Graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing

Abstract

The invention discloses a graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing. Comprising the following steps: firstly, performing low-rank pre-completion processing on an ocean sound field profile observation matrix by using a graph-guided Bayesian low-rank matrix completion method to obtain a pre-completed sound field matrix; generating a plurality of reference matrix blocks, traversing and searching similar matrix blocks of each reference matrix block in the pre-complemented sound field matrix, and further obtaining low-rank reconstruction matrixes corresponding to all the reference matrix blocks; and then, after secondary low-rank pre-completion processing is carried out on each low-rank reconstruction matrix, a corresponding reconstruction matrix is obtained, and then a final sound field reconstruction matrix is obtained. According to the invention, the high-rank sound field is reconstructed into a plurality of low-rank matrixes through the similar matrix blocks, so that the graph-guided Bayesian low-rank matrix completion method can be applied to the field of sound field reconstruction; the method can reduce the sound field reconstruction error on the basis of keeping good similarity under the condition of less observation data, and has good anti-noise performance.

Description

Technical Field

[0001] The invention relates to an ocean sound field reconstruction method in the field of ocean sound fields, and in particular to a graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing. Background Art

[0002] The ocean plays a vital role in national defense and resource development. However, the propagation of electromagnetic waves in water is severely limited. Sound waves have become the preferred carrier for ocean information transmission due to their long propagation distance. Tasks such as underwater communication, navigation, target tracking, and environmental monitoring all rely on the propagation of sound waves. Accurate reconstruction of the ocean acoustic field is crucial to the successful execution of these tasks. However, due to the coverage, resolution, and noise interference of the measurement equipment, the actual measured data is usually sparse and unevenly distributed, and cannot fully reflect the true situation of the acoustic field.

[0003] In the existing technology, traditional sound field reconstruction methods include nearest neighbor interpolation, polynomial interpolation and spline interpolation. Although these methods are simple to operate, they are not good at dealing with noise and using global information. Although methods such as iterative back projection, convex set projection and maximum a posteriori probability can improve the reconstruction effect, they have high requirements for prior information, which limits their application scenarios.

[0004] Existing graph-guided Bayesian matrix completion methods are mainly targeted at low-rank matrices and are usually used to complete low-rank environmental field data. However, the ocean acoustic field data matrix usually has a higher rank. Directly applying this method for reconstruction will result in large errors and cannot meet the requirements of reconstruction performance. Therefore, an improved method is needed to effectively handle the reconstruction problem of high-rank acoustic field data matrices. Summary of the invention

[0005] The purpose of the present invention is to provide a graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing in view of the deficiencies of the prior art.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] 1. A graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing

[0008] 1) Obtain ocean acoustic field profile observation matrix;

[0009] 2) Using the graph-guided Bayesian low-rank matrix completion method to perform low-rank pre-completion processing on the ocean acoustic field profile observation matrix, a pre-completion acoustic field matrix is ​​obtained;

[0010] 3) Generate several reference matrix blocks according to the pre-complemented full sound field matrix, then traverse and search for similar matrix blocks of each reference matrix block in the pre-complemented full sound field matrix according to the size of each reference matrix block, and reconstruct each reference matrix block and the corresponding similar matrix block to obtain the low-rank reconstruction matrix corresponding to all reference matrix blocks;

[0011] 4) After performing secondary low-rank pre-completion processing on the low-rank reconstruction matrix corresponding to each reference matrix block, the reconstruction matrix corresponding to each reference matrix block is obtained, and the prediction results of each matrix block in all reconstruction matrices are returned to the corresponding position in the matrix to be completed of the ocean sound field profile, so as to obtain the final sound field reconstruction matrix.

[0012] The 2) is specifically:

[0013] Firstly, the sound field reconstruction target optimization function is constructed. Then, based on the ocean sound field profile observation matrix, the Bayesian method is used to solve the sound field reconstruction target optimization function to obtain the pre-complemented full sound field matrix.

