Sparse signal matrix recovery method based on simultaneous structured model fast sparse Bayesian learning method, program, equipment and storage medium

Abstract

The invention belongs to the technical field of acoustic signal processing, and particularly relates to a sparse signal matrix recovery method based on a simultaneous structured model rapid sparse Bayesian learning method, a program, equipment and a storage medium. According to a signal model of an equal-interval uniform linear array, a linear equation for sparse signal recovery is established on the premise that a sensing matrix is known; a fast sparse Bayesian learning method is adopted, based on average field updating, maximized posterior distribution is converted into an evidence lower limit in a maximized average field form, a loose evidence lower limit is obtained by introducing a Lipscherz condition of a continuous function, an optimal hyper-parameter is calculated by maximizing the loose evidence lower limit, and after a convergence condition is met, the optimal hyper-parameter is calculated. And outputting the estimation of the sparse signal matrix to realize sparse signal matrix recovery. According to the method, excellent performance can still be kept when the number of array elements is small, the performance is excellent under low signal noise, the method can be effectively applied to scenes with large noise such as underwater, and a target in a reconstructed image is very clear.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of acoustic signal processing, and particularly relates to a sparse signal matrix recovery method based on a simultaneous structured model fast sparse Bayesian learning method, a program, a device and a storage medium. BACKGROUND

[0002] The sparse reconstruction algorithm is based on the CS theory and is used for recovering an original signal from compressed sampling. The algorithm can be mainly divided into three categories. The first category is a convex relaxation algorithm. The algorithm is used for solving a relaxed problem through convex relaxation of an initial non-convex sparse representation problem and then solving the relaxed problem through a corresponding optimization algorithm. The algorithm has the disadvantages of large amount of calculation and the need to determine a proper regularization parameter, and has the advantage of good performance. The algorithm mainly includes a basis pursuit (BP) algorithm, a BPDN algorithm, a Lasso algorithm, a gradient projection for sparse reconstruction (GPSR) algorithm and a smooth l0-norm approximation algorithm.

[0003] The second category is a greedy algorithm. The algorithm selects one or more basis atoms most related to a residual error as basis vectors corresponding to the original signal in each iteration. The algorithm has the characteristics of small amount of calculation and poor performance. The algorithm mainly includes a matching pursuit (MP) algorithm, an orthogonal matching pursuit (OMP) algorithm and a ROMP algorithm.

[0004] The last category is a sparse recovery algorithm based on Bayesian theory, that is, a sparse Bayesian learning (SBL) algorithm or a Bayesian compressed sensing (BCS) algorithm. The algorithm firstly applies a prior probability density function with sparse characteristics to a sparse signal, and then solves unknown parameters in the prior probability density function by maximizing a posterior probability density function of the sparse signal on the basis of compressed sampling data, so as to estimate the sparse signal. The algorithm can effectively suppress noise and improve reconstruction accuracy, but a traditional multi-shot SBL method is established on the basis of a row sparse model, that is, all shots share the same support domain. For a signal changing with distance in actual measurement, the row sparse model cannot meet the demand of detection accuracy. SUMMARY

[0005] The present application belongs to the technical field of acoustic signal processing, and particularly relates to a sparse signal matrix recovery method based on a simultaneous structured model fast sparse Bayesian learning method, a program, a device and a storage medium.

[0006] The sparse signal matrix recovery method based on the simultaneous structured model fast sparse Bayesian learning method comprises the following steps:

[0007] Input a multi-shot measurement data matrix, and establish a linear equation for sparse signal recovery under the premise of a known sensing matrix according to a signal model of an equidistant uniform linear array;

[0008] The fast sparse Bayesian learning method is adopted, the maximum posterior distribution is converted into a maximum average field form of the lower bound of the evidence based on the average field update, a loose lower bound of the evidence is obtained by introducing the Lipschitz condition of a continuous function, the optimal hyperparameter is calculated by maximizing the loose lower bound of the evidence, and the estimation of the sparse signal matrix is output after the convergence condition is met, so that the sparse signal matrix recovery is realized.

