Sparse ISAR imaging method and system based on tight frame and projection operator

Abstract

The present invention relates to the field of radar imaging technology, and in particular to a sparse ISAR imaging method and system based on a tight frame and a projection operator. The method comprises constructing an ISAR imaging generalized analysis model for directly analyzing ISAR images based on an inverse synthetic aperture radar (ISAR) imaging system and utilizing a tight frame. Furthermore, an orthogonal projection operator is set based on the analysis factor and frame size of the ISAR imaging generalized analysis model, and the ISAR imaging generalized analysis model is decomposed and solved by the orthogonal projection operator to obtain a sparse ISAR imaging result. The method constructs a sparse ISAR imaging generalized analysis model based on a tight frame, which can directly analyze ISAR images, thereby reducing the number of model unknowns and increasing training and analysis efficiency. Furthermore, the method efficiently solves the sparse ISAR imaging model based on a simple iterative algorithm using a projection operator. Each iteration requires only a simple proximal mapping, and an acceleration strategy is introduced to increase the iterative convergence speed of the proximal mapping, thereby improving imaging efficiency while ensuring imaging quality.

Description

Technical Field

[0001] The present invention relates to the field of radar imaging technology, and in particular to a sparse ISAR imaging method and system based on a tight frame and a projection operator. Background Art

[0002] Inverse synthetic aperture radar (ISAR) boasts high resolution and holds broad application prospects in target detection and recognition. Traditional ISAR imaging systems typically require long coherent processing intervals to achieve high azimuth resolution. However, due to the lack of cooperation among moving targets, collecting observation data within these long coherent processing intervals is often difficult. Furthermore, external factors such as noise interference can cause some received pulse signals to be invalid or lost. Therefore, traditional ISAR imaging methods struggle to achieve good imaging results, making the study of sparse aperture ISAR imaging methods of great significance.

[0003] To address the defocusing problem caused by sparse apertures, some studies have introduced modern signal processing methods into ISAR imaging. Compared with traditional ISAR imaging methods based on Fourier transforms, modern signal processing methods can achieve lower sidelobes and higher resolution, but are sensitive to noise and modeling errors. Imaging methods based on compressed sensing can achieve high-resolution reconstruction of sparse signals with less observation data and are therefore widely used in sparse ISAR imaging. However, the results of sparse ISAR imaging based on compressed sensing are easily affected by noise, and the imaging quality decreases sharply with the increase of noise. In addition, to solve the computational problems caused by one-dimensional data processing, some ISAR imaging methods have been extended to two-dimensional data processing, such as 2D-FISTA and 2D-SL0. However, their imaging quality is affected by the sampling rate. Summary of the Invention

[0004] To this end, the present invention provides a sparse ISAR imaging method and system based on a tight frame and projection operator, which directly analyzes ISAR images and improves imaging quality and efficiency.

[0005] According to the design scheme provided by the present invention, a sparse ISAR imaging method based on a tight frame and a projection operator is provided, comprising:

[0006] Based on the ISAR imaging system and using a tight framework, a generalized ISAR imaging analysis model for directly analyzing ISAR images is constructed.

[0007] The orthogonal projection operator is set according to the analysis factor and frame size of the ISAR imaging generalized analysis model. The ISAR imaging generalized analysis model is decomposed and solved by the orthogonal projection operator to obtain the sparse ISAR imaging results.

[0008] In the inverse synthetic aperture radar (ISAR) imaging system, the echo signal can first be pulse compressed in the range direction. The range compression signal corresponding to the range unit is obtained by discrete sampling the echo signal after range migration correction. Then, the range focusing result is obtained by combining the range compression signals corresponding to all range units. Finally, the sparse aperture matrix and additive noise matrix are combined to construct the observation signal of the inverse synthetic aperture radar (ISAR) imaging system.

