Matrix inverse-free ISAR imaging method based on gamma process-laplace prior

Abstract

The application discloses a kind of matrix inverse-free ISAR imaging methods based on gamma process-Laplacian prior, mainly solve the problem of two-dimensional reconstruction accuracy not high, long operation time in prior art.It is implementation scheme: receiving defective echo and generating echo matrix;According to defective echo matrix, obtain real Fourier dictionary Φ;According to echo matrix and real Fourier dictionary, the sparse observation model y of each distance unit is constructed q =Φω q +ε;Based on sparse observation model, the weight vector ω of each distance unit q Gamma process-Laplacian hierarchical prior is introduced;Gamma-Gaussian hierarchical prior is introduced to noise vector ε;Using matrix inverse-free fast inference method iteratively solves the weight vector of each distance unit;According to the obtained weight vector, two-dimensional high-resolution image is obtained.The reconstruction accuracy of the application is high, the operation time is short, and can be used for feature extraction and classification identification of space and air non-cooperative target under complex electromagnetic environment such as target echo low signal-to-noise ratio and existence defect.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and further relates to a matrix-inverse-free inverse synthetic aperture radar (ISAR) imaging method, which can be used for feature extraction and classification of space and air targets. Technical Background

[0002] Inverse synthetic aperture radar (ISAR) can achieve high-resolution imaging of non-cooperative targets in all weather conditions and at long ranges, enabling the acquisition of information such as target motion parameters and geometry. It has wide applications in space target surveillance and ballistic target defense. However, ISAR imaging faces two challenges: 1) Multi-task scheduling of ground-based phased array radars prevents ISAR from continuously observing targets for extended periods, resulting in azimuth echo defects; 2) When observing small targets at long distances, ISAR experiences very low echo signal-to-noise ratios, making focusing difficult. Due to the sparsity of target scattering points, high-resolution imaging under low signal-to-noise ratio and echo defect conditions can be achieved through sparse signal reconstruction.

[0003] Sparse signal reconstruction can be broadly categorized into numerical optimization and Sparse Bayesian Learning (SBL) methods. While numerical optimization methods have lower computational complexity, they suffer from unstable performance and low reconstruction accuracy in complex environments due to the lack of utilization of prior information from ISAR images and the environment. SBL methods, on the other hand, fully leverage statistical priors of the target and environment for probabilistic modeling and inference, thus providing a new approach for high-resolution ISAR imaging under complex observation conditions. However, existing SBL imaging methods suffer from two major problems: 1) inflexible target prior modeling and insufficient ability to represent the sparsity of target scattering points, leading to large solution errors; 2) the inference process requires numerous matrix inversion operations, resulting in high computational complexity and low imaging processing efficiency. Therefore, achieving accurate and rapid sparse Bayesian imaging of targets is an urgent problem to be solved.

[0004] Xi'an University of Electronic Science and Technology disclosed a "High-Resolution ISAR Imaging Method Based on Sparse Bayesian Learning in Interference Environments" in its patent application CN201711155705.0. Based on sparse signal representation theory, this method transforms the inverse synthetic aperture radar (ISAR) high-resolution imaging problem into a sparse signal reconstruction problem. It introduces sparse gamma-Gaussian priors into the weight vector and noise vector, and calculates the weight of each cell using the maximum a posteriori-maximum MAP-EM algorithm to ultimately achieve ISAR imaging. However, this method suffers from insufficient flexibility in the model constructed for the weight vector, resulting in large errors in the estimated parameters and an inability to obtain well-focused ISAR images. Furthermore, its algorithm involves numerous matrix inversion operations, leading to slow computation speed. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by proposing a matrix-inverse-free ISAR imaging method based on gamma process-Laplace prior, which improves the flexibility of target prior modeling and the accuracy of ISAR image reconstruction under conditions of low signal-to-noise ratio and echo loss; at the same time, it simplifies matrix inversion operations and improves imaging efficiency.

[0006] The technical approach of this invention is to achieve a flexible description and sparse characterization of the target's statistical properties by introducing a gamma process-Laplace hierarchical prior to the target scattering point, thereby solving the problem of large reconstruction errors in existing methods under conditions of low signal-to-noise ratio and missing echoes; and to solve the problem of high computational complexity and low imaging efficiency caused by the need for multiple matrix inversion operations in existing methods by using matrix inversion-free Bayesian inference.