[0014] In the above 2), the formula of the sound field reconstruction objective optimization function is as follows:

[0015]

[0016] Among them, λ, γ r and γ c are the first to third hyperparameters, X is the ocean acoustic profile matrix to be completed with dimension I*J, Y is the ocean acoustic profile observation matrix with dimension I*J, Ω is a mask matrix with dimension I*J composed of 0 and 1, and the element in the mask matrix Ω is 0, which means that the point corresponding to the element in the ocean acoustic profile observation matrix Y is not observed, and the element in the mask matrix Ω is 1, which means that the point corresponding to the element in the ocean acoustic profile observation matrix Y has been observed; * represents the Hadamard product; L r is the row-wise graph Laplacian matrix, L c is the column-wise graph Laplacian matrix, T denotes transpose, || || * represents the nuclear norm, |||| F stands for the Frobenius norm and tr() stands for the trace of the matrix.

[0017] In the above 3), several reference matrix blocks are generated according to the pre-complemented full sound field matrix, specifically:

[0018] The pre-complemented full sound field matrix is ​​divided into a plurality of reference matrix blocks of the same size, and the union of all the reference matrix blocks covers the pre-complemented full sound field matrix.

[0019] In the above 3), the low-rank reconstruction matrix corresponding to all reference matrix blocks is obtained according to each reference matrix block and the corresponding similar matrix block reconstruction, specifically:

[0020] After arranging the similarities of all similar matrix blocks of each reference matrix block, several similar matrix blocks and reference matrix blocks with the highest similarity are selected and rearranged and reconstructed to obtain a low-rank reconstruction matrix corresponding to each reference matrix block; after traversing, arranging and reconstructing all reference matrix blocks, a low-rank reconstruction matrix corresponding to all reference matrix blocks is obtained;

[0021] The method selects several similar matrix blocks and reference matrix blocks with the highest similarity to rearrange and reconstruct, and obtains a low-rank reconstruction matrix corresponding to each reference matrix block, specifically:

[0022] For each reference matrix block, select the N similar matrix blocks with the highest similarity to it, rearrange all elements of the current reference matrix block into a row vector by row, and rearrange all elements of the N similar matrix blocks into corresponding N row vectors by row respectively, and then rearrange the row vectors corresponding to the current reference matrix block and the N similar matrix blocks into N+1 row vectors, so as to combine them into a new matrix and record them as the low-rank reconstruction matrix of the current reference matrix block.

[0023] In the above 4), after performing secondary low-rank pre-complement processing on the low-rank reconstruction matrix corresponding to each reference matrix block, the reconstruction matrix corresponding to each reference matrix block is obtained, which is specifically:

[0024] For the low-rank reconstruction matrix corresponding to each reference matrix block, all low-rank pre-completion elements are removed and only the original elements in the ocean acoustic field profile observation matrix are retained to obtain a low-rank reconstruction matrix that only retains the original observation elements; then the graph-guided Bayesian low-rank matrix completion method is used to perform low-rank pre-completion processing on the low-rank reconstruction matrix that only retains the original observation elements to obtain the corresponding reconstruction matrix; the low-rank reconstruction matrices of each reference matrix block are traversed to obtain the reconstruction matrices corresponding to each reference matrix block, and then the restored results of each matrix block in each reconstruction matrix are returned to the corresponding positions in the ocean acoustic field profile matrix to be completed.

[0025] In the above 4), the calculation process of the final sound field reconstruction matrix includes:

[0026] The average value of the repeated prediction results at each position in the ocean sound field profile matrix to be completed is calculated to obtain the final reconstruction prediction value of the position. After traversing and processing all the repeated prediction results in the ocean sound field profile matrix to be completed, the final sound field reconstruction matrix is ​​obtained.

[0027] In the above 3), the calculation formula of the similarity between each reference matrix block and a corresponding similar matrix block is as follows:

[0028] Dist(P A ,P B )=||(P A-P B )*ω(P A )*ω(P B )|| F

[0029] Among them, Dist(P A ,P B ) represents the reference matrix block P A and similarity matrix block P B The similarity between them, ω(·) represents the weight of each element in the matrix block, * represents the Hadamard product, |||| F represents the Frobenius norm.

