Periodic Segmented Observation ISAR High-Resolution Imaging Method Based on Fast SBL Algorithm

Abstract

The present invention discloses a periodic segmented observation ISAR high-resolution imaging method based on a fast SBL algorithm, including: modeling using the obtained periodic segmented observation data to obtain a reconstruction model of the original signal to be reconstructed; constructing a hierarchical Bayesian prior model and obtaining a hierarchical prior distribution; obtaining the posterior distribution of the original signal to be reconstructed according to the hierarchical prior distribution and the observation data; constructing an iterative formula of the SBL algorithm using the posterior distribution; calculating the mean of the posterior distribution and the diagonal elements of the covariance matrix of the posterior distribution in a single iteration of the SBL algorithm using the fast SBL algorithm based on the Fourier dictionary; performing iterative calculations on the mean of the posterior distribution and the diagonal elements of the covariance matrix of the posterior distribution to obtain the final ISAR imaging result. The present invention proposes an imaging method based on the fast SBL algorithm for the case of periodic segmented observation data, which can well suppress sidelobes, reduce the main lobe width, improve the resolution, and thus achieve high-resolution imaging.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar, and particularly relates to a periodic segmented observation ISAR high-resolution imaging method based on a fast SBL algorithm. Background Art

[0002] Inverse Synthetic Aperture Radar (ISAR) can obtain high-resolution radar images of moving targets in all-weather and all-time environments, and has been applied to various fields such as space surveillance and radar astronomy. In high-resolution radar imaging of airborne targets, the azimuth resolution of the image is determined by the coherent integration angle. To obtain better azimuth resolution, a larger coherent integration angle is required, that is, a longer observation time. During this period, when continuous measurement is impossible or the measurement in some periods is invalid, the problem of periodic data loss will occur in the observation data. For example, interference and system instability will cause the echo data at this time to be corrupted or lost. In addition, the data collected from multiple perspectives is discontinuous, which leads to periodic missing data, that is, aperture sparsity. For some surveillance radars, the antenna is fixed on a rotating turntable to achieve azimuth scanning of the entire airspace. Since the target only exists in a fixed surveillance area, the collected echoes are discontinuous, and there are large gaps between available samples. If missing data is directly filled with zero padding and then azimuth compression is performed, the resulting image will have high sidelobes and ghosts. The range resolution is inversely proportional to the bandwidth of the radar. Therefore, a direct method to improve the range resolution is to increase the bandwidth and the center frequency, but this method has a high requirement for the cost of hardware.

[0003] In order to obtain higher resolution without increasing a large amount of hardware cost, many scholars have proposed a method of broadband synthesis using the inherent sparse subbands of existing imaging radars. However, the key factor of this method lies in using periodic subband data to achieve accurate scattering center estimation. Therefore, it has become a challenge for researchers to obtain high-resolution images from the ISAR raw data with periodic missing data in the azimuth dimension or range dimension (or the ISAR raw data with segmented observation). Periodic segmented observation ISAR high-resolution imaging has received increasing attention in the radar imaging community.

[0004] In radar imaging, theoretical and experimental calculations show that when there are strong scattering points in the radar echo, the echo signal of the radar target in the high-frequency band can be regarded as the superposition of the echo signals of a few scattering centers, and the target signal is sparse. To obtain a high-resolution radar image, a high-resolution radar usually operates in the high-frequency region, and thus radar imaging technology based on the sparse representation theory has been developed. This technology aims at the sparse characteristics of the radar target echo signal, transforms the radar imaging model into a sparse representation model, and uses a sparse reconstruction method to optimize and solve the radar target parameters. Since the development of the sparse representation theory, many sparse reconstruction algorithms have been developed. Among these algorithms, the Sparse Bayesian Learning (SBL) algorithm has stronger robustness and higher estimation accuracy, so it has attracted the research interest of researchers in both theory and application. The SBL algorithm is a very important Bayesian statistical optimization algorithm, which is developed on the basis of Bayesian theory and realizes signal reconstruction from a statistical perspective. That is, in the SBL framework, the signal to be restored satisfies a certain prior distribution, and then the posterior distribution information of the signal is obtained through Bayesian analysis, and the signal reconstruction is realized through continuous iteration.

[0005] However, in each iteration of the SBL algorithm, an inverse matrix needs to be solved, and the dimension of this matrix is the same as the length of the observed data. If the traditional direct inversion method is used to solve it, its computational complexity is proportional to the cube of the length of the observed data. When the number of observed data samples is large, the calculation time is often very long. To solve this problem, many scholars have proposed some fast SBL algorithms, but these fast algorithms all use some approximations, which will affect the accuracy of the imaging results. If it is used for segmented observation ISAR imaging, the imaging results will be even worse.

[0006] Segmented observation includes two types: non-periodic segmentation and periodic segmentation. Both of these situations are very common. There has been some research on ISAR high-resolution imaging for non-periodic segmented observation data, but there is less research on periodic segmentation. Therefore, it is necessary to study ISAR high-resolution imaging for periodic segmented observation. Summary of the Invention

[0007] To solve the above problems existing in the prior art, the present invention provides an ISAR high-resolution imaging method for periodic segmented observation based on the fast SBL algorithm. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0008] The present invention provides an ISAR high-resolution imaging method for periodic segmented observation based on the fast SBL algorithm, including:

[0009] S1: Use the obtained periodic segmented observation data for modeling to obtain a reconstruction model of the original signal to be reconstructed, and the reconstruction model is:

[0010]

[0011] Among them, the dictionary matrix x represents the original signal to be reconstructed, represents the observation noise, represents the valid data in the observation data, D represents the over-complete dictionary matrix, represents the selection matrix corresponding to the valid matrix;

