Sparse-aperture ISAR imaging method, device and equipment and storage medium
By performing translational compensation and joint time-frequency transformation on radar echo data of precessing targets with sparse apertures, a tensor mathematical model was constructed and optimized, which solved the problem of poor ISAR image quality under sparse apertures and achieved the generation of clear ISAR images.
Patent Information
- Application Number
- CN202310197776.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-03-03
- Publication Date
- 2026-03-03
- Estimated Expiration
- 2043-03-03
AI Technical Summary
Existing ISAR imaging methods cannot effectively eliminate sidelobe interference and microDoppler interference under sparse aperture conditions, resulting in poor ISAR image quality for cone-shaped precession targets.
By acquiring radar echo data, performing translational compensation and joint time-frequency transformation, a tensor mathematical model is constructed. Tensor matrix kernel norm and l1 norm constraints are introduced, and the alternating direction multiplier method is used to optimize the model and obtain clear ISAR images.
Under sparse aperture conditions, sidelobe and micro-Doppler interference are effectively eliminated, improving the ISAR image quality and resolution of conical precession targets.
Smart Images
Figure CN116338688B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of inverse synthetic aperture radar imaging technology, and in particular to a sparse aperture precession target ISAR imaging method, apparatus, device and storage medium. Background Technology
[0002] Inverse Synthetic Aperture Radar (ISAR) imaging has always been a crucial tool in space target surveillance and identification. Sparse aperture precession target ISAR imaging is a pressing problem in this field, aiming to obtain clear and complete target ISAR images under low data sampling rates and complex Doppler information superposition. For space cone-shaped targets, during flight, they spin around their axis of symmetry and undergo conical rotation around their center of mass; this combined spin and conical rotation motion is called precession. Precession introduces complex Doppler information, generating micro-Doppler interference in the image, posing challenges and difficulties for ISAR imaging. Furthermore, in real-world scenarios, the radar echo received is often incomplete due to switching between different channels and other interference factors; this incomplete echo is called a sparse aperture echo. Sparse apertures generate strong sidelobe interference in ISAR images, severely affecting image quality. Obtaining clear and complete ISAR images of precession cone-shaped targets under the combined effects of sparse aperture and precession is a significant challenge.
[0003] Existing ISAR imaging methods are mainly for imaging precessing targets under full aperture conditions. Under sparse aperture conditions, sidelobe interference and micro-Doppler interference will superimpose each other, and traditional methods will not be able to achieve good imaging of the target. Summary of the Invention
[0004] Therefore, it is necessary to provide an ISAR imaging method, apparatus, device, and storage medium for sparse aperture precessing targets to address the aforementioned technical problems.
[0005] A sparse aperture precession target ISAR imaging method, the method comprising:
[0006] Acquire radar echo data and convert it into a one-dimensional range profile;
[0007] By performing translational compensation and joint time-frequency transformation on the one-dimensional range profile, a sequence of one-dimensional range profiles of the precessing target is obtained.
[0008] A tensor mathematical model is constructed based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved.
[0009] When solving the target ISAR image sequence, the tensor matrix kernel norm and l1 norm are introduced on the basis of the tensor mathematical model to constrain the low rank and sparsity of the image sequence, respectively, so as to obtain an optimized model.
[0010] The optimization model is solved using the alternating direction multiplier method to obtain the ISAR image of the precessing target.
[0011] In one embodiment, the joint time-frequency transform of the one-dimensional range image after translational compensation is expressed as:
[0012]
[0013] In the above formula, s(t) represents the input signal, i.e. the one-dimensional range profile, and ω(t) represents the short-time window function.
[0014] In one embodiment, the tensor mathematical model is represented as:
[0015]
[0016] In the above formula, Let represent the target ISAR image sequence, the one-dimensional range image sequence, and the noise, respectively.
[0017] In one embodiment, the optimization model is represented as:
[0018]
[0019] In the above formula, This indicates a constraint on the error. This indicates that the low-rank property of the image sequence is constrained by the tensor matrix nuclear norm. This indicates that the l1 norm is used to constrain the sparsity of the image sequence.
