Ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion

Abstract

The embodiment of the invention provides an ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix complementation. The algorithm comprises the following steps: extracting a sound field data observation matrix of a selected sound field reconstruction area; constructing a row diagram and column diagram model according to the sound field data observation matrix; adding regular terms of the line-by-line graph and the column-by-column graph into an optimization objective function; solving by using a Bayesian method based on improvement; and observing whether the number of iterations reaches a preset number, and if the number of iterations reaches the preset maximum number of iterations, taking the result of the last iteration as the final reconstruction result of the sound field of the selected region as the output result of the algorithm. And utilizing an inherent low-rank structure of the two-dimensional ocean sound propagation loss field to predict a low-rank matrix, namely the two-dimensional ocean sound propagation loss field, based on the improved information by utilizing a Bayesian method such as guidance, and finally obtaining a complete two-dimensional ocean sound propagation loss field in the selected region. The hidden structure of the acoustic propagation loss observation data matrix can be found, global and local information can be utilized more fully, the anti-noise performance is good, and the calculation efficiency is improved.

Description

Technical Field

[0001] The present application relates to the technical field of ocean sound field reconstruction, and in particular to an ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion. Background Art

[0002] The ocean is a vital barrier to national defense. Due to severe attenuation, the propagation distance of electromagnetic waves in water is very limited. Therefore, sound waves are the most commonly used information carrier in marine engineering. Underwater communications, underwater navigation, underwater target tracking, and underwater environmental monitoring are usually carried out using underwater vehicles equipped with sonar equipment. These marine tasks are inseparable from underwater perception based on sonar, and they need to rely on sound propagation loss to predict the sonar range in order to make correct decisions. Therefore, obtaining reliable sound propagation loss is of great significance to improving the reliability of sonar work.

[0003] In some practical scenarios, the sound field can be measured by using buoys, towed arrays, etc. However, affected by factors such as the coverage range, resolution, position error, and noise interference of the measurement equipment, the measured data is often sparse and unevenly distributed, and there are also certain errors, which cannot accurately present the overall picture of the sound field. When the measured sound field has a certain information coverage range, the sound field can be reconstructed to provide more comprehensive and accurate sound field information, providing support for application scenarios such as sonar range prediction. At the same time, since the measurement process is easily affected by noise, the sound field reconstruction method needs to have a certain noise resistance.

[0004] The algorithm for sound field reconstruction using traditional methods in the field of image reconstruction, such as the nearest neighbor interpolation process, is relatively simple and cannot fully utilize information. The curve generated by polynomial interpolation is not smooth enough. Spline interpolation is only a local method and cannot fully utilize global information. In addition, the above interpolation has poor resistance to noise. The iterative back projection method, convex set projection method, maximum a posteriori probability method and other methods perform reverse reconstruction based on the image degradation process. Therefore, they have high requirements for prior information and are generally not practical. Summary of the invention

[0005] The purpose of the present invention is to provide an ocean sound propagation loss reconstruction algorithm based on an improved graph-guided Bayesian low-rank matrix completion in view of the deficiencies in the prior art.

[0006] The embodiment of the present invention provides an ocean sound propagation loss reconstruction algorithm based on an improved graph-guided Bayesian low-rank matrix completion, comprising:

[0007] Step 1, extracting the sound field data measurement matrix of the selected sound field reconstruction area;

[0008] Step 2, constructing a row graph and a column graph model according to the sound field data observation matrix;

[0009] Step 3, adding row-by-row graph and column-by-column graph regularization terms to the optimization objective function;

[0010] Step 4, solving using the improved Bayesian method;

[0011] Step 5, observe whether the number of iterations reaches a preset number. If it reaches a preset maximum number of iterations, the result of the last iteration is used as the final reconstruction result of the sound field in the selected area as the output result of the algorithm.

[0012] In some embodiments, the step 1 of extracting the sound field data measurement matrix of the selected sound field reconstruction area includes:

[0013] According to the selected area where the sound field needs to be reconstructed, the observation data matrix of sound propagation loss in the area is obtained through experiments.

[0014] In some embodiments, the step of reconstructing the sound field in the selected area according to the need and obtaining the acoustic propagation loss observation data matrix in the area through experiments includes:

[0015] Select the area where the ocean sound propagation loss field reconstruction is to be carried out, obtain relevant parameter information such as its sound velocity profile and seabed bottom quality, and specify the location, depth and frequency information of the transmitting sound source;

[0016] The parabolic equation model is used to construct the sound field and obtain the complete two-dimensional ocean sound propagation loss data matrix X in the specified area;

[0017] According to the specified sampling probability p, the sound field calculated by the parabolic equation model is randomly sampled, where the sampling matrix is ​​a matrix Ω with exactly the same size as the sound field data matrix of the selected area and only elements of 0 or 1, and the randomly sampled sound field, that is, the sound propagation loss observation data matrix Y, is obtained. This matrix is ​​used as the input of the subsequent process of the algorithm;

[0018] The acoustic propagation loss optimization problem is modeled as:

[0019]

[0020] Where X is the I*J dimension matrix to be completed, Y is the I*J dimension observation matrix, Ω is an I*J dimension matrix composed of 0 and 1, 0 represents that the point is not observed, 1 represents that the point is observed, and * represents the Hadamard product;

[0021] Replacing the rank function with the nuclear norm, the problem becomes:

[0022]

[0023] Among them, ||·|| *Represents the nuclear norm, considers noise modeling, relaxes the constraints to regularization terms, and the problem is redefined as:

[0024]

[0025] In some embodiments, the step 2, constructing a row graph and a column graph model according to the sound field data observation matrix, includes:

[0026] According to the characteristic of spatial correlation between rows and columns of the sound field matrix, a row correlation graph structure and a column correlation graph structure are constructed for the measurement matrix respectively to obtain a row correlation graph and a column correlation graph.