[0012] S2: Construct a hierarchical Bayesian prior model for the original signal to be reconstructed and obtain the hierarchical prior distribution of the original signal to be reconstructed;

[0013] S3: Obtain the posterior distribution of the original signal to be reconstructed according to the hierarchical prior distribution and the periodic segmented observation data;

[0014] S4: Use the posterior distribution to construct an iterative formula for the SBL algorithm;

[0015] S5: Use the fast SBL algorithm based on the Fourier dictionary to calculate the mean of the posterior distribution and the diagonal elements of the posterior distribution covariance matrix in a single iteration of the SBL algorithm;

[0016] S6: Substitute the mean of the posterior distribution and the diagonal elements of the posterior distribution covariance matrix into the iterative formula for iterative calculation to obtain the final ISAR imaging result.

[0017] In an embodiment of the present invention, the S2 includes:

[0018] Construct a hierarchical Bayesian prior model, where the first layer of the hierarchical Bayesian prior model is the modeling of the original signal to be reconstructed x and the noise e, and the probability density functions of the original signal to be reconstructed x and the noise e are obtained:

[0019]

[0020]

[0021] Among them, represents being subject to a complex Gaussian distribution, x k represents the (k + 1)-th element of the original signal vector x to be reconstructed, γ k represents x k 's inverse variance, Λ is a diagonal matrix composed of 1 / γ k in sequence, e n represents the (n + 1)-th element of the noise data vector e, β represents e n 's inverse variance;

[0022] Set the second layer of the hierarchical Bayesian prior model to be γk Modeling of α and β, the probability density functions are respectively:

[0023]

[0024]

[0025] where gamma(·) represents the gamma distribution, a and b respectively represent the shape and scale parameters of γ k The shape and scale parameters, c and d respectively represent the shape and scale parameters of β, and Γ(a) represents the gamma function.

[0026] In one embodiment of the present invention, the S3 includes:

[0027] Based on the prior distribution of the sparse signal x and the observed data, the posterior distribution of the original signal x to be reconstructed is obtained by using the Bayesian formula and the expectation maximization algorithm, and the covariance Σ and the mean μ of the posterior distribution are respectively:

[0028]

[0029]

[0030] where,

[0031] In one embodiment of the present invention, the iterative formula includes:

[0032]

[0033] ε (j) = diag(Σ (j) )

[0034]

[0035] where the superscript (j) represents the iteration number, Σ represents the covariance of the signal posterior distribution, ε = diag(Σ) means that ε is a vector composed of the elements on the diagonal of the matrix Σ, μ represents the mean of the signal posterior distribution, β represents the precision of the noise, represents the dictionary matrix, Λ is a diagonal matrix composed of 1 / γ k in sequence, and γ k represents the precision of the (k + 1)-th value in the signal vector x.

[0036] In one embodiment of the present invention, the S5 includes:

[0037] S51: Construct the Fourier dictionary matrix of the periodic segmented observed data, and calculate and obtain by using the Fourier dictionary matrix

[0038] S52: Use to find the parameters ε and μ in a single iteration of the fast SBL algorithm.

[0039] In an embodiment of the present invention, the S51 includes:

[0040] S511: Construct the Fourier dictionary matrix of the periodic segmented observation data:

[0041]

[0042] where ω k = 2πk / K, k = 0, ..., K - 1, represents the Fourier basis corresponding to the i-th segment of valid data;

[0043] S512: Use the constructed dictionary matrix to obtain the expression of the parameter :

[0044]

[0045] S513: Set the permutation matrix and use the permutation matrix and the parameter to construct the parameter obtain the inverse matrix of the parameter and the shifted expression of the inverse matrix ;

[0046]

[0046] S514: Obtain the G-S decomposition form and G-S decomposition factors of the inverse matrix based on the shifted expression of the inverse matrix ;

[0047] S515: Solve the G-S decomposition factors of ;

[0048] S516: Use the G-S decomposition factors of to obtain the calculation result of ;

[0049] In an embodiment of the present invention, the S6 includes:

[0050] Set the convergence threshold δ, and determine whether the μ value obtained in each iteration satisfies the convergence condition

[0051]

[0052] If the convergence condition is not satisfied, repeat steps S51 and S52 to continue the iteration; if the convergence condition is satisfied, the obtained optimal mean value is the reconstructed sparse signal.

[0053] Another aspect of the present invention provides a storage medium storing a computer program for executing the steps of the periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm according to any one of the above embodiments.

[0054] Another aspect of the present invention provides an electronic device including a memory and a processor. A computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps of the periodic segmented observation ISAR high-resolution imaging method according to any one of the above embodiments are implemented.

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0056] 1. In view of the case of periodic segmented observation data, the present invention proposes a high-resolution imaging method based on the fast SBL algorithm, which can well suppress sidelobes, reduce the main lobe width, and improve the resolution. The fast SBL algorithm uses G-S decomposition and FFT (Fast Fourier Transform) to solve the inverse matrix and the multiplication operation involving the inverse matrix respectively, without using any approximation. Therefore, the computational complexity can be reduced by several orders of magnitude while ensuring the accuracy of the result. Compared with the proposed fast SBL algorithm for non-periodic segmentation, the method of the present invention has a lower computational complexity.

