, and further obtains the super-resolution ISAR image of the target. Based on the meshless compressive sensing framework, a sparse representation of the missing azimuth echo within a single range cell is established. The super-resolution one-dimensional azimuth imaging is modeled as an underdetermined inverse problem based on OANM and solved by a fast algorithm. After reconstructing the positive semi-definite Toeplitz matrix and the echo signal of the azimuth echo of this range cell, the Vandermonde decomposition is performed on the reconstructed Toeplitz matrix to obtain the super-resolution one-dimensional azimuth image, and the complete super-resolution ISAR image of the target is drawn, realizing the technical effects of avoiding off-grid errors under the conditions of sparse aperture and short aperture radar measurements, being not restricted by the minimum atom distance, and improving the quality of the ISAR image.

Description

Technical Field

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

[0002] Inverse synthetic aperture radar (ISAR) has the advantages of all-weather and all-day operation, and has now been widely used in various industrial fields. The obtained ISAR image can characterize the backscattering distribution of the target, which is the basis for subsequent tasks such as 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 the target, and noise interference, the received echo data usually has equivalent missing in the slow time dimension, and the sparse aperture phenomenon occurs from time to time. In addition, the effective imaging period contained in the received echo data is usually short (either the radar illumination time is short due to limited radar resources, or it is difficult to perform effective motion compensation on the long-term observed echo due to the limited performance of existing motion compensation methods), resulting in a small effective cumulative rotation angle, and short aperture observation is inevitable. At this time, the ISAR image obtained based on the traditional Range-Doppler (RD) imaging method will face challenges of defocusing and low resolution in the azimuth dimension, specifically manifested as significant problems of strong grating lobes, wide main lobes, and high side lobes in the ISAR image.

[0003] Most of the existing SA-ISAR imaging methods adopt grid-based compressive sensing technology, which suppresses the strong grating lobes caused by the sparse aperture and reduces the side lobes to a certain extent. However, these existing methods inherently have off-grid errors caused by the scattering center deviating from the preset grid, and there is still a large room for improving the quality of the ISAR image. On this basis, the existing SA-ISAR imaging methods based on meshless compressive sensing technology avoid off-grid errors and improve the quality of the ISAR image, but they usually do not have the ability of super-Rayleigh resolution, and their application is restricted by the minimum atom distance. When the minimum atom distance constraint cannot be satisfied, robust sparse recovery cannot be guaranteed, and low-quality ISAR images may be generated. Therefore, how to improve the quality of the ISAR image under the conditions of sparse aperture and short aperture radar observation has become a technical problem to be solved, and solving this technical problem has important engineering application value. Summary of the Invention

[0004] Aiming at the problems existing in the above traditional technologies, the present invention proposes a meshless azimuth super-resolution sparse aperture ISAR imaging method and a meshless azimuth super-resolution sparse aperture ISAR imaging system, which can avoid off-grid errors, are not restricted by the minimum atom distance, and improve the quality of the ISAR image under the conditions of sparse aperture and short aperture radar observation.

[0005] In order to achieve the above object, the embodiments of the present invention adopt the following technical solutions:

[0006] On the one hand, a meshless azimuth super-resolution sparse aperture ISAR imaging method is provided, including the steps of:

[0007] After receiving the broadband radar echo, perform demodulation and pulse compression to obtain the echo model;

[0008] Based on the echo model, perform sparse characterization on the missing azimuth echo corresponding to a single range cell after motion compensation;

[0009] Convert the super-resolution one-dimensional imaging of the sparse aperture azimuth echo into an orthogonal atomic norm minimization problem;

[0010] Adopt the iterative Vandermonde shrinkage threshold algorithm to quickly solve the orthogonal atomic norm minimization problem and obtain the optimal solution;

[0011] Use Vandermonde decomposition on the optimal solution to obtain the super-resolution one-dimensional azimuth image of the target;

[0012] According to the orthogonal atomic norm minimization problem, quickly solve and process the missing azimuth echoes of all effective range cells, obtain the super-resolution one-dimensional azimuth images of each effective range cell, and draw the azimuth super-resolution ISAR image of the target.