[0007] Based on the above ideas, the implementation steps of the present invention include the following:

[0008] (1) Receive the missing echo matrix S′ and generate the real transpose echo matrix S;

[0009] (2) Obtain the real Fourier dictionary Φ based on the missing echo matrix S′;

[0010] (3) Construct a sparse observation model for each distance cell based on S and Φ: y q =Φω q +ε,

[0011] Among them, y q Let ω represent the q-th column vector of the real transpose echo matrix S. q Let ε represent the weight vector to be reconstructed in the q-th distance cell, and let ε represent the noise vector.

[0012] (4) Introduce a gamma process-Laplace hierarchical prior for the weight vector of each distance unit:

[0013] (4a) According to the following formula, the weight vector ω of the q-th distance cell is... q Introducing the Laplace prior:

[0014]

[0015] in, This represents the nth element in the weight vector of the qth distance cell. The probability density, express Obey the scale parameter is The probability density of the Laplace distribution, Indicates to The absolute value operation;

[0016] (4b) For each scale parameter according to the following formula. Introducing gamma process priors:

[0017]

[0018] in, Represents the nth scale parameter The probability density, express The probability density follows a gamma distribution with parameters c and d, where Γ(c) represents the gamma function with parameter c.

[0019] (5) Introduce a gamma-Gaussian hierarchical prior to the noise vector ε:

[0020] (5a) According to the following formula, a Gaussian prior is introduced for the noise vector ε:

[0021] p(ε n ) = Normal(ε n |0,β -1 )

[0022] Where p(ε) n ) represents the nth element of the noise vector ε. n The probability density, Normal(ε) n |0,β -1 ) represents ε n The probability density follows a Gaussian distribution with mean 0 and precision β;

[0023] (5b) Introduce a gamma prior to the accuracy β according to the following formula:

[0024]

[0025] Where p(β) represents the probability density of precision β, Gamma(β;a,b) represents the probability density of β following a gamma distribution with parameters a and b, and Γ(a) represents the gamma function with parameter a.

[0026] (6) Iteratively solve for the weight vector ω of each distance cell. q :

[0027] (6a) Based on the expected value <β> of the accuracy β, the scale parameter Expectation of the reciprocal Constructing a matrix inversion-free fast inference formula:

[0028]

[0029] in, Let <β> represent the weight vector of the q-th distance unit after the k-th iteration. (k) Let β represent the expected precision of each element in the noise vector ε after the k-th iteration, (Λ -1 )(k) Indicates that the diagonal elements are The diagonal matrix, λ represents the matrix formed by each scale parameter. The vector formed, Φ T This represents the transpose operation on matrix Φ, where I represents the identity matrix, and L represents the transpose operation on matrix Φ. h =2λ max (Φ T Φ), λ max (Φ T Φ) represents matrix Φ T Φ is the maximum eigenvalue.

[0030] (6b) Set the current distance cell number q to 1, set the current iteration number k to 1, and set the termination threshold η;

[0031] (6c) Using the matrix inversion-free fast inference formula described above, calculate the weight vector of the current iteration number k of the current distance cell q.

[0032] (6d) Determine if the current iteration number k is greater than 1:

[0033] If so, proceed to step (6e);

[0034] Otherwise, increment the current iteration count by 1 and return to step (6c);

[0035] (6e) The weight vector reconstructed by the current iteration number k of the current distance cell q. The weight vector reconstructed from the previous iteration number k-1 calculate And determine if it is less than η:

[0036] If so, proceed to step (6f).

[0037] Otherwise, return to step (6c);

[0038] (6f) Determine whether the current distance cell number q is equal to the number of rows N of the missing echo S′. r :

[0039] If so, proceed to step (7);

[0040] Otherwise, increment the current distance cell number q by 1 and return to step (6b);

[0041] (7) Two-dimensional high-resolution imaging:

[0042] (7a) Concatenate the weight vectors ω of each distance unit into a weight matrix S1 by column;

[0043] (7b) Generate a complex weight matrix S2 based on the weight matrix S1, wherein the real part of S2 is the first,...,Nth weight matrix in S1.a Line, the imaginary part is the Nth line in S1 a ,...,2N a OK;

[0044] (7c) Transpose the complex weight matrix S2 to obtain the two-dimensional high-resolution inverse synthetic aperture radar (ISAR) imaging results.