[0057] 2. The imaging method based on the fast SBL algorithm of the present invention improves the computational speed without sacrificing accuracy. The core of the fast SBL algorithm is to use the Fourier dictionary. In each iteration of SBL, the inverse matrix to be solved is a Toeplitz-block-Toeplitz matrix. Based on this matrix, another Toeplitz-block-Toeplitz matrix can be constructed and can be quickly solved by FFT. The inverse matrix can be expressed by G-S decomposition, avoiding the problem of high computational complexity caused by directly solving the inverse matrix. It should be noted that the fast SBL algorithm proposed by the present invention is based on the Fourier dictionary. Although SBL has no requirement for the type of dictionary, in many fields, signals are sparse in the dictionary composed of Fourier bases.

[0058] 3. The fast algorithm proposed by the present invention also utilizes the property of displacement rank, resulting in the computational complexity of the algorithm being related to the number of segments in the periodic segmented observation data. The fewer the number of segments, the shorter the imaging time.

[0059] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0060] Figure 1It is a flowchart of a periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm provided by an embodiment of the present invention;

[0061] Figure 2 It is a model diagram of periodic segmented observation data provided by an embodiment of the present invention;

[0062] Figure 3 It is an imaging result diagram of periodic segmented data of various methods;

[0063] Figure 4 It is an imaging performance diagram of periodic segmented data of various methods with the change of the length of the observation data;

[0064] Figure 5 It is an imaging performance diagram of periodic segmented data of various methods with the change of the missing rate of the observation data;

[0065] Figure 6 It is an imaging performance diagram of periodic segmented data of various methods with the change of the number of segments of the observation data;

[0066] Figure 7 It is a high-resolution range image of complete measured data and imaging result diagrams of the traditional range-Doppler algorithm and the SBL method;

[0067] Figure 8 It is a high-resolution range image of periodic segmented measured data and imaging result diagrams of the traditional range-Doppler algorithm and the FD-GPSBL algorithm. Detailed implementation manners

[0068] In order to further elaborate on the technical means and effects adopted by the present invention to achieve the intended invention purpose, the following provides a detailed description of a periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm proposed according to the present invention in combination with the accompanying drawings and specific implementation manners.

[0069] The foregoing and other technical contents, features, and effects of the present invention can be clearly presented in the following detailed description in conjunction with the accompanying drawings. Through the description of the specific implementation manners, a more in-depth and specific understanding of the technical means and effects adopted by the present invention to achieve the intended purpose can be obtained. However, the accompanying drawings are only for reference and illustration, and are not used to limit the technical solutions of the present invention.

[0070] It should be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant is intended to cover non-exclusive inclusion, so that an article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed. Without further limitation, an element defined by the statement "comprising an..." does not exclude the existence of additional identical elements in the article or device comprising the element.

[0071] Embodiment 1

[0072] Please refer to Figure 1 , Figure 1 , which is a flowchart of a periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm provided by an embodiment of the present invention. The imaging method includes:

[0073] S1: Use the obtained periodic segmented observation data for modeling to obtain a reconstruction model of the original signal to be reconstructed.

[0074] The original signal to be reconstructed is a sparse signal. The reconstruction of the sparse signal refers to the process of solving the original sparse signal x according to the observation data y on the premise that the original signal to be reconstructed x has a certain sparsity. The model of the observation data y can be described by an underdetermined linear system with noise, such as:

[0075] y = Dx + e

[0076] where is the observation data; is an overcomplete dictionary matrix and K >> N; x represents the original sparse signal to be reconstructed, that is, most of the elements in the vector x are zero; represents the observation noise, N represents the length of the observation data, and K / N is the super-resolution multiple.

[0077] For the segmented observation data, the schematic diagram of its signal reconstruction is as Figure 2 shown. The gray boxes represent valid sampling samples, and the white boxes represent missing sampling samples. All the observation data y can be Ns divided into q segments according to the positions of the missing samples, the length of each segment of data is N sp , the length of the valid data contained in each segment of data is N gp , and the length of the missing data is N mp . The length of all the observation data is N s , the total length of the valid data is N g , and the total length of the missing data is N m. Their relationship is: qN gp = N g , qN mp = N m , qN sp = N s = N g + N m . It can be seen that the total effective data and the total missing data are respectively the sets of effective data and missing data for each segment, and they have the following relationship:

[0078]

[0079]

[0080] Among them, represents the observed data, and respectively represent the selection matrices corresponding to the effective data and the missing data . The missing rate of the original observed data is

[0081] The reconstruction model is:

[0082]

[0083] Among them, the dictionary matrix x represents the original signal to be reconstructed, represents the observation noise, represents the effective data in the observed data.

[0084] S2: Construct a hierarchical Bayesian prior model for the original signal to be reconstructed and obtain the hierarchical prior distribution of the original signal to be reconstructed.

[0085] First, a brief introduction to the SBL (Sparse Bayesian Learning) algorithm is given. SBL is based on the Bayesian framework, and the original signal to be reconstructed is assumed to have a heavy-tailed density distribution, such as the Laplace or Student's T distribution. For the convenience of derivation, a scale mixture distribution based on the hierarchical Bayesian model is usually used to replace the original heavy-tailed distribution. Gaussian scale mixtures (GSMs) and Laplace scale mixtures (LSMs) are commonly used in SBL. Then, SBL estimates the parameters of these distribution models based on the observed data and then reconstructs the signal.

[0086] To effectively improve the sparsity of signals, a hierarchical Bayesian prior model is usually used to describe the signals in SBL. The first layer of this hierarchical Bayesian prior model is the modeling of the original signal x to be reconstructed and the noise e. It is assumed that the original sparse signal x to be reconstructed follows a zero-mean covariance complex Gaussian distribution Λ, and the noise e follows a zero-mean covariance complex Gaussian distribution β -1 I, then the probability density functions (PDFs) of the original signal x to be reconstructed and the noise e are respectively:

[0087]

[0088]

[0089] where, denotes following a complex Gaussian distribution, x k represents the (k + 1)-th element of the original sparse signal vector x and each element in the original sparse signal vector x is independent of each other, γ k represents the precision (inverse variance) of x k , Λ is a diagonal matrix composed of 1 / γ k in sequence. e n represents the (n + 1)-th element of the noise data vector e, and β represents the precision (inverse variance) of e n .