[0013] On the other hand, a meshless azimuth super-resolution sparse aperture ISAR imaging system is also provided, including:

[0014] An echo acquisition module, configured to perform demodulation and pulse compression on the received broadband radar echo to obtain the echo model;

[0015] An echo characterization module, configured to perform sparse characterization on the missing azimuth echo corresponding to a single range cell after motion compensation based on the echo model;

[0016] A problem transformation module, configured to convert the super-resolution one-dimensional imaging of the sparse aperture azimuth echo into an orthogonal atomic norm minimization problem;

[0017] A fast solution module, configured to adopt the iterative Vandermonde shrinkage threshold algorithm to quickly solve the orthogonal atomic norm minimization problem and obtain the optimal solution;

[0018] An azimuth image acquisition module, configured to use Vandermonde decomposition on the optimal solution to obtain the super-resolution one-dimensional azimuth image of the target;

[0019] A super-resolution imaging module, configured to quickly solve and process the missing azimuth echoes of all effective range cells according to the orthogonal atomic norm minimization problem, obtain the super-resolution one-dimensional azimuth images of each effective range cell, and draw the azimuth super-resolution ISAR image of the target.

[0020] One of the above technical solutions has the following advantages and beneficial effects:

[0021] The above gridless azimuth super-resolution sparse aperture ISAR imaging method and system obtain the super-resolution one-dimensional azimuth image of the target by performing one-dimensional imaging processing on all effective range cells of the received echo, and then obtain the super-resolution ISAR image of the target. First, a sparse representation of the missing azimuth echo within a single range cell is established based on the gridless compressive sensing framework, and then the super-resolution one-dimensional azimuth imaging is modeled as an underdetermined inverse problem based on the orthogonal atomic norm. Furthermore, it is solved by a fast algorithm of iterative Vandermonde decomposition shrinkage threshold to reconstruct the positive semi-definite Toeplitz matrix and the echo signal of the azimuth echo of this range cell. Then, the positive semi-definite Toeplitz matrix after reconstruction is subjected to Vandermonde decomposition to sequentially estimate the number, position, and amplitude of the scattering centers within this range cell. Finally, super-resolution one-dimensional azimuth imaging processing is performed on all effective range cells and the complete super-resolution ISAR image of the target is drawn. It alleviates the problem of low image quality caused by strong grating lobes, wide main lobes, high side lobes, off-grid errors, and non-satisfaction of the minimum atom constraint condition in the existing ISAR imaging methods, and realizes the technical effect of avoiding off-grid errors, being not restricted by the minimum atom distance, and improving the ISAR image quality under the radar observation conditions of sparse aperture and short aperture. Description of the Drawings

[0022] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or in the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0023] Figure 1 It is a flowchart of a gridless azimuth super-resolution sparse aperture ISAR imaging method in an embodiment;

[0024] Figure 2 It is a schematic diagram of the specific implementation process of a gridless azimuth super-resolution sparse aperture ISAR imaging method in an embodiment;

[0025] Figure 3 It is a schematic diagram of a point simulation aircraft target model in an embodiment;

[0026] Figure 4 It is a schematic diagram of the imaging of the point simulation aircraft target under the full aperture condition in an embodiment, where Figure 4 (a) is a sequence of one-dimensional range images, Figure 4 (b) is the ISAR image by the RD method;

[0027] Figure 5Schematic diagram of imaging of a point-simulated aircraft target under the condition of 50% sparsity in an embodiment, where Figure 5 (a) is a sequence of one-dimensional range profiles, Figure 5 (b) is an ISAR image obtained by the RD method, Figure 5 (c) is an ISAR image obtained by the method of the present invention;

[0028] Figure 6 Cross-sectional view (one-dimensional azimuth profile) of ISAR images obtained by different methods for the 171st range cell of a point-simulated aircraft target under the condition of 50% sparsity in an embodiment;

[0029] Figure 7 Schematic diagram of imaging of a cone combination target under the condition of full aperture in an embodiment, where Figure 7 (a) is a sequence of one-dimensional range profiles, Figure 7 (b) is an ISAR image obtained by the RD method;