[0009] Furthermore, the present invention also provides a sparse ISAR imaging system based on a tight frame and a projection operator, comprising: a model building module and a model solving module, wherein:

[0010] A model building module is used to build an ISAR imaging generalized analysis model for directly analyzing ISAR images based on the ISAR imaging system and using a tight framework;

[0011] The model solving module is used to set the orthogonal projection operator according to the analysis factor and frame size of the ISAR imaging generalized analysis model, decompose and solve the ISAR imaging generalized analysis model through the orthogonal projection operator, and obtain sparse ISAR imaging results.

[0012] Beneficial effects of the present invention:

[0013] The present invention constructs a generalized analysis model for sparse ISAR imaging based on a tight framework, and makes it similar to a synthetic model. It can directly analyze ISAR images instead of redundant sparse coefficients, resulting in fewer model unknowns and higher training and analysis efficiency. A simple iterative algorithm based on the projection operator is used to efficiently solve the sparse ISAR imaging model. Each iteration only requires a simple proximal mapping. By introducing an acceleration strategy to improve the iterative convergence speed of the proximal mapping, the imaging efficiency can be improved while ensuring imaging quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of the sparse ISAR imaging process based on the tight frame and projection operator in the embodiment;

[0015] Figure 2 Schematic diagram of the sparse ISAR imaging algorithm in the embodiment;

[0016] Figure 3 Schematic diagram of full-aperture ISAR imaging results obtained by the traditional RD algorithm in the embodiment;

[0017] Figure 4 Schematic diagram of sparse ISAR imaging results obtained by the SBL algorithm and the present method using 50% pulse number when the signal-to-noise ratio is 10 dB in the embodiment;

[0018] Figure 5This is a schematic diagram of the sparse ISAR imaging results obtained by the SBL algorithm and the method of this embodiment using 50% pulse number when the signal-to-noise ratio is 0 dB. DETAILED DESCRIPTION

[0019] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention is further described in detail below with reference to the accompanying drawings and technical solutions.

[0020] In order to improve the quality of sparse ISAR imaging, various prior information is introduced into the sparse ISAR imaging model to improve the imaging quality. The sparse ISAR imaging method based on the Bayesian framework assumes that the signal satisfies a certain sparse distribution to obtain ISAR imaging results, but its computational efficiency is not high, and the imaging quality is poor under low signal-to-noise ratio. The sparse ISAR imaging method based on low rank utilizes the low rank of the received ISAR signal to improve the ISAR imaging quality, but its imaging quality decreases as the noise increases. In addition to spatial sparsity, the sparsity of the imaging scene in different transform domains can also be used to improve the ISAR imaging results. At present, the imaging methods related to sparse ISAR usually use point-based models or orthogonal dictionaries to sparsely represent ISAR images, because orthogonal dictionaries are conducive to theoretical analysis and algorithm design. However, the sparse representation based on the orthogonal dictionary cannot sensitively capture the different features of the ISAR image, so the imaging quality is limited. In order to further improve the ISAR imaging effect, the embodiments of the present invention, see Figure 1 As shown, a sparse ISAR imaging method based on a tight frame and a projection operator is provided, comprising:

[0021] S101, constructing an ISAR imaging generalized analysis model for directly analyzing ISAR images based on an inverse synthetic aperture radar (ISAR) imaging system and using a tight framework;

[0022] S102. Setting an orthogonal projection operator according to the analysis factor and frame size of the ISAR imaging generalized analysis model, decomposing and solving the ISAR imaging generalized analysis model through the orthogonal projection operator, and obtaining a sparse ISAR imaging result.

[0023] The echo signal received by the ISAR system is pulse compressed in the range direction, and then the signal after range migration correction is discretely sampled to obtain a range compression signal corresponding to a range unit. The range compression signals corresponding to all range units are combined together to obtain the range focusing result:

[0024] S=ΦX (1)

[0025] Where Φ is the dictionary matrix and X is the ISAR image to be obtained.

[0026] Under non-ideal conditions, some measurement echo signals are lost or the received signals are invalid in certain time periods. In addition, the received echo signals are often affected by noise. Therefore, the observation signal of the ISAR system can be expressed as

[0027] Y=RS+N=RΦX+N (2)

[0028] Where R represents the sparse aperture matrix and N is the additive noise matrix. Therefore, the purpose of ISAR imaging is to recover the unknown image result X from the noise-contaminated signal matrix Y.