[0045] Compared with the prior art, the present invention has the following advantages:

[0046] First, by fully utilizing the sparse characteristics of ISAR target scattering points, this invention introduces a sparse gamma process-Laplace hierarchical prior to the weight vector, overcoming the shortcomings of existing technologies such as inflexible prior modeling and poor sparse representation capabilities, thereby improving the ISAR imaging accuracy under conditions of low signal-to-noise ratio and echo loss.

[0047] Secondly, because the present invention constructs a fast matrix inversion-free solution formula, it can transform the matrix to be inverted into a diagonal matrix through scaling and simplification. This overcomes the problems of high computational complexity and low imaging processing efficiency caused by the need for multiple matrix inversions in the prior art, greatly reducing computational complexity and improving imaging efficiency. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0049] Figure 2 Range pulse compression diagram for radar receiving incomplete echoes;

[0050] Figure 3 The images shown are simulation results of the imaging effects of the present invention and the prior art. Detailed Implementation

[0051] The embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.

[0052] Reference Figure 1 The implementation steps for this example are as follows:

[0053] Step 1: Receive the missing echo S′ and generate the real transpose echo matrix S.

[0054] 1.1) Transmit linear frequency modulated (LFM) signals to moving targets using inverse synthetic aperture radar (IRAR), and obtain the N-value of the LFM signals transmitted under noisy conditions. r ×N a The azimuth dimension missing echo matrix S′, where N r N represents the number of distance units to S′. a This represents the number of azimuth units of S′.

[0055] In an embodiment of the present invention, N r =256, Na =512;

[0056] 1.2) Using the distance from the inverse synthetic aperture radar to the center of the scene as the reference distance, select a carrier frequency and frequency modulation frequency that are the same as the transmitted signal of the inverse synthetic aperture radar. Use the linear frequency modulation signal of the reference distance as the reference signal. Multiply the conjugate of the reference signal with the missing echo matrix S′ to obtain the matrix S1′ after de-linear frequency modulation.

[0057] 1.3) Perform a Fourier transform on the de-frequency modulated matrix S1′ along the range direction to obtain the range-direction pulse-compressed matrix S′2;

[0058] 1.4) Transpose the distance-dimensional pulse compression matrix S′2 to obtain the complex transposed echo matrix S′3;

[0059] 1.5) Construct a 2N dimension echo matrix using the real part Re(S′3) and imaginary part Im(S′3) of the complex transpose echo matrix S′3. a ×N r The real transpose echo matrix:

[0060] Step 2: Obtain the real Fourier dictionary Φ based on the missing echo matrix S′.

[0061] 2.1) with exp(j2πmn / N a Let ) be the elements, and construct a dimension of N. a ×N a The Fourier dictionary Φ a ,

[0062] Where N a The azimuth element of the missing echo matrix S′ is represented by exp(·), which represents the exponential operation with the natural constant as the base, j represents the imaginary unit, and m represents the complex Fourier dictionary Φ. a The row number, n, represents the complex Fourier dictionary Φ. a The column number, row number m, and column number n all take values ​​in the range [-N]. a / 2,N a / 2-1];

[0063] 2.2) Using the complex Fourier dictionary Φ a Construct a real Fourier dictionary

[0064] Step 3: Construct a sparse observation model for each distance cell.

[0065] Let the weight vector to be reconstructed in the q-th distance cell be ω. q According to the weight vector ω to be reconstructed q Construct the q-th column vector y in the real transpose echo matrix S using the real Fourier dictionary Φ.q Sparse observation model: y q =Φω q +ε, where ε represents the noise vector.

[0066] Step 4, for each distance cell, the weight vector ω q Introduce gamma process-Laplace hierarchy priors.

[0067] 4.1) The weight vector ω of the q-th distance cell is calculated according to the following formula. q Introducing the Laplace prior:

[0068]

[0069] in, This represents the nth element in the weight vector of the qth distance cell. The probability density, express Obey the scale parameter is The probability density of the Laplace distribution, Indicates to The absolute value operation;

[0070] 4.2) For each scale parameter, according to the following formula... Introducing gamma process priors:

[0071]

[0072] in, The probability density, express The probability density follows a gamma distribution with parameters c and d, where Γ(c) represents the gamma function with parameter c.