[0030] 2. A computer device

[0031] The computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing are implemented.

[0032] 3. A computer-readable storage medium

[0033] The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing are implemented.

[0034] IV. A COMPUTER PROGRAM PRODUCT

[0035] The computer program product comprises a computer program / instruction, which, when executed by a processor, implements the steps of the graph-guided Bayesian ocean acoustic field reconstruction method based on pre-completion processing.

[0036] The beneficial effects of the present invention are:

[0037] 1. In view of the problem that the traditional graph-guided Bayesian matrix completion method is mainly applied to low-rank matrices and cannot be directly applied to the reconstruction of high-rank sound field data matrices, the present invention enhances the applicability of the method by introducing a low-rank preprocessing step, thereby significantly improving the reconstruction accuracy.

[0038] 2. Due to the large noise interference in the marine environment, the sound field measurement data is often affected by noise. The present invention can effectively suppress noise interference, enhance the anti-noise performance of the reconstruction method, and ensure the stability and reliability of the reconstruction results through the Bayesian method and low-rank preprocessing.

[0039] 3. When the observed data is sparse and unevenly distributed, the present invention can still maintain high reconstruction performance. The combination of the low-rank preprocessing step and the graph-guided Bayesian completion method enables the method to fully utilize the global and local information of the sound field data in an environment with severe data loss, still achieve high-quality sound field reconstruction, and improve the accuracy of the reconstruction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of the graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing proposed by the present invention.

[0041] Figure 2 It is a sound field map of the real complete data matrix within the selected area.

[0042] Figure 3 It is a sound field diagram of only partial observation data with 30% data sampling of the real complete sound field.

[0043] Figure 4 It is a predicted map after reconstructing the sound field using a graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing.

[0044] Figure 5 It is a schematic diagram of searching for a similar matrix based on a reference matrix.

[0045] Figure 6 It is a schematic diagram of a method for reconstructing a reference matrix and a similarity matrix into a new matrix.

[0046] Figure 7 is the root mean square error between the reconstruction result of the method and the real sound field under four different sound source frequency conditions.

[0047] Figure 8 It is the structural similarity between the reconstruction results of the method and the real sound field under four different sound source frequency conditions. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solution and advantages of the implementation of the present invention clearer, the technical solution in the embodiment of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiment of the present invention.

[0049] The present invention proposes a graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing. The present invention first uses the graph-guided Bayesian ocean sound field completion method to complete the observed data, then finds the similar matrices corresponding to each reference matrix, reconstructs it into a new matrix, and then uses the graph-guided Bayesian ocean sound field reconstruction method again to complete and reconstruct the reconstructed matrix, and after returning to the original position, the average value is obtained to obtain the final ocean reconstruction sound field.

[0050] like Figure 1As shown, the method proposed by the present invention comprises the following steps:

[0051] 1) Obtain the ocean acoustic field profile observation matrix. Some data in the ocean acoustic field profile are missing;

[0052] 1) Specifically:

[0053] First, the area where the ocean sound field is to be reconstructed is selected, and relevant parameter information such as its sound velocity profile and seabed sediment is obtained. The location, depth and frequency information of the transmitting sound source are specified, and then the parabolic equation model is used to construct a complete and real ocean sound field in the area, and the following is obtained: Figure 2 The complete two-dimensional ocean sound propagation loss data matrix X of the specified area is shown in . Then, according to the specified sampling probability p, the sound field calculated by the parabolic equation model is randomly sampled. After sampling, only part of the data values ​​of the sound field matrix known is the original sound field that needs to be reconstructed and predicted, that is, the ocean sound field observation profile matrix, as shown in Figure 3 shown.