[0029] In order to solve the ISAR imaging problem more effectively, this paper uses a tight frame to perform a sparse representation of ISAR images, because the tight frame can obtain a more stable and sparse signal representation than the orthogonal transformation. Since the sparse representation obtained using the tight frame is not unique, there are two related ISAR imaging models, namely the analytical model and the synthetic model. The classical analytical model of ISAR imaging based on the tight frame can be expressed as

[0030]

[0031] In the analysis model (3), the optimization problem is directly applied to the ISAR image X to make the analyzed signal sparse, where Ω represents the analysis operator and λ represents the regularization parameter.

[0032] When analytical operators contain redundancy, analytical models can achieve better reconstruction results than synthetic models. Furthermore, analytical models process images directly, while synthetic models process redundant sparse coefficients. Consequently, analytical models have fewer unknowns and are more efficient. While they have many shortcomings, synthetic models can be solved quickly and at a low computational cost. However, compared to synthetic models, solving analytical models quickly remains a challenge.

[0033] Combining the advantages of these two models, the present invention proposes a general analysis model based on tight frame and projection operator. In the classical analysis model (3) of ISAR imaging system, let ΩX=Z, if the frame D satisfies D=Ω + =(ΩΩ * ) -1 Ω * , that is, choose the frame D as the pseudo-inverse of Ω, then X can be recovered from Z by the following formula

[0034] X=Ω + Z=DZ (4)

[0035] According to the definition of Z, the constraint Z∈span(Ω) is added to the ISAR sparse imaging analysis model, and then X in Equation (3) is replaced by Z. The generalized analysis model of sparse ISAR imaging can be obtained as follows:

[0036]

[0037] Where e(Z) represents the constraint condition of Z, which is defined as

[0038]

[0039] The generalized analytical model of sparse ISAR imaging constructed at this time has a form similar to that of the synthetic model.

[0040] In order to effectively obtain sparse ISAR imaging results, the orthogonal projection operator is used in this embodiment to decompose Equation (5) into two steps for operation. According to the constraints satisfied by the framework D, the orthogonal projection operator on the spatial span (Ω) is defined as P Ω =ΩD.

[0041] Since Z∈span(Ω), the orthogonal projection operator P Ω Introducing model (5), the generalized analysis model of sparse ISAR imaging can be equivalent to

[0042]

[0043] For the first term in formula (7), let Using the Lipschitz continuous gradient constructor of f(Z)

[0044]

[0045] Then the solution of the first term in equation (7) is

[0046]

[0047] Using proximal mapping, we can obtain The solution is

[0048]

[0049] Among them, τ λ (x)=sgn(x)·max(|x|-λ,0).

[0050] Will and D = Ω + Substituting into (10), we get

[0051]

[0052] Then, combining the second term in (7) and (11), we can obtain

[0053]

[0054] For a tight frame, there exists Ω * Ω=Ι. In addition, and Substituting Z in formula (12), we can get

[0055] X i+1 =Dτ λγ (ΩX i +γΩΦ * R T (Y-RΦX i )) (13)

[0056] It can be seen from formula (13) that the proposed algorithm only introduces one variable γ in addition to the regularization parameter, and the calculation mainly comes from the proximal mapping.

[0057] In order to further improve the efficiency of sparse ISAR calculation, in this embodiment, an acceleration strategy for sparse ISAR imaging is further set. When solving the sparse ISAR image, the near-end mapping is not applied to the previous point X. i , but acts on the first two points X i and X i-1 The combination of , thereby improving the iterative convergence speed of the proximal mapping. Figure 2 In the iterative process of obtaining ISAR images, set It's X i and X i-1 combination of

[0058]

[0059] where t i The value is

[0060]

[0061] Substituting formula (14) into formula (13), we get

[0062]

[0063] When the iteration ends, the final sparse ISAR imaging result X is obtained.