[0020] In one embodiment, solving the optimization model using the alternating direction multiplier method includes:
[0021] Auxiliary variables are introduced to transform the optimization model, and the augmented Lagrangian function of the transformed optimization model is constructed.
[0022] The optimization model is transformed into solving multiple subproblems based on the augmented Lagrangian function.
[0023] In one embodiment, when the subproblems are solved alternately:
[0024] The augmented Lagrange function is used to update the introduced auxiliary variables, the target ISAR image sequence, and the augmented Lagrange multipliers.
[0025] In one embodiment, when solving each of the sub-problems alternately, the final target ISAR image sequence is obtained by setting the number of iterations or the error precision.
[0026] When the number of iterations reaches a preset number or the error accuracy reaches a preset value, the ISAR image sequence obtained in that iteration is the final target ISAR image sequence.
[0027] A sparse aperture precession target ISAR imaging device, the device comprising:
[0028] The one-dimensional range image acquisition module is used to acquire radar echo data and convert it into a one-dimensional range image;
[0029] A one-dimensional range image sequence preprocessing module is used to perform translational compensation and joint time-frequency transformation on the one-dimensional range image to obtain the one-dimensional range image sequence of the precessing target;
[0030] The tensor mathematical model construction module is used to construct a tensor mathematical model based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved.
[0031] The optimization model module is used to solve the target ISAR image sequence. Based on the tensor mathematical model, the tensor matrix kernel norm and l1 norm are introduced to constrain the low rank and sparsity of the image sequence, respectively, thereby obtaining the optimization model.
[0032] The target ISAR image sequence solution module is used to solve the optimization model using the alternating direction multiplier method to obtain the ISAR image of the precessing target.
[0033] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:
[0034] Acquire radar echo data and convert it into a one-dimensional range profile;
[0035] By performing translational compensation and joint time-frequency transformation on the one-dimensional range profile, a sequence of one-dimensional range profiles of the precessing target is obtained.
[0036] A tensor mathematical model is constructed based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved.
[0037] When solving the target ISAR image sequence, the tensor matrix kernel norm and l1 norm are introduced on the basis of the tensor mathematical model to constrain the low rank and sparsity of the image sequence, respectively, so as to obtain an optimized model.
[0038] The optimization model is solved using the alternating direction multiplier method to obtain the ISAR image of the precessing target.
[0039] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:
[0040] Acquire radar echo data and convert it into a one-dimensional range profile;
[0041] By performing translational compensation and joint time-frequency transformation on the one-dimensional range profile, a sequence of one-dimensional range profiles of the precessing target is obtained.
[0042] A tensor mathematical model is constructed based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved.
[0043] When solving the target ISAR image sequence, the tensor matrix kernel norm and l1 norm are introduced on the basis of the tensor mathematical model to constrain the low rank and sparsity of the image sequence, respectively, so as to obtain an optimized model.
[0044] The optimization model is solved using the alternating direction multiplier method to obtain the ISAR image of the precessing target.
[0045] The aforementioned sparse aperture ISAR imaging method, apparatus, device, and storage medium for precessing targets obtains a one-dimensional range image sequence of the precessing target by performing translational compensation and joint time-frequency transformation on the acquired one-dimensional range image. A tensor mathematical model is then constructed based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved. Subsequently, when solving the target ISAR image sequence, the tensor matrix kernel norm and l1 norm are introduced on the tensor mathematical model to constrain the low-rank and sparsity of the image sequence, respectively, thus obtaining an optimized model. Finally, the alternating direction multiplier method is used to solve the optimized model to obtain the target's ISAR image sequence. This method can improve the ISAR image quality of precessing targets under sparse aperture conditions. Attached Figure Description
[0046] Figure 1 This is a flowchart illustrating a sparse aperture precession target ISAR imaging method in one embodiment;
[0047] Figure 2 This is a schematic diagram of the iterative update process using this method in one embodiment;
[0048] Figure 3 Here are the experimental results for one embodiment with a 50% sparsity: (a) a one-dimensional range profile of the target; (b) an ISAR image of the target obtained by the range-instantaneous-Doppler method; and (c) an ISAR image of the target obtained by this patent.