[0009] Further, the linear equation for sparse signal recovery is:

[0010] Y = AX + N

[0011] where Y is a multi-shot measurement data matrix, Y ∈ C N×L ; A is a sensing matrix, A ∈ C N×M ; X is a sparse signal matrix to be recovered, X ∈ C M×L ; N is a noise matrix, N ∈ C M×L ; L is the number of shots contained in each frame; M is the number of beams; and N is the number of array elements in the equidistant uniform linear array.

[0012] Further, the method for estimating the sparse signal matrix is specifically:

[0013] Step 1: randomly initialize noise precision λ (0), support domain hyperparameter vector γ l (0) of each shot, mean vector μ l (0) of each shot, l = 1, 2,..., L; and initialize the estimation of the sparse signal matrix according to the mean vector μ l (0) of each shot. Initialize the iteration number t = 1, set the maximum iteration number T and the tolerance tol;

[0014] Let Γ c (t) = diag(γ c (t)) and Γ l (t) = diag(γ l (t)); in the function diag(·), if the bracket is a diagonal matrix, the diagonal elements are extracted to generate a vector, and if the bracket is a vector, the elements in the vector are taken as diagonal elements to generate a diagonal matrix.

[0015] Step 2: update the mean vector μl (t) and variance vector σ l (t) ;

[0016] μ l (t) = (λ(t-1)) -1 (T(λ(t-1)) -1 + Γ c (t-1)) -1 + Γ l (t-1)) -1 ) -1 (Tμ l (t-1) - A H (Aμ l (t-1) - y l ))

[0017] σ l (t) = (λ(t-1)) -1 a + Γ c (t-1)) -1 + Γ l (t-1)) -1 ) -1

[0018] where a = diag(A H A) ;

[0019] Step 3: Update the noise precision λ(t) and the support domain hyperparameter vector γ l (t) of each snapshot separately according to the updated mean vector μ l (t) and variance vector σ l (t) of each snapshot;

[0020]

[0021] γ l (t) = diag(σ l (t) + μ l (t)(μ l (t)) H )

[0022] Step 4: Estimate the sparse signal matrix l (t) according to the updated mean vector μ

[0023]

[0024] Step 5: If or t = T, stop iteration and let the sparse signal matrix is recovered; otherwise, let t = t + 1 and return to Step 2.

[0025] A computer device comprises a memory, a processor and a computer program stored on the memory, the processor executes the computer program to implement the steps of the sparse signal matrix recovery method based on the simultaneous structured model fast sparse Bayesian learning method.

[0026] A computer readable storage medium has a computer program stored thereon, the computer program, when executed by a processor, implements the steps of the sparse signal matrix recovery method based on the simultaneous structured model fast sparse Bayesian learning method.

[0027] A computer program product comprises computer instructions, the computer instructions, when executed by a processor, implement the steps of the sparse signal matrix recovery method based on the simultaneous structured model fast sparse Bayesian learning method.

[0028] The present application has the following beneficial effects:

[0029] The present application adopts the simultaneous structured model fast sparse Bayesian learning method to reconstruct the target signal, and can remove most of the noise in the background due to its excellent denoising performance. The present application adopts an embedded row sparse model and introduces a double sparse prior, and the signal reconstruction accuracy in the beam where the target signal is located is greatly improved. The present application can maintain excellent performance when the number of array elements is small, the mean square error is at a very low level, and the support recovery rate is maintained above 98%. The present application performs well in low signal-to-noise ratio, can be effectively applied in scenes with large noise such as underwater, and the target in the reconstructed image is very clear. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is the framework diagram of the simultaneous structured model fast sparse Bayesian learning method in the present application.

[0031] Fig. 2(a) is a mean square error change curve diagram of each method under different target signal numbers in embodiment 1 of the present application.

[0032] Fig. 2(b) is a support recovery rate change curve diagram of each method under different target signal numbers in embodiment 1 of the present application.