[0090] The second layer of this hierarchical Bayesian prior model is the modeling of γ k and β, both of which follow a gamma distribution, and their probability density functions are respectively:

[0091]

[0092]

[0093] where, gamma(·) represents the gamma distribution, a and b respectively represent the shape and scale parameters of γ k , c and d respectively represent the shape and scale parameters of β, and they are called hyperparameters. To obtain a wide hyperprior, a, b, c, d are usually set to very small positive constants. Γ(a) represents the gamma function.

[0094] S3: Obtain the posterior distribution of the original signal to be reconstructed according to the hierarchical prior distribution and the periodic piecewise observation data.

[0095] Specifically, based on the hierarchical prior distribution and the observation data y obtained in step S21, the posterior distribution of the original signal x to be reconstructed is obtained by using Bayes' formula and the expectation maximization (EM) algorithm, and its posterior distribution can be analytically expressed as a complex Gaussian distribution:

[0096]

[0097] Among them, the covariance Σ of the complex Gaussian distribution is Σ = (βD H D + Λ -1 ) -1 , and the mean μ = βΣD H y.

[0098] According to the Woodbury matrix identity, Σ and μ can be expressed as:

[0099]

[0100] μ = βΛD H Q -1 y

[0101] Among them, Q = I + βDΛD H .

[0102] In the segmented observation model, substituting the effective measurement data and the dictionary matrix into the above formula, Σ and μ can be expressed as:

[0103]

[0104]

[0105] Among them,

[0106] S4: Construct an iterative formula for the SBL algorithm using the posterior distribution;

[0107] In the SBL algorithm, signal reconstruction is achieved through iteration. The optimal mean of the posterior distribution constructed in step S3 is the reconstructed signal. The following are the iterative steps of the SBL algorithm, which is called the direct inversion SBL (DI-SBL) here:

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] ε (j) = diag(Σ (j) )

[0114]

[0115] where ε = diag(Σ) indicates that ε is a vector composed of the elements on the diagonal of matrix Σ, and ε k represents the (k + 1)-th element of ε, represents γ obtained after the j-th iteration, k , μ and ∑ respectively represent the mean and covariance of the posterior probability of the original signal x to be reconstructed. The unknown parameters γ k and β of μ are called hyperparameters and can be solved by the expectation-maximization algorithm. ||·||2 represents the norm.

[0116] It can be seen from the above iterative process of DI-SBL that the key steps in a single iteration of SBL are to calculate ε and μ, but the calculation process requires solving The computational complexity of the traditional direct inversion method is proportional to the cube of the matrix dimension, and the matrix has the same dimension as the observation vector . If there is a large amount of observed data, the calculation time is often very long and it is difficult to implement in practical engineering.

[0117] S5: Use the fast SBL algorithm based on the Fourier dictionary to calculate the mean of the posterior distribution and the diagonal elements of the covariance matrix of the posterior distribution in a single iteration of the SBL algorithm.

[0118] To solve the above problems, the embodiments of the present invention propose a fast SBL algorithm based on the Fourier dictionary to achieve high-resolution imaging of periodic segmented observation ISAR. The innovation of this algorithm lies in that in the SBL algorithm based on the Fourier dictionary, is a Toeplitz-block-Toeplitz matrix, and another Toeplitz-block-Toeplitz matrix can be constructed using a permutation matrix By using the Gohberg-Semencul (G-S) decomposition to solve and then solving for the large computational complexity caused by direct inversion is avoided. In addition, based on the G-S decomposition factors, ε and μ can be solved by FFT / IFFT, greatly shortening the calculation time.

[0119] Specifically, step S5 of this embodiment includes:

[0120] S51: Construct a Fourier dictionary matrix for periodic segmented observation data, and calculate and obtain using the Fourier dictionary matrix

[0121] In this embodiment, step S51 includes:

[0122] S511: Construct a Fourier dictionary matrix for periodic segmented observation data.

[0123] Since the dictionary used in the embodiments of the present invention is composed of Fourier bases, when there are missing data, the dictionary matrix is not a complete Fourier dictionary. Here, it is represented by and is denoted as The Fourier basis of the (k + 1)-th column in

[0124]

[0125] where ω k = 2πk / K, k = 0,..., K - 1 The Fourier basis corresponding to the i-th segment of valid data is denoted as

[0126]

[0127] where represents a complete Fourier basis of length N gp , that is

[0128]

[0129] S512: Obtain the expression of the parameter using the constructed dictionary matrix

[0130] Based on the obtained dictionary matrix it can be expressed as

[0131]

[0132] where is a Toeplitz-block-Toeplitz matrix, that is

[0133]

[0134] Furthermore One of the sub-matrices R i of

[0135]

[0136] R i The element expression of is

[0137]

[0138] As can be seen from the above formula, r m can be obtained by performing a K-point FFT fast calculation on the vector composed of 1 / γ k . Then, and can be obtained. It can be seen that in each iteration of the SBL algorithm, the matrix to be inverted Can be quickly calculated by FFT. And, is also a Toeplitz-block-Toeplitz matrix, The structure of is the same as

[0139] S513: Set the permutation matrix and use the permutation matrix and the parameter to construct the parameter Obtain the parameter of the inverse matrix and the shift expression of the inverse matrix .