[0049] Figure 4 Here are the experimental results for one embodiment with a 25% sparsity: (a) a one-dimensional range profile of the target; (b) an ISAR image of the target obtained by the range-instantaneous-Doppler method; and (c) an ISAR image of the target obtained in this patent.
[0050] Figure 5 This is a block diagram of the device structure in one embodiment;
[0051] Figure 6 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation
[0052] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0053] like Figure 1 As shown, a sparse aperture precession target ISAR imaging method is provided, including the following steps:
[0054] Step S100: Acquire radar echo data and convert it into a one-dimensional range profile;
[0055] Step S110: Perform translational compensation and joint time-frequency transformation on the one-dimensional range image to obtain a one-dimensional range image sequence of the precessing target;
[0056] Step S120: A tensor mathematical model is constructed based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved.
[0057] Step S130: When solving the target ISAR image sequence, the tensor matrix kernel norm and l1 norm are introduced on the basis of the tensor mathematical model to constrain the low rank and sparsity of the image sequence, respectively, so as to obtain the optimized model.
[0058] Step S140: The optimization model is solved using the alternating direction multiplier method to obtain the ISAR image of the precessing target.
[0059] In this application, existing ISAR imaging methods are mainly for imaging targets under full aperture conditions. However, under sparse aperture conditions, sidelobe interference and micro-Doppler interference will superimpose, making it impossible for traditional methods to achieve good target imaging. Therefore, a sparse aperture ISAR imaging method for precessing targets is proposed, which can achieve good imaging of precessing targets under sparse aperture conditions.
[0060] Before imaging in step S120, preprocessing is required, which involves performing translational compensation and joint time-frequency transformation on the one-dimensional range image in step S110.
[0061] To address image blurring caused by time-varying Doppler frequency shift, this embodiment employs a combined time-frequency transform to effectively examine the two-dimensional ISAR image at each instant, thus eliminating Doppler blurring due to precession. The short-time Fourier transform (SFT) is a typical time-frequency transform method. As its time window shifts, it examines the frequency range of the signal and generates a two-dimensional time-frequency transform that contains information about the frequency range of the signal at different times. The specific formula is as follows:
[0062]
[0063] In formula (1), s(t) represents the input signal, which is the one-dimensional range image after translational compensation, and ω(t) represents the short-time window function.
[0064] Specifically, formula (1) is equivalent to unfolding the one-dimensional range image of the target into an image sequence along the slow time domain, where any slice along the time dimension represents the one-dimensional range image at that moment. Then, Fourier transform is performed on each frame of the one-dimensional range image along the time dimension to obtain the target ISAR image sequence.
[0065] In practical applications of ISAR imaging, taking the simultaneous imaging of multiple ballistic targets by radar as an example, the radar does not target a single target but tracks multiple targets through emitted pulse signals. This results in non-uniform observation time for individual targets within the target group. Furthermore, the influence of the radio wave propagation environment and other interference factors can also lead to missing radar echoes. Incomplete echoes are typically referred to as sparse aperture echoes. Under sparse aperture conditions, the coherence between echoes is disrupted, limiting the Fourier transform and resulting in high sidelobe and grating lobe interference in images generated by traditional methods, thus affecting the interpretation of target images. The principle of the short-time Fourier transform is equivalent to expanding a one-dimensional range image along the slow time domain into a three-dimensional tensor, i.e., an image sequence. Therefore, the target ISAR image sequence to be solved can be written in tensor form with the one-dimensional range image sequence, which is the tensor mathematical model constructed in step S120:
[0066]
[0067] In formula (2), Let A, B, C, and D represent the target ISAR image sequence, the one-dimensional range image sequence, and the noise, respectively. The operator A(·) denotes the operation of first performing a Fourier transform along the third dimension of the tensor, and then performing sparse sampling on the result.