[0030] Figure 8 Schematic diagram of imaging of a cone combination target under the condition of 50% sparsity in an embodiment, where Figure 8 (a) is a sequence of one-dimensional range profiles, Figure 8 (b) is an ISAR image obtained by the RD method, Figure 8 (c) is an ISAR image obtained by the method of the present invention;

[0031] Figure 9 Cross-sectional view (one-dimensional azimuth profile) of ISAR images obtained by different methods for the 26th range cell of a cone combination target under the condition of 50% sparsity in an embodiment;

[0032] Figure 10 Block diagram of a meshless azimuth super-resolution sparse aperture ISAR imaging system in an embodiment. Detailed implementation manners

[0033] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs. The terms used in the description of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0034] It should be noted that referring to "embodiments" in this document means that the specific features, structures, or characteristics described in connection with the embodiments can be included in at least one embodiment of the present invention. The phrase shown at various positions in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art can understand that the embodiments described herein can be combined with other embodiments. The term "and / or" used in the specification and appended claims of the present invention refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0035] Next, the embodiments of the present invention will be described in detail in conjunction with the accompanying drawings in the embodiments of the present invention.

[0036] Aiming at 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 meshless azimuth super-resolution sparse aperture ISAR imaging method.

[0037] In one embodiment, as Figure 1 shown, a meshless azimuth super-resolution sparse aperture ISAR imaging method is provided, which may include the following steps S10 to S20:

[0038] S10, After receiving the broadband radar echo, perform demodulation and pulse compression to obtain the echo model;

[0039] S12, Based on the echo model, perform sparse characterization on the missing azimuth echo corresponding to a single range cell after motion compensation;

[0040] S14, Convert the super-resolution one-dimensional imaging of the sparse aperture azimuth echo into an orthonormal atomic norm minimization problem;

[0041] S16, Use the iterative Vandermonde shrinkage threshold algorithm to quickly solve the orthonormal atomic norm minimization problem and obtain the optimal solution;

[0042] S18, Use Vandermonde decomposition on the optimal solution to obtain the super-resolution one-dimensional azimuth image of the target;

[0043] S20. Rapidly solve and process the missing azimuth echoes of all valid range cells according to the orthogonal atomic norm minimization problem, obtain the super-resolution one-dimensional azimuth image of each valid range cell, and draw the azimuth super-resolution ISAR image of the target.

[0044] The above gridless azimuth super-resolution sparse aperture ISAR imaging method obtains the super-resolution one-dimensional azimuth image of the target by performing one-dimensional imaging processing on all valid range cells of the received echo, and then obtains the super-resolution ISAR image of the target. First, establish the sparse representation of the missing azimuth echo within a single range cell based on the gridless compressive sensing framework, and then model the super-resolution one-dimensional azimuth imaging as an underdetermined inverse problem based on the orthogonal atomic norm (OANM). Furthermore, solve it through a fast algorithm of iterative Vandermonde decomposition shrinkage threshold (IVDST) to reconstruct the positive semi-definite Toeplitz matrix and the echo signal of the azimuth echo of this range cell. Then, perform Vandermonde decomposition on the reconstructed Toeplitz matrix to sequentially estimate the number, position, and amplitude of the scattering centers within this range cell. Finally, perform super-resolution one-dimensional azimuth imaging processing on all valid range cells and draw the complete super-resolution ISAR image of the target, alleviating the problem of low image quality caused by strong grating lobes, wide main lobes, high side lobes, off-grid errors, and non-satisfaction of the minimum atom constraint conditions in the existing ISAR imaging methods, achieving the technical effect of avoiding off-grid errors, being not restricted by the minimum atom distance, and improving the ISAR image quality under the sparse aperture and short aperture radar observation conditions.

[0045] Among them, as Figure 2 shown, regarding the above step S10, after receiving the broadband radar echo, perform demodulation and pulse compression to obtain the echo model.