[0033] Fig. 2(c) is an operation time change curve diagram of each method under different target signal numbers in embodiment 1 of the present application.

[0034] Fig. 3(a) is a mean square error change curve diagram of each method under different array element numbers in embodiment 1 of the present application.

[0035] Fig. 3(b) is a support recovery rate change curve diagram of each method under different array element numbers in embodiment 1 of the present application.

[0036] Figure 3(c) is a graph showing the change in computation time of each method under different signal-to-noise ratios in Embodiment 1 of the present invention.

[0037] Figure 4(a) is a graph showing the mean square error variation of each method under different signal-to-noise ratios in Embodiment 1 of the present invention.

[0038] Figure 4(b) is a graph showing the support recovery rate variation of each method under different signal-to-noise ratios in Embodiment 1 of the present invention.

[0039] Figure 4(c) is a graph showing the change in computation time of each method under different signal-to-noise ratios in Embodiment 1 of the present invention.

[0040] Figure 5(a) is an image result of a set of measured channel data after CBF processing in Embodiment 2 of the present invention.

[0041] Figure 5(b) is an image result of a set of measured channel data after FMF processing in Embodiment 2 of the present invention.

[0042] Figure 5(c) is an image result of a set of measured channel data processed by FSS-BCS in Embodiment 2 of the present invention.

[0043] Figure 5(d) is an image result of a set of measured channel data processed by MSBL in Embodiment 2 of the present invention.

[0044] Figure 5(e) is an image result of a set of measured channel data after OMP processing in Embodiment 2 of the present invention.

[0045] Figure 6(a) is an image result of a set of measured channel data after CBF processing in Embodiment 2 of the present invention.

[0046] Figure 6(b) is an image result of a set of measured channel data after FMF processing in Embodiment 2 of the present invention.

[0047] Figure 6(c) is an image result of a set of measured channel data processed by FSS-BCS in Embodiment 2 of the present invention.

[0048] Figure 6(d) is an image result of a set of measured channel data processed by MSBL in Embodiment 2 of the present invention.

[0049] Figure 6(e) is an image result of a set of measured channel data after OMP processing in Embodiment 2 of the present invention.

[0050] Figure 7(a) is an image result of a set of measured channel data after CBF processing in Embodiment 2 of the present invention.

[0051] Figure 7(b) is an image result of a set of measured channel data after FMF processing in Embodiment 2 of the present invention.

[0052] Figure 7(c) is an image result of a set of measured channel data processed by FSS-BCS in Embodiment 2 of the present invention.

[0053] Figure 7(d) is an image result of a set of measured channel data processed by MSBL in Embodiment 2 of the present invention.

[0054] Figure 7(e) is an image result of a set of measured channel data after OMP processing in Embodiment 2 of the present invention. Detailed Implementation

[0055] The present invention will now be further described with reference to the accompanying drawings.

[0056] To improve the accuracy of sparse reconstruction, this invention employs a Fast Simultaneous Structured Bayesian Compressed Sensing (FSS-BCS) algorithm based on a simultaneous structured model. According to the first type of simultaneous structured model, namely the element embedding type sparse model, each snapshot of the measurement data along the beam direction shares the same support domain, meaning it follows the same prior distribution, ensuring that elements are sparse along the beam direction. Simultaneously, each snapshot is assigned a different prior distribution, i.e., a support domain that changes over time, guaranteeing that elements are sparse within each beam. A corresponding Bayesian inference framework is established based on this model, and a fast mean-field update is used to maximize the logarithm of the evidence, indirectly maximizing the posterior probability. This invention effectively improves the estimation accuracy of signals within the same beam, thereby improving the overall accuracy.

[0057] like Figure 1 As shown, the support domain of each measurement snapshot differs temporally. An additional support domain for that specific moment is added to the traditional row-sparse model-based support domain for each snapshot; that is, the prior distribution of the signal consists of two Gaussian prior distributions. Using a Bayesian framework, the hyperparameters are updated according to the fast mean-field algorithm, and the mean vector and covariance matrix of each snapshot are updated separately until the algorithm converges.