[0054] 2) Using the graph-guided Bayesian low-rank matrix completion method to perform low-rank pre-completion processing on the ocean acoustic field profile observation matrix, a complete two-dimensional pre-completion acoustic field matrix is ​​obtained;

[0055] 2) Specifically:

[0056] Firstly, the sound field reconstruction target optimization function is constructed. Then, based on the spatial correlation characteristics and observation data of the ocean sound field profile observation matrix, the Bayesian method is used to solve the sound field reconstruction target optimization function to obtain a complete two-dimensional pre-complemented full sound field matrix, that is, the optimal ocean sound field profile matrix to be completed X is used as the pre-complemented full sound field matrix.

[0057] The formula of the sound field reconstruction objective optimization function is as follows:

[0058]

[0059] Among them, λ, γ r and γ c is the first to third hyperparameter, X is the ocean acoustic profile matrix to be completed with dimension I*J, Y is the ocean acoustic profile observation matrix with dimension I*J, Ω is a mask matrix with dimension I*J composed of 0 and 1, and the element in the mask matrix Ω is 0, which means that the point corresponding to the element in the ocean acoustic profile observation matrix Y is not observed, and the element in the mask matrix Ω is 1, which means that the point corresponding to the element in the ocean acoustic profile observation matrix Y has been observed; * represents the Hadamard product; tr(X T L r X) is the regularization term of the row-by-row graph, tr(X T L c X) is the regularization term of the column-by-column graph; L ris the row-wise graph Laplacian matrix, L c is the column-wise graph Laplacian matrix, T represents the transpose, |||| * represents the nuclear norm, |||| F stands for the Frobenius norm and tr() stands for the trace of the matrix.

[0060] The row-by-row graph is constructed based on the assumption of spatial correlation between rows of the ocean acoustic profile matrix X to be completed and the prior knowledge of observed data. Define an adjacency matrix A (dimension is I×I, I is the number of matrix rows). If the i-th row and the j-th row have spatial correlation, then A ij =1, otherwise A ij = 0. Through this adjacency matrix, a row-by-row graph Laplacian matrix L is constructed. r , satisfying L r =DA, where D is the degree matrix, defined as D ii =Σ k A ik , where A ik represents the spatial correlation between the i-th row and all possible related rows (i.e., the k-th row), and is used to traverse which rows the i-th row is related to. The regularization term of the row-by-row graph is expressed as tr(X T L r X). Similarly, we can get the column-by-column Laplace matrix L corresponding to the matrix X to be completed for the ocean acoustic field profile: c and the column-by-column regularization term tr(X T L c X).

[0061] When solving the objective optimization function of sound field reconstruction, the Bayesian method is used to perform probability modeling, updating, and inference on the parameters, and the alternating direction multiplier method (ADMM) is used to optimize and solve the objective function, specifically:

[0062] The ocean acoustic field profile matrix X to be completed is represented by two factor matrices U and V:

[0063] X=UV T

[0064] Among them, U and V are factor matrices of dimensions I×K and J×K respectively, and K is a potential low-rank dimension. The prior distribution of the two factor matrices U and V is modeled as a multivariate Gaussian distribution, as follows:

[0065]

[0066] Λ=diag(θ)

[0067] Among them, p(U|θ) is the multivariate Gaussian distribution of the factor matrix U, p(V|θ) is the multivariate Gaussian distribution of the factor matrix V, the diagonal matrix Λ represents the column precision matrix, and the prior distribution of the precision parameter vector θ is set to the gamma distribution:

[0068]

[0069] Among them, p(θ) represents the prior distribution of the precision parameter vector, θ k represents the precision parameter of the i-th column of the factor matrix (U or V). c0 and d0 are the fourth and fifth hyperparameters respectively.

[0070] Then, the optimization problem is solved using the alternating direction method of multipliers (ADMM).