[0046] Specifically, taking the linear frequency modulation ISAR radar system as an example (other ISAR radar systems can be implemented similarly according to the design concept given in this specification), the echo model obtained after demodulating and pulse compressing the received broadband radar echo can be expressed as:

[0047] (1)

[0048] In formula (1), represents the fast time, represents the slow time, , and respectively represent the carrier frequency, bandwidth, and electromagnetic propagation speed of the radar system. is the intensity of the q th scattering center, is the q th scattering center at time along the radial distance of the radar line of sight, is the number of scattering centers.

[0049] Regarding the above step S12, sparse representation is performed on the missing azimuth echo corresponding to a single range cell after motion compensation.

[0050] Specifically, the Coherent Processing Interval (CPI) time of ISAR imaging is usually short. After translational compensation, the motion of the target within this time period can be approximated as a uniform rotation with an angular velocity of . Therefore, the effective imaging accumulation angle is also usually small, ( ) can be approximated by its first-order Taylor expansion (since and is small, and ):

[0051] (2)

[0052] In formula (2), is the distance from the radar to the target rotation center , and are the abscissa and ordinate of the q -th scattering center to the rotation center respectively, represents the angular velocity, T represents the coherent processing interval. Substituting formula (2) into formula (1), the echo model after motion compensation corresponding to the received broadband radar echo can be expressed as:

[0053] (3)

[0054] 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 the key to obtaining the target azimuth coordinate .

[0055] For the convenience of writing and description, let . The discretized processing of formula (3) is further written as:

[0056] (4)

[0057] In formula (4), n ( ) represents the index of the n -th range cell, m ( ) represents them The index of a pulse, PRF representing the pulse repetition frequency of the radar system. In the case of no missing echo (i.e., full aperture), for Equation (3) regarding t m Performing Fourier transform can obtain the ISAR image of the target.

[0058] However, limited by the effective imaging accumulation angle being small, the azimuth resolution of the ISAR image obtained based on the range-Doppler (RD) method is , which is difficult to meet the requirements for high-quality ISAR images in practical applications.

[0059] Under the sparse aperture radar observation condition, there are equivalent missing azimuth pulses. Taking the n th range cell as an example, the missing azimuth echo data of this range cell can be modeled as:

[0060] (5)

[0061] where, represents the sparse aperture azimuth echo, represents the azimuth downsampling index, and the number of pulses is ; represents the observation matrix, whose row vector has only one element as 1 and the rest are 0. Consisting of Q column vectors, where and represent the steering vector and the normalized Doppler frequency (hereinafter referred to as Doppler frequency) respectively; represents the intensity of the scattering center, represents the system noise. When the non-ambiguous observation condition holds, there is a one-to-one correspondence between the Doppler frequency and the azimuth coordinate of the scattering center (by default, obtaining the azimuth Doppler of the target is equivalent to obtaining the azimuth coordinate of the target).

[0062] Regarding the above step S14, the super-resolution one-dimensional imaging of the sparse aperture azimuth echo is transformed into an orthogonal atomic norm minimization problem.

[0063] Specifically, from Equation (4), it can be seen that the essence of azimuth-range compression in ISAR imaging is to obtain the Doppler frequency .

[0064] Existing compressive sensing imaging methods based on the idea of grid division usually require the establishment of an explicit grid-complete dictionary matrix and assume that all scattering centers are located on a preset grid. Different from the above existing methods, in this embodiment, a set of Doppler frequency atoms representing arbitrary positions is defined as:

[0065] (6)

[0066] In formula (6), . Without considering system noise, the criterion of the minimum number of scattering centers can be directly used to represent , that is, the orthogonal atom norm minimization:

[0067] (7)

[0068] In formula (7), the atoms are orthogonal to each other. However, formula (7) belongs to an NP-hard problem. Therefore, a convex relaxation operation is performed on formula (7), and the orthogonal atom norm minimization (abbreviated as orthogonal atom norm) is defined:

[0069] (8)

[0070] In formula (8), the atoms are orthogonal to each other. It should be noted that the use of the orthogonal atom norm is not restricted by the minimum atom distance (the distance between any two atoms needs to meet certain constraints, for example , where and ), and it has super-resolution performance. Considering system noise, formula (8) can be further transformed into the following optimization problem:

[0071] (9)