[0140] Specifically, by setting a permutation matrix The parameter can be expressed as:

[0141]

[0142] Where, is a Toeplitz-block-Toeplitz matrix, and its form is:

[0143]

[0144] Where, Here, the superscript <·> represents the elements in the corresponding submatrix in represents q in Q0 i . Therefore, can also be quickly calculated by FFT.

[0145] In view of is a Toeplitz-block-Toeplitz matrix, it can be written in the following two different forms:

[0146]

[0147] Where, is a (N g -q)×(N g -q) submatrix in, and is also a Toeplitz-block-Toeplitz matrix. Their relationship is Where, is a matrix with all elements on the secondary diagonal being 1 and the remaining elements being 0, that is

[0148] For the above of the two forms, use the matrix inversion formula respectively to get:

[0149]

[0150] Among them,

[0151]

[0152]

[0153]

[0154]

[0155] Substitute and into the above to obtain:

[0156]

[0157] Subsequently, based on the obtained find the displacement expression.

[0158] Define a matrix:

[0159]

[0160] Among them, I q is an identity matrix of dimension q×q. Obviously, and

[0161] Then, the displacement representation of can be expressed as:

[0162]

[0163] Let

[0164]

[0165]

[0166] can be further expressed as:

[0167]

[0168] S514: Obtain the G-S decomposition formula and G-S decomposition factors of the inverse matrix based on the shift expression of the inverse matrix

[0169] Based on​ The expression of can be used to obtain the G-S decomposition of

[0170]

[0171] where is a Toeplitz-block matrix. and are called the G-S decomposition factors of Moreover, the displacement rank of

[0172] S515: Solve for the G-S decomposition factors of This embodiment uses an iterative method to quickly calculate the G-S decomposition factors of

[0173] Specifically, inspired by the Levinson-Durbin (L-D) algorithm, this embodiment of the present invention proposes an iterative method to calculate the G-S decomposition factors of The iterative process is as follows: Input: G0 and G1

[0174] Calculate the initial values:

[0175] Iterative process:

[0176] where α = 1,…,N

[0177]

[0178]

[0179] Output: gp -2.

[0180] Output:

[0181] The calculation formula of W in S513 q can be further written as Substitute the known G0, and the calculated into it, then W q can be obtained. Substitute and W q into the expression of to further obtain and That is, the G-S decomposition factors of

[0182] S516: Obtain the inverse matrix based on the G-S decomposition of the inverse matrix The G-S decomposition formula.

[0183] Specifically, based on the G-S decomposition formula, the G-S decomposition formula of

[0184]

[0185] wherein, is a block-Toeplitz matrix. Thus, the solution of is converted into some block-Toeplitz matrix operations. Moreover, at this time

[0186] S52: Use the obtained in S516 to find ε and μ in a single iteration of the fast SBL algorithm. The specific process is as follows:

[0187] Based on the obtained dictionary matrix ε and μ are expressed as:

[0188]

[0189] ε = diag(Σ)

[0190]

[0191] Specifically, the fast calculation process of ε is as follows:

[0192] Since Λ is a diagonal matrix, the calculation of ε can be divided into two steps. The specific steps are as follows:

[0193]

[0194]

[0195] wherein, ε k and δ k respectively represent the (k + 1)-th value of ε and δ. Also, since γ k and β can be calculated through the iteration formula of the SBL algorithm in (S22), only δ needs to be calculated quickly. Substitute in step S511 and in S516 into the above expression of δ, and the expression of δ k can be obtained as:

[0196]

[0197] wherein, is a block matrix, and the dimensions of its sub - matrices are all N gp ×N gp . Taking matrix blocks as units, U l,m represents a matrix composed of the sum of all sub - matrices on the m - th diagonal of this block matrix, with dimensions N gp ×N gp . is called the polynomial coefficient and is the sum of all elements on the n - th diagonal of U l,m . They can be quickly solved through FFT / IFFT. The specific solving process is as follows:

[0198] Let where represents the i - th sub - vector in . Each sub - vector in gp has a dimension of q, and there are N of them. Then where represents the vector composed of the i - th element in each sub - vector of . Let with dimensions N gp . Let

[0199]

[0200] where is a Toeplitz matrix with dimensions N gp ×N gp . It can be seen that can be solved through the sum of the products of some Toeplitz matrices and vectors. And the product of a Toeplitz matrix and a vector can be converted into FFT / IFFT. Therefore, c l,m can be quickly solved through FFT / IFFT. Similarly, can be solved in the same way, and there is

[0201] Then, δ can be quickly calculated through FFT:

[0202]

[0203] where represents taking the K - point FFT of the vector in the brackets, and

[0204]

[0205] Finally, ε is calculated through the dot - product of δ, β, and 1 / γ k .

[0206] Furthermore, the fast calculation process of μ is as follows:

[0207] From the expression of μ in step S4, the calculation of μ can be divided into three steps:

[0208]

[0209]

[0210]

[0211] Substitute the obtained in S516 into 's expression, it can be seen that the right side of is the product of some Toeplitz matrices and vectors. Therefore, can be quickly calculated by FFT / IFFT. Next, divide into q segments, each segment has a length of N gp and represents the i-th sub-vector in. Let where 's calculation formula is:

[0212]

[0213] where represents performing K-point IFFT on the vector in the parentheses.

[0214] Finally, calculate μ through the dot product of β and 1 / γ k of.

[0215] S6: Substitute the posterior distribution mean and posterior distribution covariance into the iterative formula for iterative calculation to obtain the final ISAR high-resolution imaging.