[0071] 3) Generate several reference matrix blocks according to the pre-complemented full sound field matrix, and then traverse the pre-complemented full sound field matrix to find similar matrix blocks of each reference matrix block according to the size of each reference matrix block. Different similar matrix blocks may overlap. Reconstruct each reference matrix block and the corresponding similar matrix block to obtain the low-rank reconstruction matrix corresponding to all reference matrix blocks;

[0072] 3) Specifically:

[0073] Step 1: Divide the pre-complemented full sound field matrix into multiple reference matrix blocks of the same size. Different reference matrix blocks may overlap, and the union of all reference matrix blocks covers all element positions of the pre-complemented full sound field matrix. Figure 5 As shown, the specific reference matrix selection scheme is: matrix is the pre-complementary full sound field matrix of the I×J dimensional measurement matrix Y, the reference matrix block P i,j It is a full matrix of pre-filled sound field The size of the matrix block is s×s, and the element position of the upper left corner of the reference matrix block is defined as (i, j). Then each element (i, j) in the following set corresponds to a reference matrix block:

[0074] (i,j)∈{1,...,I-s+1}×{1,...,J-s+1}

[0075] Then, the subsequent second and third steps are performed one by one on all the selected reference matrix blocks.

[0076] Step 2: Pre-fill the full matrix of the sound field Search all the s×s matrix blocks in the current reference matrix block one by one For the top N similarity matrix blocks with the highest similarity, when measuring the similarity distance l2, the weight of the original elements in the original observation matrix is ​​assigned as ω A, the weight assigned to the elements that are not in the original measurement matrix but are reconstructed in the full matrix of the pre-complemented sound field is ω B , the reference matrix block and similar matrix block for comparison are P A and P B , then the calculation formula of weighted distance l2 is as follows:

[0077] Dist(P A ,P B )=||(P A -P B )*ω(P A )*ω(P B )|| F

[0078] Among them, Dist(P A ,P B ) represents the reference matrix block P A and similarity matrix block P B The similarity between them, ω(·) represents the weight of each element in the matrix block, * represents the Hadamard product, ‖‖ F Represents the Frobenius norm.

[0079] Step 3: After arranging the similarities of all similar matrix blocks of each reference matrix block, select several similar matrix blocks and reference matrix blocks with the highest similarity and rearrange and reconstruct them to obtain the low-rank reconstruction matrix corresponding to each reference matrix block; after traversing, arranging and reconstructing all reference matrix blocks, obtain the low-rank reconstruction matrix corresponding to all reference matrix blocks;

[0080] Among them, several similar matrix blocks and reference matrix blocks with the highest similarity are selected for rearrangement and reconstruction to obtain the low-rank reconstruction matrix corresponding to each reference matrix block, specifically:

[0081] For each reference matrix block, select the N similar matrix blocks with the highest similarity, rearrange all elements of the current reference matrix block into a row vector by row, and rearrange all elements of the N similar matrix blocks into corresponding N row vectors by row, and then rearrange the row vectors corresponding to the current reference matrix block and the N similar matrix blocks into N+1 row vectors, so as to combine them into a new matrix and record it as the low-rank reconstruction matrix of the current reference matrix block, such as Figure 6 shown.

[0082] After traversing and processing each reference matrix block, a low-rank reconstruction matrix corresponding to each reference matrix block is obtained.

[0083] 4) After performing secondary low-rank pre-completion processing on the low-rank reconstruction matrix corresponding to each reference matrix block, the reconstruction matrix corresponding to each reference matrix block is obtained, and the prediction results of each matrix block in all reconstruction matrices are returned to the corresponding position in the matrix to be completed of the ocean sound field profile, so as to obtain the final sound field reconstruction matrix, such as Figure 4 The other parameters of the fixed scene remain unchanged, and the sound source frequencies are set to 50Hz, 100Hz, 200Hz, and 400Hz respectively. The method obtains the following under different sound source frequency conditions: Figure 4 The final sound field reconstruction matrix shown is similar to Figure 2 The root mean square error RMSE and structural similarity SSIM between the real sound field matrices shown are as follows: Figure 7 and Figure 8 shown.