[0068] For ISAR image sequences, since each frame along the time dimension represents the radar's observation of the same target at different times, there is a certain correlation between each frame along the time dimension. This makes the tensor... It exhibits the low-rank property of tensors. Furthermore, for each frame of an ISAR image, relative to the image background, the target mainly consists of isolated, strongly scattering points; therefore, the tensor... Each frame of an ISAR image along the time dimension has a sparse property, meaning that the entire tensor is sparse in three-dimensional space.
[0069] Therefore, when solving for ISAR images of precessing targets, tensor matrix kernel norms and l1 norms are introduced to constrain them. The tensor matrix kernel norm, composed of tensor kernel norms and matrix kernel norms, not only constrains the low rank of the spatial information of the image sequence but also fully utilizes the temporal correlation of each frame. To address the sparsity of the images, the l1 norm is introduced to constrain image sparsity, thereby improving the focusing effect of target ISAR images under sparse apertures. In summary, the following optimized model can be obtained for the radar observation model:
[0070]
[0071] In formula (3), This indicates a constraint on the error. and This indicates that the low-rank property of the image sequence is constrained by the tensor matrix nuclear norm. This indicates that the l1 norm is used to constrain the sparsity of the image sequence.
[0072] Next, in step S140, the method of alternating direction multipliers is used to solve the optimization model, which includes: introducing auxiliary variables to transform the optimization model, constructing an augmented Lagrangian function of the transformed optimization model, and converting the transformed optimization model into an iterative solution of multiple sub-problems based on the augmented Lagrangian function. In each iteration, the target ISAR image sequence is updated. Finally, by setting the number of iterations or the error precision, the final target ISAR image sequence is obtained.
[0073] Specifically, introduce auxiliary variables Formula (3) can then be transformed into:
[0074]
[0075] Based on the principle of the alternating direction multiplier method, the augmented Lagrangian function of formula (4) is first constructed. as follows:
[0076]
[0077] In formula (5), Y2 and y3 represent Lagrange multipliers, and μ1, μ2, and μ3 represent punishment factors. Therefore, formula (4) can be transformed into solving the following subproblems:
[0078]
[0079] When solving each of the subproblems alternately, the auxiliary variables, the target ISAR image sequence, and the augmented Lagrange multipliers are solved and updated sequentially.
[0080] Specifically, first update the introduced auxiliary variables:
[0081] Updating auxiliary variables When, in fixed formula (5) Substitute formula (5) into formula (6) and omit the... For irrelevant variables, we can obtain:
[0082]
[0083] Equation (7) is a minimization TNN problem, which can be solved using the TNN proximal operator, as follows:
[0084]
[0085] Update Z2, fix Z2 in formula (5), substitute formula (5) into formula (6) and omit variables unrelated to Z2, and we get:
[0086]
[0087] Equation (9) is a problem of minimizing the matrix nuclear norm, which can be solved using the singular value contraction operator, as follows:
[0088]
[0089] Update z3, fix z3 in formula (5), substitute formula (5) into formula (6) and omit variables unrelated to z3, and we get:
[0090]
[0091] Formula (11) is a problem of minimizing the l1 norm, which can be solved using the soft thresholding operator:
[0092]
[0093] Next, the target ISAR image sequence is updated based on the updated auxiliary variables and the augmented Lagrangian function:
[0094] renew Fixed formula (5) Substitute formula (5) into formula (6) and omit the... For irrelevant variables, we can obtain:
[0095]
[0096] Formula (13) is a convex smooth problem. Taking its derivative and setting its first derivative to zero, we can obtain its analytical solution as follows:
[0097]
[0098] In formula (14), And utilize the properties of Fourier transform We can obtain:
[0099]
[0100] Next, the augmented Lagrange multipliers are updated based on the updated auxiliary variables and the target ISAR image sequence:
[0101]
[0102]
[0103]
[0104] In this embodiment, the final target ISAR image sequence is obtained by setting the number of iterations or an error threshold. Specifically, when the iteration rounds or error accuracy reach a preset value, the updated target ISAR image sequence obtained in that round of iteration becomes the final target ISAR image sequence.