[0058] Step (1): Given the sensing matrix and measurement matrix, establish the linear equation for sparse signal recovery. For an equally spaced linear array containing N elements, the expression is as follows:

[0059] Y = AX + N (1)

[0060] Where, A∈C N×M Let Y = [y1, y2, ..., y] represent the perception matrix. L ]∈C N×L Let X ∈ C represent the measurement matrix. M×L Let N ∈ C be the sparse signal matrix to be recovered. M×LLet L represent the noise matrix, and L represent the number of snapshots contained in each frame.

[0061] Step (2): Given the prior information of the signal to be estimated and the noise model, construct the measurement likelihood function based on the simultaneous structured model and derive the expression for the posterior distribution.

[0062] Based on the Gaussian mixture scale prior (GSM) and the additive white noise model, the likelihood function under the row sparse model is expressed as:

[0063]

[0064] And each snapshot in X l They all follow the same prior distribution:

[0065]

[0066] Where, γ c Γ is the hyperparameter vector that controls the sparse distribution of X across M beams. c =diag(γ) c This vector does not change over time, meaning it is unrelated to the snapshot number and is only related to the overall sparse distribution of the signal on the beam.

[0067] The first type of simultaneous structured model, also known as embedded row sparsity, assigns a different support domain to each snapshot. This support domain is only related to the snapshot number, which corresponds to the sampling time. In other words, the support domain is different at different distances.

[0068]

[0069] Where, γ l If the hyperparameter vector is only related to the k-th snapshot, then the complete prior distribution of the signal is:

[0070]

[0071] According to Bayes' theorem, we can obtain the posterior probability distribution:

[0072]

[0073] Step (3): Using the fast mean-field algorithm, the maximization of the posterior distribution is transformed into the maximization of the mean-field form of the lower bound of evidence. The Lipschitz condition of the continuous function is introduced to obtain a relaxed lower bound of evidence. The optimal hyperparameter is calculated by maximizing this relaxed lower bound of evidence.

[0074] Step (3.1): When performing a fast mean-field update, x l The approximate posterior distribution is q(x) l ;θ l ), θl Let θ be a variational parameter. l ={μ l ,σ l}, μ l The mean of the l-th snapshot, σ l =[σ l1 ,σ l2 ,...,σ lM The covariance matrix of the l-th snapshot is diag(σ). l Let ) be a diagonal matrix, and let the joint probability be applied to all q(x) l ;θ l Marginalization allows us to obtain the lower limit of evidence:

[0075]

[0076] Where θ=[θ1,θ2,...,θ L The joint probability density can be written as the product of the likelihood function and the prior distribution:

[0077]

[0078] Step (3.2): Use the expectation-maximization algorithm to solve for the optimal hyperparameters, thereby maximizing the lower bound of evidence; a) Solve for the noise accuracy λ;

[0079]

[0080] Taking its derivative until it is zero, we can obtain the updated value of λ under the variational parameter θ:

[0081]

[0082] b) Solve for the common support domain hyperparameter γ c ;

[0083]

[0084] For γ c Differentiate each element individually and find its extreme points to obtain γ. c Iterative:

[0085]

[0086] c) Solve for the individual support domain hyperparameter γ for each snapshot. l ;

[0087]

[0088] Similarly, we obtain γ l Iterative:

[0089]

[0090] Since the form of the variational parameters is fixed, under this form

[0091]

[0092] a = diag(A) H A) (18)

[0093] Substitute the above expectations into (11), (13), and (15).

[0094]

[0095] Step (3.3): Substitute the updated values ​​of the hyperparameters into the lower bound of evidence and introduce the Lipschitz condition for continuous functions to obtain a relaxed lower bound of evidence. Solve for the updated values ​​of the variational parameters on this lower bound of evidence.