[0084] Among them, after performing secondary low-rank pre-completion processing on the low-rank reconstruction matrix corresponding to each reference matrix block, the reconstruction matrix corresponding to each reference matrix block is obtained, which is specifically:

[0085] For the low-rank reconstruction matrix corresponding to each reference matrix block, all low-rank pre-completion elements therein, i.e., the elements calculated in 2), are removed, and only the original elements in the ocean sound field profile observation matrix are retained to obtain a low-rank reconstruction matrix that only retains the original observation elements; then, the graph-guided Bayesian low-rank matrix completion method is used to perform low-rank pre-completion processing on the low-rank reconstruction matrix that only retains the original observation elements, and the corresponding reconstruction matrix is ​​obtained, that is, the low-rank reconstruction matrix that only retains the original observation elements is used to replace the ocean sound field profile observation matrix Y of the sound field reconstruction objective optimization function in 2), and the row-by-row graph Laplacian matrix L is updated. r , column-by-column graph Laplacian matrix L c , the optimal ocean acoustic field profile to be completed matrix X obtained by solving the problem is used as the reconstruction matrix corresponding to the low-rank reconstruction matrix that only retains the original observation elements; the low-rank reconstruction matrix of each reference matrix block is traversed to obtain the reconstruction matrix corresponding to each reference matrix block, and then the recovery results of each matrix block in each reconstruction matrix are returned to the corresponding position in the ocean acoustic field profile to be completed matrix.

[0086] The calculation process of the final sound field reconstruction matrix includes:

[0087] The average value of the repeated prediction results at each position in the ocean sound field profile matrix to be completed is calculated to obtain the final reconstruction prediction value of the position. After traversing and processing all the repeated prediction results in the ocean sound field profile matrix to be completed, the final sound field reconstruction matrix is ​​obtained.

[0088] Finally, it should be noted that the above embodiments and explanations are only used to illustrate the technical solution of the present invention rather than to limit it. Those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope disclosed in the technical solution of the present invention, which should be included in the scope of protection of the claims of the present invention.

Claims

1. A graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing, characterized in that: The steps include: 1) Obtain ocean acoustic field profile observation matrix; 2) Using the graph-guided Bayesian low-rank matrix completion method to perform low-rank pre-completion processing on the ocean acoustic field profile observation matrix, a pre-completion acoustic field matrix is ​​obtained; 3) Generate several reference matrix blocks according to the pre-complemented full sound field matrix, then traverse and search for similar matrix blocks of each reference matrix block in the pre-complemented full sound field matrix according to the size of each reference matrix block, and reconstruct each reference matrix block and the corresponding similar matrix block to obtain the low-rank reconstruction matrix corresponding to all reference matrix blocks; 4) After performing secondary low-rank pre-completion processing on the low-rank reconstruction matrix corresponding to each reference matrix block, the reconstruction matrix corresponding to each reference matrix block is obtained, and the prediction results of each matrix block in all reconstruction matrices are returned to the corresponding position in the matrix to be completed of the ocean sound field profile, so as to obtain the final sound field reconstruction matrix.

2. The method for reconstructing ocean sound fields based on graph-guided Bayesian pre-completion processing according to claim 1, characterized in that: The 2) is specifically: Firstly, the sound field reconstruction target optimization function is constructed. Then, based on the ocean sound field profile observation matrix, the Bayesian method is used to solve the sound field reconstruction target optimization function to obtain the pre-complemented full sound field matrix.

3. The method for reconstructing ocean sound fields based on graph-guided Bayesian pre-completion processing according to claim 1, characterized in that: In the above 2), the formula of the sound field reconstruction objective optimization function is as follows: Among them, λ, γ r and γ c are the first to third hyperparameters, X is the ocean acoustic profile matrix to be completed with dimension I*J, Y is the ocean acoustic profile observation matrix with dimension I*J, Ω is a mask matrix with dimension I*J composed of 0 and 1, and the element in the mask matrix Ω is 0, which means that the point corresponding to the element in the ocean acoustic profile observation matrix Y is not observed, and the element in the mask matrix Ω is 1, which means that the point corresponding to the element in the ocean acoustic profile observation matrix Y has been observed; * represents the Hadamard product; L r is the row-wise graph Laplacian matrix, L c is the column-wise graph Laplacian matrix, T denotes transpose, || || * represents the nuclear norm, || || F stands for the Frobenius norm and tr() stands for the trace of the matrix.