[0072] In formula (9), the atoms are orthogonal to each other, is a constant related to the noise level. Formula (9) is an infinite-dimensional optimization problem and is difficult to solve directly. Therefore, formula (9) is further transformed into an optimization problem constrained by SDP (Semidefinite Programming, semi-definite programming) (that is, the orthogonal atom norm minimization problem):

[0073] (10)

[0074] In formula (10), is a low-rank, positive semi-definite and Hermitian symmetric Toeplitz matrix, is an auxiliary variable, represents the inner product operation of vectors, and 。It should be noted that since has a positive semi - definite Toeplitz structure and has a unique Vandermonde decomposition, that is, once is reconstructed, the number, position, and amplitude of the scattering centers can all be uniquely estimated.

[0075] Regarding the above 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, it may include the steps:

[0076] Convert the orthogonal atomic norm minimization problem into an optimization problem without explicit constraints;

[0077] Use the proximal gradient framework to solve the optimization problem without explicit constraints; among them, the matrices T and Z are updated successively by alternating iterative projection to obtain the optimal solution, and the alternating iterative projection includes low - rank constraint projection, positive semi - definite constraint projection, and Toeplitz structure projection.

[0078] Specifically, in order to achieve fast solution, equation (10) is further converted into an optimization problem without explicit constraints:

[0079] (11)

[0080] where is the composite variable to be optimized, is a constant coefficient related to the noise level, and the matrix regarding the variable to be optimized is and there is . Note that equation (11) is a convex function, where is differentiable while is not differentiable, and the proximal gradient framework is used to solve it.

[0081] Perform a smoothing operation on the variable to be optimized:

[0082] (12)

[0083] In equation (12) .

[0084] On this basis, update along the negative gradient direction of, and the accelerated composite variable is:

[0085] (13)

[0086] In equation (13) is a step size related to the Lipschitz constant, is the gradient operator. Since only depends on is related to Equation (13) can be further specified as:

[0087] (14)

[0088] Theoretically, the proximal projection operation is:

[0089] (15)

[0090] Since Equation (15) has no analytical solution, inspired by the low-rank property, positive semi-definiteness, and Toeplitz structure of T in the orthogonal atomic norm, the matrices T and Z are updated alternately by iterative projection to approximate Equation (15).

[0091] (1) Low-rank constraint projection.

[0092] Specifically, perform Vandermonde decomposition on :

[0093] (16)

[0094] In Equation (16), is a Vandermonde matrix with as eigenvectors, and the column vectors are orthogonal to each other; is a diagonal matrix of eigenvalues corresponding to the respective eigenvectors. The orthogonality of the columns in ensures the orthogonality of the atoms in the iterative optimization.

[0095] The low-rank constraint of is determined by the shrinkage threshold. Set the values on the diagonal of less than the preset threshold to 0:

[0096] (17)

[0097] Replace with in (16), and then complete the low-rank projection operation:

[0098] (18)

[0099] After the low-rank projection operation, the matrix is updated to:

[0100] (19)

[0101] (2) Positive semi-definite constraint projection.

[0102] Specifically, theoretically, The positive semi - definite projection can be achieved by retaining the eigen - components with eigenvalues greater than 0. To impose a more compact positive semi - definite constraint, for the matrix the rank is . For this purpose, partial eigenvalue decomposition is adopted to calculate the of s principal eigen - components:

[0103] (20)

[0104] where and . After the positive semi - definite constraint projection operation, is updated as:

[0105] (21)

[0106] (3) Toeplitz structure projection.

[0107] Specifically, to ensure that has a Toeplitz structure, the Toeplitz structure operator is defined as follows:

[0108] (22)

[0109] In equation (22), is the conjugate operator, is determined by the following formula:

[0110] (23)

[0111] It can be seen that after the Toeplitz structure projection operation, is updated as:

[0112] (24)

[0113] Therefore, after the i th iteration, the variables in are determined according to the following formula respectively:

[0114] (25)

[0115] Before the algorithm iteration, let and . To ensure the orthogonality of the initial atoms, Vandermonde decomposition is performed on to determine and . On this basis, according to the SORTE (Second Order Statistic of Eigenvalues) algorithm, the rank of (number of atoms). Let and , is determined by least squares estimation, i.e., . Therefore, the algorithm initializes the composite variable as:

[0116] (26)

[0117] When or , the iteration terminates and and are taken as the optimal solutions.