[0064] Furthermore, based on the above method, an embodiment of the present invention further provides a sparse ISAR imaging system based on a tight frame and a projection operator, comprising: a model building module and a model solving module, wherein:

[0065] A model building module is used to build an ISAR imaging generalized analysis model for directly analyzing ISAR images based on the ISAR imaging system and using a tight framework;

[0066] The model solving module is used to set the orthogonal projection operator according to the analysis factor and frame size of the ISAR imaging generalized analysis model, decompose and solve the ISAR imaging generalized analysis model through the orthogonal projection operator, and obtain sparse ISAR imaging results.

[0067] To verify the effectiveness of this solution, the following is a further explanation based on the test data:

[0068] Data used in the experiment: The measured echo data of the Yak-42 aircraft is used to verify the sparse ISAR imaging method proposed in this case.

[0069] The main radar parameters are as follows: carrier frequency is 5.6 GHz, bandwidth is 400 MHz, pulse repetition frequency is 800 Hz, number of azimuth pulses is 256, and number of range units is 256.

[0070] Input: Yak-42 aircraft measured echo data matrix, Fourier transform matrix Φ, available pulse number, signal-to-noise ratio value.

[0071] First, the measured Yak-42 aircraft echo signal is pulse compressed in the range direction, followed by range migration correction to obtain the range focusing result S. The sparse sampling matrix R is determined based on the preset number of available pulses, and the noise matrix N is determined based on the preset signal-to-noise ratio. The observation signal Y of the sparse ISAR system is obtained by Y = RS + N.

[0072] The detailed process of iterative solution can be described as:

[0073] 1) The initial solution X0 of the ISAR image is obtained by partial Fourier transform of the observation signal Y, the number of iterations i = 0, t i =1.

[0074] 2) In the i-th iteration, use Update X i+1 value.

[0075] 3) Utilize Update i+1 value.

[0076] 4) Utilize renew value.

[0077] 5) Determine ||X i+1 -X i Is ||2 less than the preset iteration termination threshold? If so, set i=i+1 and return to step 2). Otherwise, the iteration is terminated and the final estimation result X is output. i+1 .

[0078] Table 1: Comparison of running time of the sparse Bayesian algorithm SBL and the proposed algorithm

[0079]

[0080] Figure 3 The ISAR imaging results obtained using the traditional RD algorithm at full aperture are: Figure 4 The sparse ISAR imaging results obtained by the SBL algorithm and the proposed algorithm using 50% pulse number when the signal-to-noise ratio is 10dB. Figure 5 The sparse ISAR imaging results obtained by the SBL algorithm and the proposed algorithm using 50% pulse number when the signal-to-noise ratio is 0dB are shown in Table 1. The running time comparison of the SBL and proposed methods is shown in Table 1. Figures 3 to 5 It can be seen that the proposed algorithm can still obtain good imaging results under low signal-to-noise ratio, suppress the influence of noise, and maintain the target structure and edges. Table 1 compares the running time of SBL and the proposed algorithm on Yak-42 data at a 50% sampling rate. The running time of SBL reaches 22.1374 seconds because it requires parameter learning and estimation. The calculation of the proposed algorithm only comes from approximate mapping, and an acceleration strategy is introduced to accelerate convergence. Therefore, the running time of the proposed algorithm is much shorter than that of SBL, which is 2.1927 seconds. The experimental results further verify that the proposed solution can effectively improve imaging quality and efficiency, and facilitate the scene application function of radar imaging technology in detection platforms.

[0081] Unless otherwise specifically stated, the relative steps, numerical expressions and values ​​of the components and steps set forth in these embodiments do not limit the scope of the present invention.

[0082] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0083] The units and method steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of function in the above description. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. A person of ordinary skill in the art may use different methods to implement the described functions for each specific application, but such implementation is not considered to be beyond the scope of the present invention.