4. The method for reconstructing ocean sound fields based on graph-guided Bayesian pre-completion processing according to claim 1, characterized in that: In the above 3), several reference matrix blocks are generated according to the pre-complemented full sound field matrix, specifically: The pre-complemented full sound field matrix is ​​divided into a plurality of reference matrix blocks of the same size, and the union of all the reference matrix blocks covers the pre-complemented full sound field matrix.

5. The method for reconstructing ocean sound fields based on graph-guided Bayesian pre-completion processing according to claim 1, characterized in that: In the above 3), the low-rank reconstruction matrix corresponding to all reference matrix blocks is obtained according to each reference matrix block and the corresponding similar matrix block reconstruction, specifically: After arranging the similarities of all similar matrix blocks of each reference matrix block, several similar matrix blocks and reference matrix blocks with the highest similarity are selected and rearranged and reconstructed to obtain the low-rank reconstruction matrix corresponding to each reference matrix block; after traversing, arranging and reconstructing all reference matrix blocks, the low-rank reconstruction matrix corresponding to all reference matrix blocks is obtained.

6. The method for reconstructing ocean sound fields based on graph-guided Bayesian pre-completion processing according to claim 5, characterized in that: The method selects several similar matrix blocks and reference matrix blocks with the highest similarity to rearrange and reconstruct, and obtains a low-rank reconstruction matrix corresponding to each reference matrix block, specifically: For each reference matrix block, select the N similar matrix blocks with the highest similarity to it, rearrange all elements of the current reference matrix block into a row vector by row, and rearrange all elements of the N similar matrix blocks into corresponding N row vectors by row respectively, and then rearrange the row vectors corresponding to the current reference matrix block and the N similar matrix blocks into N+1 row vectors, so as to combine them into a new matrix and record them as the low-rank reconstruction matrix of the current reference matrix block.

7. The method for reconstructing ocean sound fields based on graph-guided Bayesian pre-completion processing according to claim 1, characterized in that: In the above 4), after performing secondary low-rank pre-complement processing on the low-rank reconstruction matrix corresponding to each reference matrix block, the reconstruction matrix corresponding to each reference matrix block is obtained, which is specifically: For the low-rank reconstruction matrix corresponding to each reference matrix block, all low-rank pre-completion elements are removed and only the original elements in the ocean sound field profile observation matrix are retained to obtain a low-rank reconstruction matrix that only retains the original observation elements; then the graph-guided Bayesian low-rank matrix completion method is used to perform low-rank pre-completion processing on the low-rank reconstruction matrix that only retains the original observation elements to obtain the corresponding reconstruction matrix; the low-rank reconstruction matrices of each reference matrix block are traversed to obtain the reconstruction matrices corresponding to each reference matrix block, and then the restored results of each matrix block in each reconstruction matrix are returned to the corresponding positions in the ocean sound field profile matrix to be completed.

8. The method for reconstructing ocean sound fields based on graph-guided Bayesian pre-completion processing according to claim 1, characterized in that: In the above 4), the calculation process of the final sound field reconstruction matrix includes: The average value of the repeated prediction results at each position in the ocean sound field profile matrix to be completed is calculated to obtain the final reconstruction prediction value of the position. After traversing and processing all the repeated prediction results in the ocean sound field profile matrix to be completed, the final sound field reconstruction matrix is ​​obtained.

9. The method for reconstructing ocean sound fields based on graph-guided Bayesian pre-completion processing according to claim 5, characterized in that: In the above 3), the calculation formula of the similarity between each reference matrix block and a corresponding similar matrix block is as follows: Dist(P A ,P B )=||(P A -P B )*ω(P A )*ω(P B )|| F Among them, Dist(P A ,P B ) represents the reference matrix block P A and similarity matrix block P B The similarity between them, ω(·) represents the weight of each element in the matrix block, * represents the Hadamard product, || || F represents the Frobenius norm.

10. A storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the graph-guided Bayesian ocean sound field reconstruction method based on pre-completion processing described in any one of claims 1 to 9 is implemented.

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