[0105] In this embodiment, by performing a single imaging process on the one-dimensional range image of a precessing target using this method, multiple consecutive ISAR images of the target within a time period can be obtained. The motion information of the precessing target within that time period can be obtained through this series of ISAR images.
[0106] In this embodiment, the iterative update process of this method is as follows: Figure 2 As shown.
[0107] In this paper, experiments were also conducted based on the proposed method to verify its effectiveness.
[0108] like Figure 3As shown, a one-dimensional range profile and ISAR image of a cone target with a 50% sparsity are provided. From Figure 4 As can be seen, under the combined effects of precession and sparse aperture, the range-instantaneous-Doppler method can no longer obtain a clear target ISAR image; while the image obtained by this method has higher clarity, and micro-motion interference and sidelobe interference have been effectively removed, and the target outline is displayed more completely in the ISAR image.
[0109] like Figure 4 As shown, a one-dimensional range profile and ISAR image of a cone target with a 25% sparsity are provided. From Figure 5 As can be seen, as the sparsity decreases, the target ISAR image obtained by the range-instantaneous-Doppler method becomes more severely defocused; while the present method can still achieve good focusing on the target and obtain a clear target ISAR image, which further verifies the effectiveness of the present method.
[0110] In summary, this invention can effectively eliminate side lobes, grating lobes, and micro-Doppler interference caused by precessing targets under sparse apertures, and obtain high-resolution ISAR images of the targets. It remains effective even at low sparsity rates and has high engineering application value.
[0111] In the aforementioned sparse aperture ISAR imaging method for precessing targets, time-frequency transformation and tensor feature models are used to fully constrain the one-dimensional range profile of the precessing target, resulting in a three-dimensional ISAR image sequence. The tensor matrix kernel norm is employed to fully exploit the correlation between image frames and the spatial structure information of a single frame. The l1 norm is used to constrain the sparsity of the image, further improving the ISAR image quality of precessing targets under sparse aperture conditions. This method can generate precessing target ISAR images in batches under sparse aperture conditions and improve the resolution of precessing target ISAR images.
[0112] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed 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 in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.
[0113] In one embodiment, such as Figure 5As shown, a sparse aperture precession target ISAR imaging device is provided, comprising: a one-dimensional range image acquisition module 200, a one-dimensional range image sequence generation module 210, a tensor mathematical model construction module 220, an optimization model generation module 230, and a target ISAR image sequence solution module 240, wherein:
[0114] The one-dimensional range image acquisition module 200 is used to acquire radar echo data and convert it into a one-dimensional range image; the one-dimensional range image sequence preprocessing module 210 is used to perform translational compensation and joint time-frequency transformation on the one-dimensional range image to obtain the one-dimensional range image sequence of the precessing target.
[0115] Tensor mathematical model construction module 220 is used to construct a tensor mathematical model based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved.
[0116] The optimized model module 230 is used to solve the target ISAR image sequence. Based on the tensor mathematical model, the tensor matrix kernel norm and l1 norm are introduced to constrain the low rank and sparsity of the image sequence, respectively, so as to obtain the optimized model.
[0117] The target ISAR image sequence solving module 240 is used to solve the optimization model using the alternating direction multiplier method to obtain the target ISAR image sequence.
[0118] Specific limitations regarding the sparse aperture precessing target ISAR imaging device can be found in the limitations of the sparse aperture precessing target ISAR imaging method described above, and will not be repeated here. Each module in the aforementioned sparse aperture precessing target ISAR imaging device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.
[0119] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 6As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a sparse aperture precession target ISAR imaging method. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.
[0120] Those skilled in the art will understand that Figure 6 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.
[0121] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:
[0122] Acquire radar echo data and convert it into a one-dimensional range profile;
[0123] By performing translational compensation and joint time-frequency transformation on the one-dimensional range profile, a sequence of one-dimensional range profiles of the precessing target is obtained.
[0124] A tensor mathematical model is constructed based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved.
[0125] When solving the target ISAR image sequence, the tensor matrix kernel norm and l1 norm are introduced on the basis of the tensor mathematical model to constrain the low rank and sparsity of the image sequence, respectively, so as to obtain an optimized model.