[0118] Regarding the above step S18, the Vandermonde decomposition is used for the optimal solution to obtain the super-resolution one-dimensional azimuth image of the target.

[0119] It can be understood that after obtaining the optimal solutions and of Equation (10), the scattering components embedded in are solved by Vandermonde decomposition. Among them, the number of scattering centers is determined by the SORTE algorithm; the Doppler frequency is determined by the MPM (Matrix Pencil Method); based on to form the matrix and the reconstructed signal , the scattering intensity is determined according to the least squares estimation . Thus, the super-resolution one-dimensional azimuth image of the missing echo in a single range cell can be obtained.

[0120] Regarding the above step S20, according to the orthogonal atomic norm minimization problem, the missing azimuth echoes of all effective range cells are quickly solved to obtain the super-resolution one-dimensional azimuth images of each effective range cell and draw the azimuth super-resolution ISAR image of the target.

[0121] It can be understood that usually the effective scattering components of a radar target are only distributed within a certain range of range cells, and the effective range cell range is determined. For the above range cells, Equation (10) is repeatedly solved to obtain the super-resolution one-dimensional azimuth images of the corresponding range cells. Subsequently, the super-resolution one-dimensional azimuth images of single range cells are sequentially drawn in the two-dimensional plane, and then the complete azimuth super-resolution ISAR image of the target is obtained. Specifically, when drawing the ISAR image, the intensity position of the scattering center is jointly determined by the index of the range cell (or the calibrated range) and the Doppler frequency (or the coordinates after azimuth calibration), and the intensity of the scattering center is jointly reflected by solid circles of different sizes and different colors.

[0122] The above gridless azimuth super-resolution sparse aperture ISAR imaging method avoids off-grid errors and is not restricted by the minimum atom distance, and can improve the ISAR image quality under sparse aperture and short aperture radar observation conditions. Specifically, by adopting orthogonal atomic norm minimization to model the azimuth missing echoes and using the Iterative Vandermonde Decomposition Shrinkage Threshold (IVDST) algorithm for fast solution, there is no need to establish a dictionary matrix, avoiding off-grid errors, effectively suppressing strong grating lobe artifacts caused by sparse apertures, and resolving adjacent scattering centers below the Rayleigh resolution distance caused by short apertures, with the ability of super-Rayleigh resolution. The obtained ISAR image has no main lobe broadening and side lobes in the azimuth dimension, has the advantages of characterizing the number, position and intensity of scattering centers within a single range cell, has a clear physical meaning of the ISAR image, and has great engineering application value.

[0123] In some embodiments, Figure 3 For the point simulation aircraft target model, it makes a uniform rotation of 2° / s. The radar system simulation parameters can be as follows: center frequency 10 GHz, bandwidth 300 MHz, pulse repetition frequency 200 Hz, and pulse accumulation time 0.6 s. The full aperture echo contains 121 pulses, each pulse contains 201 frequency sampling points, and the corresponding range Rayleigh resolution is , and the azimuth Rayleigh resolution is . Figure 3 The scattering center shown in is the closest scattering center in the azimuth direction of the simulation target, and the azimuth distance between the two is 0.5 m, which is lower than the azimuth Rayleigh resolution distance

[0124] Figure 4 (a), Figure 4 (b) are respectively the one-dimensional range image sequence and the ISAR image of the point simulation target under full aperture conditions. As can be seen from Figure 4 (b), the ISAR image obtained by the traditional RD method has high side lobe phenomena.