[0084] Those skilled in the art will appreciate that all or part of the steps in the above method can be performed by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a read-only memory, a magnetic disk, or an optical disk. Alternatively, all or part of the steps in the above embodiment can be implemented using one or more integrated circuits. Accordingly, each module / unit in the above embodiment can be implemented in the form of hardware or software functional modules. The present invention is not limited to any specific combination of hardware and software.

[0085] Finally, it should be noted that the above-described embodiments are only specific implementation methods of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the above-described embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily conceive of changes to the technical solutions described in the above-described embodiments within the technical scope disclosed by the present invention, or replace some of the technical features therein with equivalents. Such modifications, changes, or replacements do not deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A sparse ISAR imaging method based on a tight frame and projection operator, characterized in that: Include: Based on the inverse synthetic aperture radar (ISAR) imaging system and using a tight framework, a generalized ISAR imaging analysis model for directly analyzing ISAR images is constructed. The generalized ISAR imaging analysis model is expressed as: Y is the observation signal matrix of the inverse synthetic aperture radar (ISAR) imaging system, D is the frame representation set by the analysis operator, R is the sparse aperture matrix, Φ is the dictionary matrix, Z is the equivalent signal representation of the sparse ISAR imaging generalized analysis model, and e(Z) represents the constraint condition of Z; According to the analysis factor and frame size of the ISAR imaging generalized analysis model, the orthogonal projection operator is set. The ISAR imaging generalized analysis model is decomposed and solved by the orthogonal projection operator to obtain the sparse ISAR imaging results. In the setting process, the orthogonal projection operator is set on the space span (Ω) according to the constraints satisfied by the frame representation D. The orthogonal projection operator is represented as P Ω =ΩD, Ω represents the model analysis operator.

2. The sparse ISAR imaging method based on a tight frame and projection operator according to claim 1, characterized in that: In the Inverse Synthetic Aperture Radar (ISAR) imaging system, the echo signal is first pulse compressed in the range direction. The range-compressed signal corresponding to the range unit is obtained by discretely sampling the echo signal after range migration correction. Then, the range-compressed signal corresponding to all range units is combined to obtain the range-focusing result. Then, the sparse aperture matrix and additive noise matrix are combined to construct the observation signal of the inverse synthetic aperture radar (ISAR) imaging system.

3. The sparse ISAR imaging method based on tight frame and projection operator according to claim 1, characterized in that: In the model decomposition solution, first, through the orthogonal projection operator P Ω The generalized analysis model of ISAR imaging is decomposed into Next, let Using the f(Z) Lipschitz continuous gradient constructor and proximal mapping Solve; then, the framework representation D is used to construct the sparse ISAR image formula, and the sparse ISAR imaging results are obtained by iteratively solving the formula.

4. The sparse ISAR imaging method based on a tight frame and projection operator according to claim 3, characterized in that: The sparse ISAR image formula is expressed as: X i+1 =Dτ λγ (ΩX i +γΩΦ * R T (Y-RΦX i )), γ is the variable parameter, Ω represents the model analysis operator, X i+1 is the pixel point of the sparse ISAR image to be solved, and i is the iteration round.

5. The sparse ISAR imaging method based on tight frame and projection operator according to claim 4, characterized in that: In the iterative solution of the sparse ISAR image formula, the proximal mapping is applied to the first two pixel estimation combinations of the pixel to be solved, and the sparse ISAR image formula is adjusted to: in, t i Represents the pixel estimated combining factor.

6. A sparse ISAR imaging system based on a tight frame and projection operator, characterized in that: The method according to claim 1 is implemented, comprising: a model building module and a model solving module, wherein: A model building module is used to build an ISAR imaging generalized analysis model for directly analyzing ISAR images based on the ISAR imaging system and using a tight framework; The model solving module is used to set the orthogonal projection operator according to the analysis factor and frame size of the ISAR imaging generalized analysis model, decompose and solve the ISAR imaging generalized analysis model through the orthogonal projection operator, and obtain sparse ISAR imaging results.

7. An electronic device, characterized in that: The method comprises a memory and a processor, wherein the processor and the memory communicate with each other via a bus; the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the method according to any one of claims 1 to 4.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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