[0216] Specifically, repeat the steps of S51 (S512 - S516) and S52 until the convergence condition is met and stop the iteration to complete the high-resolution imaging. In this embodiment, set the convergence threshold δ, and judge whether the μ value obtained in each iteration meets the convergence condition according to the following formula

[0217]

[0218] If the convergence condition is not met, continue to repeat the steps of S512 - S516 and S52 for iteration; if the convergence condition is met, the optimal mean can be obtained, which is the reconstructed sparse signal, and high-resolution imaging is achieved.

[0219] The following further illustrates the periodic segmented observation ISAR high-resolution imaging method of the embodiment of the present invention through simulation experiments.

[0220] (1.1) Experimental conditions:

[0221] Parameter settings of the SBL algorithm: Initial value Hyperparameters a = b = c = d = 10 -6 ; Convergence threshold δ = 10 -3 ; Frequency sampling factor K / N s = 4. To clearly show the performance of the imaging method based on the fast SBL algorithm of the present invention, some existing typical sparse signal reconstruction methods are added in this embodiment for comparison, including the fast iterative adaptive algorithm (FIAA), orthogonal matching pursuit (OMP), S-ESBL, and DI-SBL algorithms. Here, the S-ESBL algorithm is an approximate fast SBL algorithm that has been proposed, and DI-SBL refers to the direct calculation of the SBL algorithm.

[0222] Simulation experiment: The simulated observation data comes from a simulated signal with 25 random frequency points. Signal-to-noise ratio is 10 dB.

[0223] Experiment with measured data: The measured observation data comes from the Yak-42 aircraft. The radar used to collect ISAR data operates in the C band, with a frequency band of 400 MHz and a pulse repetition frequency of 300 Hz. The distance window has 256 sampling points, and the imaging time includes 256 pulses.

[0224] To show the signal reconstruction performance of various methods, the normalized root mean square error (nRMSE) of signal reconstruction is defined as:

[0225]

[0226] Among them, represents the reconstructed signal value, and x represents the true signal value.

[0227] (1.2) Experimental content and results

[0228] Step 1: Use the software MATLAB R2020b to perform signal reconstruction on the simulated observation data. The length of this simulated data is 512, divided into 8 segments, and the length of each segment of data is 64. The missing rate is 50%, that is, the effective data length in each segment of data is 32. The reconstruction results of various algorithms are as Figure 3 shown. Among them, Figure 3 (a) is the reconstruction result diagram of the imaging method based on the FIAA algorithm; Figure 3 (b) is the reconstruction result diagram of the imaging method based on the OMP algorithm; Figure 3 (c) is the reconstruction result diagram of the imaging method based on the S-ESBL algorithm; Figure 3 (d) is the reconstruction result diagram of the imaging method based on the DI-SBL algorithm; Figure 3(e) is the imaging method based on the FD-GPSBL algorithm, that is, the reconstruction result diagram of the imaging method proposed in the embodiments of the present invention.

[0229] Table 1 gives the signal reconstruction time and normalized root mean square error of the above various methods.

[0230] Table 1 Comparison of signal reconstruction time and normalized root mean square error of various algorithms

[0231] FIAA OMP S-ESBL DI-SBL FD-GPSBL Reconstruction time / s 0.8519 0.0204 5.2275 13.1587 0.6844 nRMSE 0.1781 0.6650 0.3123 0.0675 0.0675

[0232] Step 2: Conduct Monte Carlo experiments to compare the performance diagrams of various methods under different parameters. The results are as Figure 4 、 Figure 5 and Figure 6 shown. Figure 4 is the performance curve diagram of various methods when the observation data length is different. Among them, Figure 4 (a) The figure is the reconstruction calculation time. Note that the time values on the curve diagram are after taking logarithms; Figure 4 (b) is the reconstructed normalized root mean square error; Figure 4 (c) is the variance of the normalized root mean square error. Figure 5 is the performance curve diagram of various methods when the observation data missing rate is different. Among them, Figure 5 (a), Figure 5 (b) and Figure 5 (c) The figures respectively represent the calculation time, normalized root mean square error and variance. Figure 6 is the performance curve diagram of various algorithms when the number of segments of periodically segmented observation data is different. Among them, Figure 6 (a), Figure 6 (b) and figure (c) respectively represent the calculation time, normalized root mean square error and variance.

[0233] Step 3: Use the software MATLAB R2020b to image the measured data. In order to reflect the imaging effect of periodically segmented observation data, first, Figure 7 gives the imaging result diagram of the complete "Yak-42" aircraft data for comparison. Among them, Figure 7 (a) is the high-resolution range profile (HRRP). The abscissa of this figure represents the fast time dimension, and the ordinate represents the range dimension; Figure 7 (b) is the imaging result of the traditional range-Doppler algorithm; Figure 7 (c) is the imaging result of the DI-SBL algorithm. Figure 7 (b) and Figure 7(c) The abscissas all represent the azimuth dimension, and the ordinates all represent the range dimension. For the segmented observation data, assuming that the data of the Yak-42 aircraft is periodically missing in the azimuth dimension, MR is 50%, and q is 4. The HRRP of the periodically segmented Yak-42 data and the imaging results using the traditional range-Doppler algorithm and the FD-GPSBL algorithm are respectively as shown in Figure 8 (a), Figure 8 (b) and Figure 8 (c). The range dimension oversampling factor for the imaging of the complete data and the missing data is 4. The dynamic display range of all the imaging diagrams is 40 dB.

[0234] Table 2 gives the average running times of the implementation methods of the DI-SBL and the FD-GPSBL algorithm proposed in the embodiment of the present invention in the imaging experiment of the above-mentioned periodically segmented observation measured data.