[0126] The optimization model is solved using the alternating direction multiplier method to obtain the ISAR image of the precessing target.
[0127] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:
[0128] Acquire radar echo data and convert it into a one-dimensional range profile;
[0129] By performing translational compensation and joint time-frequency transformation on the one-dimensional range profile, a sequence of one-dimensional range profiles of the precessing target is obtained.
[0130] A tensor mathematical model is constructed based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved.
[0131] When solving the target ISAR image sequence, the tensor matrix kernel norm and l1 norm are introduced on the basis of the tensor mathematical model to constrain the low rank and sparsity of the image sequence, respectively, so as to obtain an optimized model.
[0132] The optimization model is solved using the alternating direction multiplier method to obtain the ISAR image of the precessing target. Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
[0133] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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.
[0134] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
Claims
1. A sparse aperture precession target ISAR imaging method, characterized in that, The method includes: Acquire radar echo data and convert it into a one-dimensional range profile; By performing translational compensation and joint time-frequency transformation on the one-dimensional range profile, a sequence of one-dimensional range profiles of the precessing target is obtained. A tensor mathematical model is constructed based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved. The tensor mathematical model is expressed as follows: In the above formula, , , Let represent the target ISAR image sequence, the one-dimensional range image sequence, and the noise, respectively, and let represent the operator. This indicates that a Fourier transform is first performed along the third dimension of the tensor, and then sparse sampling is performed on the result. When solving the target ISAR image sequence, the tensor matrix nuclear norm and, based on the tensor mathematical model, are introduced. l The L1 norm is used to constrain the low-rank and sparsity of the image sequence, respectively, to obtain an optimized model, which is expressed as: In the above formula, This indicates a constraint on the error. and This indicates that the low-rank property of the image sequence is constrained by the tensor matrix nuclear norm. Indicates adoption l The 1-norm constrains the sparsity of image sequences; The optimization model is solved using the alternating direction multiplier method to obtain the ISAR image of the precessing target.
2. The sparse aperture precession target ISAR imaging method according to claim 1, characterized in that, Solving the optimization model using the alternating direction multiplier method includes: Auxiliary variables are introduced to transform the optimization model, and the augmented Lagrangian function of the transformed optimization model is constructed. The optimization model is transformed into solving multiple subproblems based on the augmented Lagrangian function.
3. The sparse aperture precession target ISAR imaging method according to claim 2, characterized in that, When solving the subproblems alternately: The augmented Lagrange function is used to update the introduced auxiliary variables, the target ISAR image sequence, and the augmented Lagrange multipliers.
4. The sparse aperture precession target ISAR imaging method according to claim 3, characterized in that, When solving each of the sub-problems alternately, the final target ISAR image sequence is obtained by setting the number of iterations or the error precision. When the number of iterations reaches a preset number or the error accuracy reaches a preset value, the ISAR image sequence obtained in that iteration is the final target ISAR image sequence.
5. A sparse aperture precession target ISAR imaging device, characterized in that, The apparatus implements the sparse aperture precession target ISAR imaging method according to any one of claims 1 to 4, and the apparatus comprises: The one-dimensional range image acquisition module is used to acquire radar echo data and convert it into a one-dimensional range image; A one-dimensional range image sequence preprocessing module is used to perform translational compensation and joint time-frequency transformation on the one-dimensional range image to obtain the one-dimensional range image sequence of the precessing target. The tensor mathematical model construction module is used to construct a tensor mathematical model based on the relationship between the one-dimensional range image sequence and the target ISAR image sequence to be solved. The optimized model module, used to solve the target ISAR image sequence, introduces the tensor matrix nuclear norm and, based on the tensor mathematical model, the tensor matrix nuclear norm when solving the tensor mathematical model. l The 1-norm is used to constrain the low-rank and sparsity of the image sequence, respectively, thus obtaining the optimized model; The target ISAR image sequence solution module is used to solve the optimization model using the alternating direction multiplier method to obtain the ISAR image of the precessing target.
6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 4.
7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 4.