[0073] Step 5: Introduce a gamma-Gaussian hierarchical prior to the noise vector ε.

[0074] 5.1) Introduce a Gaussian prior for the noise vector ε according to the following formula:

[0075] p(ε n ) = Normal(ε n |0,β -1 )

[0076] Where p(ε) n ) represents the nth element of the noise vector ε. n The probability density, Normal(ε) n |0,β -1 ) represents ε n The probability density follows a Gaussian distribution with mean 0 and precision β;

[0077] 5.2) Introduce a gamma prior to the accuracy β according to the following formula:

[0078]

[0079] Where p(β) represents the probability density of precision β, Gamma(β;a,b) represents the probability density of β following a gamma distribution with parameters a and b, and Γ(a) represents the gamma function with parameter a.

[0080] Step 6: Iteratively solve for the weight vector ω of each distance cell. q .

[0081] 6.1) Calculate the lower bound function of evidence L(ω) according to the following formula. q ):

[0082]

[0083] Where, ω q Let represent the weight vector of the q-th distance cell. Represents ω q The nth element, y q Let Φ represent the q-th column vector of the real transpose echo matrix S, Φ represent the real Fourier dictionary, and λ represent the vector formed by each scale parameter. The vector formed Represents ω q The scaling parameter of the nth element in the distribution follows a Laplace distribution, <·> q(·) This expresses the expectation of q(·), such as <β>. q(β) Let represent the expectation of β with respect to q(β), where β represents ε. n Precision follows a Gaussian distribution, const denotes the relationship with ω. q Irrelevant constant, N a This represents the number of azimuth elements in the missing echo matrix S′;

[0084] 6.2) Introducing the following theorem, for the lower bound function L(ω) q Scaling:

[0085] For any L h - A continuously differentiable function of the Lipschitz gradient For any The following equations hold true:

[0086]

[0087] Where L represents a constant and satisfies L≥L h L h This represents the Lipschitz constant. Let h(δ) denote the gradient of h(δ) with respect to x, where x and δ are arbitrary vectors. Then the lower bound function of the evidence after scaling is L′(ω) q ) is represented as:

[0088]

[0089] Where, Φ T Indicates the transpose of Φ;

[0090] 6.3) The scaled lower bound function of evidence L′(ω) q Regarding ω q Find the partial derivative, set it to 0, and make δ equal to the weight vector of the previous iteration number k-1 for the current distance cell q. Right now Obtain the weight vector of the current iteration number k for the current distance cell q. Iterative formula:

[0091]

[0092] Among them, <β> (k) Let Λ represent the expected precision of each element in the noise vector after the k-th iteration. -1 ) (k) Indicates that the diagonal elements are Let I be a diagonal matrix, and let [·] denote the identity matrix. -1 L represents the matrix inversion operation. h =2λ max (Φ T Φ), λ max (Φ T Φ) represents Φ T Φ is the maximum eigenvalue.

[0093] The weight vector Precision expectation <β> in the iterative formula (k) and diagonal matrix (Λ -1 ) (k) The value varies depending on the value of k:

[0094] When k = 1, for <β> (k) and (Λ) -1 ) (k) Perform initialization;

[0095] When k>1, calculate <β> according to the following formula. >k) and (Λ) -1 ) (k) :

[0096]

[0097]

[0098] in, Let represent the weight vector of the q-th distance unit after the (k-1)-th iteration. express The nth element, a and b, represent parameters where the precision β follows a gamma distribution, (Λ n -1 ) (k) Indicates (Λ) -1 ) (k) The nth diagonal element, Let denote the modified Bessel function of the second kind, and c and d denote the scaling parameter λ, which follows a gamma distribution.

[0099] In an embodiment of the present invention, when k = 1, <β> (k) =1, a=b=10 -4 , (Λ -1 ) (k) The diagonal elements are 9×10 -5 c = 1 / 2N a =9.7656×10 -4 , d = 1.

[0100] 6.4) Set the current distance cell number q to 1, set the current iteration number k to 1, and set the termination threshold η. In this embodiment, η = 10. -6 ;

[0101] 6.5) Using the matrix inversion-free fast inference formula described above, calculate the weight vector of the current iteration number k for the current distance cell q.