[0235] Table 2 Comparison of the average running times of the DI-SBL and FD-GPSBL algorithms in the experiment

[0236] Algorithm DI-SBL FD-GPSBL Time / s 9.1078 1.8541

[0237] (1.3) Result analysis

[0238] From Figure 3 it can be seen that when the two frequency values of the signal differ by a minimum frequency resolution unit, the signal reconstruction results based on the FIAA, DI-SBL, and FD-GPSBL algorithms are very good, indicating that they have higher resolution. The signal reconstruction results of the DI-SBL and the FD-GPSBL algorithm proposed in the embodiment of the present invention are the same. In addition, the nRMSE of various methods listed in Table 1 also proves the above conclusion, that is, the nRMSE of the FIAA, DI-SBL, and FD-GPSBL algorithms is relatively small, and the nRMSE of the DI-SBL and FD-GPSBL algorithms is the same. By comparing the calculation times in Table 1, we notice that the calculation time of the OMP algorithm is the shortest. FD-GPSBL is more than 19 times faster than DI-SBL.

[0239] Figure 4 、 Figure 5 and Figure 6 show the influence of some variables on the algorithm performance. From Figure 4 (a) and Figure 4 (b) it can be seen that as the total length of the observation data increases, the calculation time of the algorithm becomes longer and the nRMSE gradually decreases; for different MRs, the larger the MR of the data, the less the effective data. The time for a single iteration of the SBL class of algorithms decreases, but when the convergence threshold is reached, the total number of iterations increases. As shown in Figure 5 (a) and Figure 5As shown in (b), as MR increases, the computational time of the algorithm decreases within a certain range, while the nRMSE increases. The computational time of the FD-GPSBL algorithm is several times shorter than that of the DI-SBL algorithm. In addition, when MR is greater than 40%, the nRMSE of the S-ESBL algorithm becomes larger and increases rapidly as MR increases. This is because S-ESBL adopts a certain approximation. The more missing samples there are, the worse the reconstruction effect. When MR is greater than 70%, the nRMSE of FIAA becomes larger. The nRMSE of the DI-SBL and FD-GPSBL algorithms also increases, but the increase is very small. Even when MR is 80%, the error value is acceptable. From Figure 6 It can be seen from (a) and (b) that the q value only affects the computational complexity of the FIAA and FD-GPSBL algorithms and has no effect on their reconstruction errors. Moreover, as the q value increases, the computational time of the FD-GPSBL algorithm proposed in the embodiments of the present invention becomes longer, and the computational time of the FIAA algorithm becomes shorter. This is because the displacement rank of the inverse matrix in the FD-GPSBL algorithm is 2q, and the displacement rank of the inverse covariance matrix in the FIAA algorithm is 2N gp . Here, since the computational time of the FD-GPSBL algorithm is relatively large when the q value is higher than 16, the computational time, normalized root mean square error, and variance when the q value is small are only given in Figure 6 . In addition, to compare the stability of the algorithms, the variance diagrams of the nRMSE of the algorithms are also given in Figure 4 (c), Figure 5 (c) and Figure 6 (c). Obviously, the variance values of these algorithms are all less than 0.03, indicating that all the algorithms have good stability.

[0240] To verify the effectiveness of the fast algorithm proposed in the present invention, the traditional range-Doppler algorithm and the SBL / FD-GPSBL algorithm are used to image the measured data of the "Yak-42" aircraft respectively. The high-resolution range images and imaging results of the complete measurement data are as shown in Figure 7 , and the high-resolution range images and imaging results of the periodically segmented measurement data are as shown in Figure 8 . It can be seen from Figure 7 that the sidelobe level of the imaging result of the range-Doppler algorithm is relatively high, and the imaging result of the SBL algorithm is better. It can be seen from Figure 8 that compared with the imaging result of the complete data, the imaging result of the range-Doppler algorithm for the segmented data has a higher sidelobe level, while the imaging result of the FD-GPSBL algorithm proposed in the present invention is better, indicating that the FD-GPSBL algorithm has a higher imaging resolution.

[0241] Table 2 gives the computation times of the DI-SBL and FD-GPSBL algorithms for periodic segmented observations in the measured experiments. Obviously, compared with DI-SBL, the computation time of the FD-GPSBL algorithm is very short. Since the length of the measured data used in the experiment is only 128 and the MR is 50%, the amount of effective data is small, so the acceleration effect of the FD-GPSBL algorithm is not obvious. In summary, it can be seen that even when the MR is relatively large, the FD-GPSBL algorithm can obtain better imaging results and has a shorter computation time.

[0242] In summary, in view of the case of periodic segmented observation data, the embodiment of the present invention proposes a high-resolution imaging method based on the fast SBL algorithm, which can well suppress sidelobes, reduce the main lobe width, and improve the resolution. The fast SBL algorithm uses GS decomposition and FFT (Fast Fourier Transform) to solve the inverse matrix and the multiplication operation involving the inverse matrix respectively, without any approximation, so the computational amount can be reduced by several orders of magnitude while ensuring the result accuracy. Compared with the proposed fast SBL algorithm for non-periodic segmentation, the method of the present invention has a lower computational complexity. The imaging method based on the fast SBL algorithm in the embodiment of the present invention improves the computational speed without sacrificing accuracy. The core of the fast SBL algorithm is to utilize the Fourier dictionary. In each iteration of SBL, the inverse matrix to be solved is a Toeplitz-block-Toeplitz matrix. Based on this matrix, another Toeplitz-block-Toeplitz matrix can be constructed and can be quickly solved by FFT. The inverse matrix can be expressed by G-S decomposition, avoiding the problem of high computational complexity caused by directly solving the inverse matrix. It should be noted that the fast SBL algorithm proposed in the present invention is based on the Fourier dictionary. Although SBL has no requirement on the type of dictionary, in many fields, signals are sparse in the dictionary composed of Fourier bases.