[0125] From Figure 4 (a) shown in the full aperture data, 60 pulses are randomly selected to simulate the sparse aperture radar observation conditions with a sparsity of 50%. Figure 5 (a) shows the missing one-dimensional range image sequence of the point simulation target with a sparsity of 50%. Figure 5 (b), Figure 5 (c) are respectively the imaging results of the RD method and the method of the present invention. As can be seen from Figure 5As can be seen from (b), the ISAR image obtained by the RD method is severely defocused and seriously interfered by strong grating lobes. The scattering centers are almost completely submerged in the grating lobes, making it difficult to reflect the scattering distribution of the target. From Figure 5 As can be seen from (c), the above method of the present invention eliminates the grating lobe artifacts and azimuth side lobes, and the obtained ISAR image can clearly reflect the scattering distribution of the target.

[0126] For further analysis, Figure 6 Figure Figure 5 shows the cross-sectional views (one-dimensional azimuth images) of the 171st range cell of the RD method and the above method of the present invention in (b) and Figure 5 (c), where the normalized scattering amplitude is in units of the value "1" and is a relative value. As can be seen from Figure 6 , under the full-aperture condition, the azimuth image obtained by the RD method has a broadened main lobe and cannot resolve adjacent scattering centers. When sparse apertures occur, 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 the grating lobe and side lobe artifacts, has no main lobe broadening, can resolve 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.

[0127] When taking the cone combined target anechoic chamber measurement model as an example, the height of the model is 1.2 m, the bottom radius is 0.26 m, and it rotates at a uniform speed of 4° / s. The radar system measurement parameters are as follows: center frequency 9 GHz, bandwidth 1 GHz, pulse repetition frequency 20 Hz, and pulse accumulation time 1.55 s. The full-aperture data contains 32 pulses, each pulse contains 51 frequency sampling points, and the corresponding range Rayleigh resolution is , and the azimuth Rayleigh resolution is .

[0128] Figure 7 (a) and Figure 7 (b) are respectively the one-dimensional range image sequence and the ISAR image of the cone combined target under the full-aperture condition. As can be seen from Figure 7 (b), the ISAR image obtained by the traditional RD method can resolve 6 strong scattering centers, but there are main lobe broadening and high side lobe phenomena for each scattering center.

[0129] Randomly extract 16 pulses 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 combined target with a sparsity of 50%. Figure 8 (b) and Figure 8 (c) are respectively the imaging results of the RD method and the above method of the present invention. As can be seen from Figure 8As can be seen from (b), the ISAR image obtained by the RD method is defocused and interfered by strong grating lobes, making it difficult to distinguish the structure of the cone combination target. From Figure 8 As can be seen from (c), the above method of the present invention eliminates grating lobe artifacts and azimuth sidelobes, successfully extracts 6 strong scattering centers, and the obtained ISAR image can clearly reflect the target structure.

[0130] For further analysis, Figure 9 gives Figure 8 the profiles (one-dimensional azimuth images) of the RD method and the method of the present invention for the 26th range cell in (b) and Figure 8 (c). As can be seen from Figure 9 , under the full aperture condition, the azimuth image obtained by the RD imaging method has a broadened main lobe and high sidelobes. When sparse aperture occurs, the one-dimensional azimuth image obtained by the RD method also has strong grating lobe artifacts, making it difficult to distinguish the scattering centers of the target. In contrast, the above method of the present invention can still effectively extract the strong scattering centers of the cone combination target, further verifying the effectiveness of the above method of the present invention.

[0131] In summary, the above method of the present invention can work under the conditions of sparse aperture and short aperture radar observation, avoid the off-grid error, have no main lobe broadening, can effectively suppress grating lobes and sidelobe artifacts; is not restricted by the minimum atom distance, can resolve adjacent scattering centers under the super-Rayleigh resolution condition, and improve the ISAR image quality; has the ability to characterize the number, position and intensity of scattering centers within a single range cell, with clear physical meaning and high engineering application value.

[0132] In one embodiment, as Figure 10 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 transformation 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 perform demodulation and pulse compression to obtain an echo model. The echo characterization module 13 is used to sparsely characterize the missing azimuth echo corresponding to a single range cell after motion compensation based on the echo model. The problem transformation module 15 is used to transform 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 quickly solve the orthogonal atomic norm minimization problem by using the iterative Vandermonde shrinkage threshold algorithm to obtain the optimal solution. The azimuth image acquisition module 19 is used to obtain the super-resolution one-dimensional azimuth image of the target by using Vandermonde decomposition for the optimal solution. The super-resolution imaging module 21 is used to quickly solve and process the missing azimuth echoes of all effective range cells according to the orthogonal atomic norm minimization problem, obtain the super-resolution one-dimensional azimuth images of each effective range cell and draw the azimuth super-resolution ISAR image of the target.