[0102] 6.6) Determine if the current iteration number k is greater than 1:

[0103] If so, proceed to step 6.7);

[0104] Otherwise, increment the current iteration count by 1 and return to step 6.5);

[0105] 6.7) The weight vector reconstructed using the current iteration number k of the current distance cell q The weight vector reconstructed from the previous iteration number k-1 calculate And determine whether it is less than η:

[0106] If so, proceed to step 6.8.

[0107] Otherwise, return to step 6.5);

[0108] 6.8) Determine whether the current distance cell number q is equal to the number of distance cells N of the missing echo matrix S′. r :

[0109] If so, proceed to step 7;

[0110] Otherwise, increment the current distance cell number q by 1 and return to step 6.4);

[0111] Step 7, two-dimensional high-resolution imaging.

[0112] 7.1) Concatenate the weight vectors ω of each distance cell into a weight matrix S1 by column;

[0113] 7.2) Generate a complex weight matrix S2 based on the weight matrix S1, where the real part of S2 is the first, ..., Nth weight matrix in S1. a Line, the imaginary part is the Nth line in S1 a ,...,2N a OK;

[0114] 7.3) Transpose the complex weight matrix S2 to obtain the two-dimensional high-resolution inverse synthetic aperture radar (ISAR) imaging results.

[0115] The effectiveness of this invention can be further demonstrated through the following simulation.

[0116] I. Simulation Experiment Conditions.

[0117] 1. The software platform for the simulation experiment is: Windows 10 operating system and Matlab R2020a.

[0118] 2. Simulation data:

[0119] The echo of the Yak-42 aircraft was obtained using radar measurements. The radar operated in the C-band with a bandwidth of 0.4 GHz, and the azimuth cell number N of the echo was [data missing]. a The distance unit N of the echo is 512. r It is 256;

[0120] The wavenumber domain echoes of columns 1-128 and 257-384 were missing, with a loss rate of 50%. Range pulse compression was performed on these echoes and 0dB random noise was added. The range pulse compression echoes after the loss were plotted as follows: Figure 2 The horizontal axis represents the azimuth cell of the range pulse pressure echo after the defect, and the vertical axis represents the range cell of the range pulse pressure echo after the defect.

[0121] 3. Simulation content and result analysis.

[0122] Under the above simulation conditions, the existing high-resolution ISAR imaging method for interfering environments based on sparse Bayesian learning and the present invention are used respectively to perform... Figure 2 Two-dimensional ISAR imaging was performed on the range-direction pulse compression echo of the defect shown, and the results are as follows: Figure 3 ,in, Figure 3 (a) An ISAR image obtained using the existing ISAR imaging method based on gamma-Gaussian priors and sparse Bayesian methods. Figure 3 (b) is an ISAR image obtained by two-dimensional imaging of radar defect echoes using the method of the present invention.

[0123] Depend on Figure 3 (a) It can be seen that the imaging results obtained by using the sparse Bayesian reconstruction based on gamma-Gaussian prior in the existing technology have poor focusing, cannot effectively suppress noise, and have a lot of false points.

[0124] from Figure 3 (b) It can be seen that the imaging results obtained by the present invention can clearly present the geometric structure of the aircraft target, with fewer false points and better focusing, and can effectively suppress background noise.

[0125] The image entropy of the ISAR 2D images obtained by the two methods above was calculated, and the running time of each method was recorded. The results are shown in Table 1.

[0126] Table 1 Image entropy of ISAR 2D images

[0127] Existing technology This invention Image entropy 5.950 5.226 Running time (s) 1373.737 26.502

[0128] As can be seen from Table 1, the image entropy of the ISAR image generated by this invention is significantly reduced compared with the existing sparse Bayesian learning imaging method, and the time consumption is greatly reduced compared with the existing sparse Bayesian learning algorithm, with a speed improvement of about 51.84 times, which proves the superiority of this invention in terms of computational complexity.