[0243] Another embodiment of the present invention provides a storage medium storing a computer program for performing the steps of the periodic segmented observation ISAR high-resolution imaging method in the above embodiments. Another aspect of the present invention provides an electronic device including a memory and a processor, where the memory stores a computer program, and when the processor calls the computer program in the memory, the steps of the periodic segmented observation ISAR high-resolution imaging method as described in the above embodiments are implemented. Specifically, the integrated modules implemented in the form of software functional modules can be stored in a computer-readable storage medium. The above software functional modules stored in a storage medium include several instructions for causing an electronic device (which may be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disc that can store program codes.

[0244] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm, characterized in that Including: S1: Use the obtained periodic segmented observation data for modeling to obtain a reconstruction model of the original signal to be reconstructed, The reconstruction model is: Among them, the dictionary matrix x represents the original signal to be reconstructed, represents the observation noise, represents the valid data in the observation data, D represents the over-complete dictionary matrix, represents the selection matrix corresponding to the valid matrix; S2: Construct a hierarchical Bayesian prior model of the original signal to be reconstructed and obtain the hierarchical prior distribution of the original signal to be reconstructed; S3: Obtain the posterior distribution of the original signal to be reconstructed according to the hierarchical prior distribution and the periodic segmented observation data; S4: Use the posterior distribution to construct an iterative formula for the SBL algorithm; S5: Use the fast SBL algorithm based on the Fourier dictionary to calculate the mean of the posterior distribution and the diagonal elements of the covariance matrix of the posterior distribution in a single iteration of the SBL algorithm; S6: Substitute the mean of the posterior distribution and the diagonal elements of the covariance matrix of the posterior distribution into the iterative formula for iterative calculation to obtain the final ISAR imaging result.

2. The periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm according to claim 1, wherein The S2 includes: Construct a hierarchical Bayesian prior model, where the first layer of the hierarchical Bayesian prior model is the modeling of the original signal to be reconstructed x and the noise e, and the probability density functions of the original signal to be reconstructed x and the noise e are obtained: Among them, denotes being subject to a complex Gaussian distribution, and x k denotes the (k + 1)-th element of the original signal vector x to be reconstructed, and γ k denotes the inverse variance of x k and Λ is a diagonal matrix formed by 1 / γ k in sequence, and e n denotes the (n + 1)-th element of the noise data vector e, and β denotes the inverse variance of e n i.e., β is the precision of the noise; Set the second layer of the hierarchical Bayesian prior model to be γ k and the modeling of β, and the probability density functions are respectively as follows: where gamma(·) represents the gamma distribution, a and b represent the shape and scale parameters of γ k respectively, c and d represent the shape and scale parameters of β respectively, and Γ(a) represents the gamma function.

3. The periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm according to claim 2, characterized in that The S3 includes: Based on the prior distribution of the original signal to be reconstructed x and the observation data, use the Bayesian formula and the expectation maximization algorithm to obtain the posterior distribution of the original signal to be reconstructed x, and obtain the covariance Σ and mean μ of the posterior distribution respectively as: Among them, 4. The periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm according to claim 3, characterized in that, The iterative formula includes: ε (j) = diag(Σ (j) ) where the superscript (j) represents the iteration number, Σ represents the covariance of the posterior distribution of the signal, ε = diag(Σ) indicates that ε is a vector composed of the elements on the diagonal of the matrix Σ, μ represents the mean of the posterior distribution of the signal, and β represents the precision of the noise. represents the dictionary matrix, and Λ is a diagonal matrix composed of 1 / γ k in sequence, and γ k represents the precision of the (k + 1)-th value in the signal vector x.

5. The periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm according to claim 4, characterized in that The S5 includes: S51: Construct a Fourier dictionary matrix of the periodic segmented observation data, and calculate and obtain by using the Fourier dictionary matrix S52: Using to obtain the parameters ε and μ in a single iteration of the fast SBL algorithm.

6. The periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm according to claim 5, characterized in that The S51 includes: S511: Construct a Fourier dictionary matrix of the periodic segmented observation data: where ω k = 2πk / K, k = 0, …, K - 1, represents the Fourier basis corresponding to the i-th segment of valid data; S512: Obtain the expression of the parameter using the constructed dictionary matrix: S513: Set the permutation matrix and use the permutation matrix and parameters to construct parameters obtain parameters of the inverse matrix and the shift expression of the inverse matrix ; S514: Obtain the inverse matrix based on the shift expression of the inverse matrix to obtain the G-S (Gohberg-Semencul) decomposition formula and G-S decomposition factors of the inverse matrix; S515: Solve for the G-S decomposition factors; S516: Obtain the calculation result using the G-S decomposition factor of .

7. The periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm according to claim 6, characterized in that, The S6 includes: Set a convergence threshold δ, and judge whether the μ value obtained in each iteration satisfies the convergence condition If the convergence condition is not satisfied, repeat steps S51 and S52 to continue the iteration; if the convergence condition is satisfied, the obtained optimal mean is the reconstructed sparse signal.

8. A storage medium, characterized in that, The storage medium stores a computer program, and the computer program is used to execute the steps of the periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm according to any one of claims 1 to 7.

9. An electronic device, characterized in that, Including a memory and a processor, the memory stores a computer program, and when the processor calls the computer program in the memory, the steps of the periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm according to any one of claims 1 to 7 are implemented.

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