[0133] The above-mentioned gridless azimuth super-resolution sparse aperture ISAR imaging system 100 performs one-dimensional imaging processing on all effective range cells of the received echo to obtain the super-resolution one-dimensional azimuth image of the target, and then obtains the super-resolution ISAR image of the target. First, a sparse representation of the missing azimuth echo within a single range cell is established based on the gridless compressive sensing framework, and then the super-resolution one-dimensional azimuth imaging is modeled as an underdetermined inverse problem based on OANM. Furthermore, it is solved by a fast algorithm of IVDST to reconstruct the positive semi-definite Toeplitz matrix and the echo signal of the azimuth echo of this range cell. Then, the Vandermonde decomposition is performed on the reconstructed Toeplitz matrix to sequentially estimate the number, position, and amplitude of the scattering centers within this range cell. Finally, super-resolution one-dimensional azimuth imaging processing is performed on all effective range cells, and the complete super-resolution ISAR image of the target is drawn. It alleviates the problem of low image quality caused by strong grating lobes, wide main lobes, high side lobes, off-grid errors, and non-satisfaction of the minimum atom constraint condition in the existing ISAR imaging methods, and realizes the technical effects of avoiding off-grid errors, being not restricted by the minimum atom distance, and improving the ISAR image quality under the radar observation conditions of sparse aperture and short aperture.

[0134] In one embodiment, the orthogonal atomic norm minimization problem is:

[0135] ;

[0136] where is a low-rank, positive semi-definite, and Hermitian symmetric Toeplitz matrix, represents the full-aperture azimuth echo of the th range cell, the superscript H in the upper right corner of denotes the conjugate transpose, M is an auxiliary variable, represents the trace of the matrix, represents the observation matrix, represents the sparse-aperture azimuth echo of the th range cell, is a constant related to the noise level, and respectively represent the steering vector and the normalized Doppler frequency, represents the inner product operation of vectors, , and , is the number of scattering centers.

[0137] In one embodiment, when the fast solution module 17 quickly solves the orthogonal atomic norm minimization problem by using the iterative Vandermonde shrinkage threshold algorithm and obtains the optimal solution, the orthogonal atomic norm minimization problem is converted into an optimization problem without explicit constraints, and the proximity gradient framework is used to solve the optimization problem without explicit constraints; wherein, the matrices T and Z are sequentially updated by using alternating iterative projection to obtain the optimal solution, and the alternating iterative projection includes low-rank constraint projection, positive semi-definite constraint projection, and Toeplitz structure projection.

[0138] For the specific limitations of a meshless azimuth super-resolution sparse aperture ISAR imaging system 100, reference can be made to the corresponding limitations of a meshless azimuth super-resolution sparse aperture ISAR imaging method in the above text, which will not be elaborated here.

[0139] It should be understood that although the steps in the above flowchart are sequentially shown in the direction of the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise clearly stated in this article, the execution of these steps has no strict order limit, 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. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or alternately with at least a part of other steps or sub-steps or stages of other steps.

[0140] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. 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 methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided by the present invention can include non-volatile and / or volatile memories. 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. By way of 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 (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), memory bus dynamic random access memory (Rambus DRAM, abbreviated as RDRAM), and interface dynamic random access memory (DRDRAM), etc.

[0141] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, 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, it should be considered as the scope described in this specification.

[0142] The above embodiments only represent several implementation manners of the present invention, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the protection scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, which all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended 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 and processed 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; Among them, 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.

2. The gridless azimuth super-resolution sparse aperture ISAR imaging method according to claim 1, 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.

3. 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; Among them, 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.

4. The gridless azimuth super-resolution sparse aperture ISAR imaging system according to claim 3, 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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