[0129] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A matrix-inverse-free ISAR imaging method based on gamma process-Laplace prior, characterized in that, Includes the following steps: (1) Receive the missing echo matrix S′ and generate the real transpose echo matrix S; (2) Obtain the real Fourier dictionary Φ based on the missing echo matrix S′; (3) Construct a sparse observation model for each distance cell based on S and Φ: y q =Φω q +ε, Among them, y q Let ω represent the q-th column vector of the real transpose echo matrix S. q Let ε represent the weight vector to be reconstructed in the q-th distance cell, and let ε represent the noise vector. (4) Introduce a gamma process-Laplace hierarchical prior for the weight vector of each distance unit: (4a) According to the following formula, the weight vector ω of the q-th distance cell is... q Introducing the Laplace prior: in, This represents the nth element in the weight vector of the qth distance cell. The probability density, express Obey the scale parameter is The probability density of the Laplace distribution, Indicates to The absolute value operation; (4b) For each scale parameter λ, according to the following formula. qn Introducing gamma process priors: in, Represents the nth scale parameter The probability density, express The probability density follows a gamma distribution with parameters c and d, where Γ(c) represents the gamma function with parameter c. (5) Introduce a gamma-Gaussian hierarchical prior to the noise vector ε: (5a) Introduce a Gaussian prior to the noise vector ε according to the following formula: p(e n )=Normal(e n |0,b -1 ) Where p(ε) n ) represents the nth element of the noise vector ε. n The probability density, Normal(ε) n |0,β -1 ) represents ε n The probability density follows a Gaussian distribution with mean 0 and precision β; (5b) Introduce a gamma prior to the accuracy β according to the following formula: Where p(β) represents the probability density of precision β, Gamma(β;a,b) represents the probability density of β following a gamma distribution with parameters a and b, and Γ(a) represents the gamma function with parameter a. (6) Iteratively solve for the weight vector ω of each distance cell. q : (6a) Based on the expected value <β> of the accuracy β, the scale parameter Expectation of the reciprocal Constructing a matrix inversion-free fast inference formula: in, Let <β> represent the weight vector of the q-th distance unit after the k-th iteration. (k) Let β represent the expected precision of each element in the noise vector ε after the k-th iteration, (Λ -1 ) (k) Indicates that the diagonal elements are The diagonal matrix, λ represents the matrix formed by each scale parameter. The vector formed, Φ T This represents the transpose operation on matrix Φ, where I represents the identity matrix, and L represents the transpose operation on matrix Φ. h =2λ max (Φ T Φ), λ max (Φ T Φ) represents matrix Φ T Φ is the maximum eigenvalue. (6b) Set the current distance cell number q to 1, set the current iteration number k to 1, and set the termination threshold η; (6c) Using the matrix inversion-free fast inference formula described above, calculate the weight vector of the current iteration number k of the current distance cell q. (6d) Determine if the current iteration number k is greater than 1: If so, proceed to step (6e); Otherwise, increment the current iteration count by 1 and return to step (6c); (6e) The weight vector reconstructed by the current iteration number k of the current distance cell q. The weight vector reconstructed from the previous iteration number k-1 calculate And determine if it is less than η: If so, proceed to step (6f). Otherwise, return to step (6c); (6f) Determine whether the current distance cell number q is equal to the number of distance cells N of the missing echo matrix S′. r : If so, proceed to step 7; Otherwise, increment the current distance cell number q by 1 and return to step (6b); (7) Two-dimensional high-resolution imaging: (7a) Concatenate the weight vectors ω of each distance unit into a weight matrix S1 by column; (7b) Generate a complex weight matrix S2 based on the weight matrix S1, wherein the real part of S2 is the first,...,Nth weight matrix in S1. a Line, the imaginary part is the Nth line in S1 a ,...,2N a OK; (7c) Transpose the complex weight matrix S2 to obtain the two-dimensional high-resolution inverse synthetic aperture radar (ISAR) imaging results.