[0096] a) Substitute the updated hyperparameter values ​​into the lower bound of evidence, and set it to be...

[0097]

[0098] That is, for q(x) l ;θ l Take the gradient and update the variables;

[0099] b) Introducing the Lipschitz condition for continuous functions yields a relaxed lower bound of evidence;

[0100] make If the function is convex, then it has the following properties:

[0101]

[0102] Where T = 2λ max (A H A), Substitute (23) into (22), and for each h(μ) l Replace with the lower bound h(μ) l ;z l To obtain a lenient lower bound on evidence, let it be... Next, we take the gradient of the variational parameter, and the value at which the gradient is 0 is the updated value.

[0103] c) Update σ l

[0104]

[0105] Setting the gradient to 0, we obtain σ. l The updated version:

[0106] σl =(λ -1 a+(Γ c ) -1 +(Γ l ) -1 ) -1 (25)

[0107] d) Similarly, update μ by taking the value at which the gradient is 0. l (t), let z l =μ l The iteration values ​​are as follows:

[0108]

[0109] Based on the above theoretical derivation, the sparse signal matrix recovery method based on the simultaneous structured model fast sparse Bayesian learning method provided by this invention specifically includes the following steps:

[0110] Step 1: Input the multi-shot measurement data matrix Y = [y1, y2, ..., y L Based on the signal model of a uniform linear array with N elements, and given the known sensing matrix A, a linear equation for sparse signal recovery is established.

[0111] Y = AX + N

[0112] Where, A∈C N×M , Y∈C N×L X is the sparse signal matrix to be recovered, X∈C M×L N is the noise matrix, N∈C M ×L L represents the number of snapshots per frame; M represents the number of beams.

[0113] Step 2: Using the fast sparse Bayesian learning method, based on mean-field update, the maximization of the posterior distribution is transformed into the maximization of the mean-field form of the lower bound of evidence. The Lipschitz condition of the continuous function is introduced to obtain a relaxed lower bound of evidence. The optimal hyperparameters are calculated by maximizing the relaxed lower bound of evidence. After the convergence condition is met, the estimate of the sparse signal matrix is ​​output to realize the sparse signal matrix recovery.

[0114] Step 2.1: Initialize the random noise precision λ(0) and the individual support domain hyperparameter vector γ for each snapshot. l (0) The mean vector μ of each snapshot l (0), l=1,2,...,L; based on the mean vector μ of each snapshot l (0), initialization of the sparse signal matrix estimation Initialize the number of iterations t = 1, and set the maximum number of iterations T and the tolerance tol;

[0115] Let Γ c (t)=diag(γ c (t)), Γ l (t)=diag(γ l (t)); In the function diag(·), if the parentheses contain a diagonal matrix, then the diagonal elements are extracted to generate a vector; if the parentheses contain a vector, then the elements in the vector are used as diagonal elements to generate a diagonal matrix.

[0116] Step 2.2: Update the mean vector μ for each snapshot. l (t) and variance vector σ l (t);

[0117] μ l (t)=(λ(t-1)) -1 (T(λ(t-1)) -1 +(Γ c (t-1)) -1 +(Γ l (t-1)) -1 ) -1 (Tμ l (t-1)-A H (Aμ l (t-1)-y l ))

[0118] σ l (t)=(λ(t-1)) -1 a+(Γ c (t-1)) -1 +(Γ l (t-1)) -1 ) -1

[0119] Where, a = diag(A) H A);

[0120] Step 2.3: Based on the updated mean vector μ of each snapshot l (t) and variance vector σ l (t), update the noise accuracy λ(t) and the individual support domain hyperparameter vector γ for each snapshot. l (t);

[0121]

[0122] γ l (t)=diag(σ l (t)+μ l (t)(μ l (t)) H )

[0123] Step 2.4: Based on the updated mean vector μ of each snapshot l (t), estimate the sparse signal matrix

[0124]

[0125] Step 2.5: If If t = T, then stop iterating and let Perform sparse signal matrix recovery; otherwise, let t = t + 1 and return to step 2.2.

[0126] Example 1

[0127] This example verifies the performance of the FSS-BCS method based on simulation experiments. The waveform parameters are as follows: velocity 1480 / s, frequency 40kHz. The array parameters are as follows: number of array elements 96, element spacing is half a wavelength. Within the azimuth angle range [-65°, 65°], pulse signals with amplitudes following a Gaussian distribution, mean 0, and variance 1 are generated at random distances in five random directions as the target signal for this simulation. The pulse duration is 10 seconds. -3 The pulse sampling frequency is 300kHz. The initial signal-to-noise ratio (SNR) is 5dB, and a total of 4096 snapshots are generated. Four other sparse reconstruction methods (MSBL, FMF, OMP, SPICE) are introduced as comparative algorithms. The support recovery rate (SRR), root mean square error (RMSE), and running time of various algorithms are analyzed under different SNRs, target signal numbers, and array element numbers. The definitions of SRR and RMSE are as follows:

[0128]

[0129] Where X represents the original signal, and The estimated signal is used to calculate the SRR. If the absolute error is less than 0.01, the reconstruction is considered successful.

[0130] Based on the simulation results shown in Figures 2(a), 2(b), and 2(c), the RMSE of SPICE did not change significantly with the increase of the number of target signals, while the RMSE of the other four methods increased to varying degrees. However, the RMSE of FSS-BCS remained the lowest. An increase in the number of target signals inevitably leads to a decrease in reconstruction accuracy, so the SRR of each method decreased. The SRR of FSS-BCS and SPICE are relatively close, the highest among all methods, and are least affected by the number of signals. MSBL has the lowest SRR, and its decrease is the most significant with the increase of the number of signals. In terms of runtime, OMP and SPICE, the two compressed sensing algorithms, have lower computational complexity. When the number of signals exceeds 6, SPICE has an advantage over OMP. Meanwhile, the runtimes of MSBL and FSS-BCS are similar.

[0131] Based on the simulation results shown in Figures 3(a), 3(b), and 3(c), as the number of array elements increases from 56 to 112, the RMSE of all methods except SPICE shows a decreasing trend, with FMF showing the smallest change. When the number of array elements is less than 72, MSBL and OMP show more significant changes, then tend to stabilize. MSBL and FMF are close, while OMP surpasses FMF, but FSS-BCS consistently has the lowest RMSE, showing a clear advantage. Regarding SRR, FSS-BCS, OMP, and SPICE are less sensitive to the number of array elements, while MSBL's SRR decreases significantly when the number of array elements is small. When the number of array elements is less than 88, the result of FMF is also relatively stable. After exceeding 88, it begins to decrease, and after 104, it is surpassed by MSBL. Among the five methods, FSS-BCS consistently has the highest SRR. As the number of array elements increases, the running time of the two compressed sensing methods continuously increases, while the computation time of the other three sparse Bayesian learning methods shows a decreasing trend.

[0132] Based on the simulation results shown in Figures 4(a), 4(b), and 4(c), SPICE consistently exhibits the worst RMSE due to insufficient reconstruction accuracy of signals within the same beam. The RMSE of the other four methods tends to decrease with increasing signal-to-noise ratio (SNR), i.e., decreasing noise, with FSS-BCS consistently showing the lowest RMSE. FMF and MSBL show significant reductions in SRR at lower SNRs, while FSS-BCS and SPICE exhibit relatively stable SRRs. Furthermore, FSS-BCS demonstrates a clear advantage over SPICE as the SNR increases. Regarding runtime, SPICE and OMP show virtually no change, MSBL's runtime decreases, while FMF and FSS-BCS's computation time increases.