2. The method according to claim 1, characterized in that, In step (1), the radar receives the missing echo S′ and generates the real transpose echo matrix S, as follows: (1a) Transmit a linear frequency modulated (LFM) signal to a moving target using an inverse synthetic aperture radar (IRSAR) and obtain the N-score of the LFM signal transmitted under noisy conditions. r ×N a The azimuth dimension missing echo matrix S′, where N r N represents the number of distance units to S′. a Indicates the number of azimuth units of S′; (1b) Using the line frequency modulation demodulation method, S′ is demodulated to obtain the demodulated matrix S′1: (1b1) The distance from the inverse synthetic aperture radar to the center of the scene is used as the reference distance; (1b2) Select a linear frequency modulated signal with the same carrier frequency and frequency modulation frequency as the inverse synthetic aperture radar transmitted signal and a distance of the reference distance as the reference signal; (1b3) Multiply the conjugate of the reference signal by the missing echo matrix S′ to obtain the de-frequency modulated matrix S′1; (1c) Perform a Fourier transform on the de-frequency modulated matrix S′1 along the range direction to obtain the range-direction pulse compressed matrix S′2; (1d) Transpose the distance dimension pulse compression matrix S′2 to obtain the complex transposed echo matrix S′3; (1e) Construct a 2N dimension using the real part Re(S′3) and the imaginary part Im(S′3) of S′3. a ×N r The real transpose echo matrix:

3. The method according to claim 1, characterized in that, In step (2), the real Fourier dictionary Φ is obtained based on the missing echo matrix S′, as follows: (2a) with exp(j2πmn / N) a Let ) be the elements, and construct a dimension of N. a ×N a The Fourier dictionary Φ a , where N a The azimuth element of the missing echo matrix S′ is represented by exp(·), which represents the exponential operation with the natural constant as the base, j represents the imaginary unit, and m represents the complex Fourier dictionary Φ. a The row number, n, represents the complex Fourier dictionary Φ. a The column number, row number m, and column number n all take values ​​in the range [-N]. a / 2,N a / 2-1]; (2b) Using the complex Fourier dictionary Φ a Construct a real Fourier dictionary 4. The method according to claim 1, characterized in that, In step (6a), the matrix inversion-free fast inference formula is constructed as follows: (6a1) Calculate the lower bound function of evidence L(ω) according to the following formula. q ): Where, ω q Let represent the weight vector of the q-th distance cell. Represents ω q The nth element, y q Let Φ represent the q-th column vector of the real transpose echo matrix S, Φ represent the real Fourier dictionary, and λ represent the vector formed by each scale parameter. The vector formed Represents ω q The scaling parameter of the nth element in the distribution follows a Laplace distribution. This expresses the expectation of q(·), such as <β>. q(β) Let represent the expectation of β with respect to q(β), where β represents ε. n Precision follows a Gaussian distribution, const denotes the relationship with ω. q Irrelevant constant, N a This represents the number of azimuth elements in the missing echo matrix S′; (6a2) Introducing the following theorem, for the lower bound function L(ω) q Scaling: For any L h - A continuously differentiable function of the Lipschitz gradient For any The following equations hold true: Where L represents a constant and satisfies L≥L h L h This represents the Lipschitz constant. Let h(δ) denote the gradient of h(δ) with respect to x, where x and δ are arbitrary vectors. Then the lower bound function of the evidence after scaling is L′(ω) q ) is represented as: Where, Φ T Indicates the transpose of Φ; (6a3) The updated lower bound function of evidence L′(ω) q Regarding ω q Find the partial derivative and make Let k-1 be the weight vector of the previous iteration number of the current distance cell q, and calculate the weight vector of the current iteration number k of the current distance cell q. Among them, <β> (k) Let Λ represent the expected precision of each element in the noise vector after the k-th iteration. -1 ) (k) Indicates that the diagonal elements are Let I be a diagonal matrix, and let [·] denote the identity matrix. -1 L represents the matrix inversion operation. h =2λ max (Φ T Φ), λ max (Φ T Φ) represents Φ T Φ is the maximum eigenvalue.

5. The method according to claim 4, characterized in that, The scaled lower bound function of evidence L′(ω) q The expected precision <β> in ) (k) and diagonal matrix (Λ -1 ) (k) The value varies depending on the value of k, specifically: When k = 1, for <β> (k) and (Λ) -1 ) (k) Perform initialization; When k>1, calculate <β> according to the following formula. (k) and (Λ) -1 ) (k) : in, Let represent the weight vector of the q-th distance unit after the (k-1)-th iteration. express The nth element, a and b, represent parameters where the precision β follows a gamma distribution. Indicates (Λ) -1 ) (k) The nth diagonal element, Let denote the modified Bessel function of the second kind, and c and d denote the scaling parameter λ, which follows a gamma distribution.

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