[0133] Example 2

[0134] This example provides a set of acoustic test results collected at Songhua Lake. Only data within 15m of the sonar center was used in this experiment. Beamforming was performed on the collected channel data using CBF, FMF, FSS-BCS, MSBL, and OMP, respectively. The imaging results for three groups are shown below. Figures 5(a) to 5(e) , Figures 6(a) to 6(e) , Figures 7(a) to 7(e) As shown, the bright spots marked with white circles represent the actual targets. In the CBF image, not only the target is visible, but also noise and interference. After MSBL and FMF processing, most of the noise is removed, but some noise remains in a few beams. OMP provides slightly better image quality; signals in beams other than the target are largely suppressed, but some noise remains in the target beam, ultimately forming a bright band that contrasts sharply with its surroundings. FSS-BCS provides the best image quality; the image shows only the target, other interference is largely removed, and noise in the target beam is also well eliminated, making the target very clear in the entire image.

[0135] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A sparse signal matrix recovery method based on a fast sparse Bayesian learning method using a simultaneous structured model, characterized by: Input a multi-shot measurement data matrix, and based on the signal model of an equally spaced uniform linear array, establish a linear equation for sparse signal recovery under the premise of a known sensing matrix; We employ a fast sparse Bayesian learning method based on mean-field updates. We transform the maximization of the posterior distribution into the maximization of the mean-field form of the lower bound of evidence, and introduce the Lipschitz condition for continuous functions to obtain a relaxed lower bound of evidence. By maximizing the relaxed lower bound of evidence, we can calculate the optimal hyperparameters. After satisfying the convergence condition, we output the estimate of the sparse signal matrix to achieve sparse signal matrix recovery.

2. The sparse signal matrix recovery method based on the fast sparse Bayesian learning method using a simultaneous structured model as described in claim 1, characterized in that: The linear equation for the sparse signal recovery is: Y = AX + N Where Y is a multi-shot measurement data matrix, Y∈C N×L A is the perception matrix, A∈C N×M X is the sparse signal matrix to be recovered, X∈C M×L N is the noise matrix, N∈C M×L L is the number of snapshots per frame; M is the number of beams; N is the number of array elements in a uniformly spaced linear array.

3. The sparse signal matrix recovery method based on the fast sparse Bayesian learning method of the simultaneous structured model according to claim 2, characterized in that: The method for estimating the sparse signal matrix is ​​as follows: Step 1: Initialize the random noise precision λ(0) and the individual support domain hyperparameter vector γ for each snapshot. l (0) The mean vector μ of each snapshot l (0), l=1,2,...,L; based on the mean vector μ of each snapshot l (0), initialization of the sparse signal matrix estimation Initialize the number of iterations t = 1, and set the maximum number of iterations T and the tolerance tol; Let Γ c (t)=diag(γ c (t)), Γ l (t)=diag(γ l (t)); In the function diag(·), if the parentheses contain a diagonal matrix, then the diagonal elements are extracted to generate a vector; if the parentheses contain a vector, then the elements in the vector are used as diagonal elements to generate a diagonal matrix. Step 2: Update the mean vector μ for each snapshot. l (t) and variance vector σ l (t); μ l (t)=(λ(t-1)) -1 (T(λ(t-1)) -1 +(Γ c (t-1)) -1 +(Γ l (t-1)) -1 ) -1 (Tμ l (t-1)-A H (Aμ l (t-1)-y l )) s l (t)=(λ(t-1)) -1 a+(C c (t-1)) -1 +(C l (t-1)) -1 ) -1 Where, a = diag(A) H A); Step 3: Based on the updated mean vector μ of each snapshot l (t) and variance vector σ l (t), update the noise accuracy λ(t) and the individual support domain hyperparameter vector γ for each snapshot. l (t); c l (t)=diag(σ l (t)+μ l (t)(μ) l (t)) H ) Step 4: Based on the updated mean vector μ of each snapshot l (t), estimate the sparse signal matrix Step 5: If If t = T, then stop iterating and let Perform sparse signal matrix recovery; otherwise, let t = t + 1 and return to step 2.

4. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 3.

6. A computer program product comprising computer instructions, characterized in that: When executed by a processor, the computer instructions implement the steps of the method according to any one of claims 1 to 3.

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