[0027] In some embodiments, based on the characteristic that there is spatial correlation between each row and column of the sound field matrix, respectively constructing a row correlation graph structure and a column correlation graph structure for the measurement matrix to obtain a row correlation graph and a column correlation graph includes:

[0028] The row-by-row correlation graph is modeled to obtain a row correlation graph. The sound field data matrix X is I*J dimensional, and each row of the matrix is ​​denoted as x i , in the graph structure {x 1 , x 2 , ..., x l} represents a node, ε={x i x k , i=1,...I,k=1,…,I,i≠k} represents an edge connecting two nodes. If x i x k ∈ε, then the adjacency matrix A i,k =1, otherwise 0;

[0029] Similarly, the column-by-column diagram is operated to obtain the column correlation diagram.

[0030] In some embodiments, the step 3, adding row-by-row graph and column-by-column graph regularization terms to the optimization objective function, includes:

[0031] The regularization term of the row-by-row graph is represented by the row-by-row graph Laplace matrix, the regularization term of the column-by-column graph is represented by the column-by-column graph Laplace matrix, and the row-column spatial correlation regularization term is added to the original optimization objective function to obtain a new optimization objective function.

[0032] In some embodiments, the regularization term of the row-by-row graph is represented by a row-by-row graph Laplace matrix, the regularization term of the column-by-column graph is represented by a column-by-column graph Laplace matrix, and the row-column spatial correlation regularization term is added to the original optimization objective function to obtain a new optimization objective function, including:

[0033] The adjacency matrix A is defined as an I*J dimensional matrix consisting of elements 0 and 1. If row i has spatial correlation, then Aij =1, otherwise A ij =0;

[0034] If rows i and j have spatial correlation, then x i ≈x j , introduce the row-by-row graph Laplacian matrix L r =DA, where D is called the degree matrix, D i，j =∑ k A i,k , this regularization term is expressed as:

[0035]

[0036] The column space correlation regularization term is:

[0037]

[0038] Add the row-column spatial correlation regularization term to the formula The new optimization problem is:

[0039]

[0040] In some embodiments, the step 4, solving the problem based on an improved Bayesian method, includes:

[0041] The input sound field data matrix is ​​decomposed into the product of two factor matrices. The sparse promoted Student's t distribution is obtained through the marginal distribution of the two factor matrices. According to the improved graph-guided Bayesian low-rank matrix completion algorithm, the hyperparameters are automatically learned from the data, and the factor matrix and hyperparameters of the input sound field matrix are continuously updated.

[0042] In some embodiments, the input sound field data matrix is ​​decomposed into the product of two factor matrices, a sparse promoted Student's t distribution is obtained through the marginal distribution of the two factor matrices, and hyperparameters are automatically learned from the data according to an improved graph-guided Bayesian low-rank matrix completion algorithm, and the factor matrix and hyperparameters of the input sound field matrix are continuously updated, including:

[0043] Decompose the matrix X into the factor matrix X = UV T , each factor matrix U and V is considered to be normally distributed, where the row precision matrix is ​​the graph Laplacian matrix and the column precision matrix is ​​the diagonal matrix Λ = diag(λ), so:

[0044]

[0045] Among them, the parameter λ=[λ 1 ,λ 2 , ..., λ K ]T The prior distribution is modeled by gamma distribution as:

[0046]

[0047] Among them, c 0 d 0 is a hyperparameter and uses the gamma distribution as the prior distribution for the columns in U and V.

[0048] In some embodiments, the input sound field data matrix is ​​decomposed into the product of two factor matrices, a sparse promoted Student's t distribution is obtained through the marginal distribution of the two factor matrices, and hyperparameters are automatically learned from the data according to an improved graph-guided Bayesian low-rank matrix completion algorithm, and the factor matrix and hyperparameters of the input sound field matrix are continuously updated, and further includes:

[0049] Low-rank modeling is achieved by enhancing the sparsity of columns in the factor matrices U and V in the form of posterior probabilities.

[0050] The above-mentioned embodiment of the present invention addresses the problem that the local interpolation method of the ocean sound propagation loss field cannot fully utilize the global information and has poor resistance to noise. The present invention chooses to use the inherent low-rank structure of the data to fill in the missing values, which helps to discover the hidden structure of the sound propagation loss observation data matrix, makes more full use of global and local information, and has good noise resistance.

[0051] The above embodiments of the present invention aim at the low global computational efficiency and high computational resource usage of ocean sound propagation loss reconstruction methods such as Kriging interpolation method or Gaussian process regression method. The ocean sound propagation loss reconstruction algorithm proposed in the present invention has much higher computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The drawings illustrate generally, by way of example and not limitation, various embodiments discussed herein.

[0053] Figure 1 It is a flow chart of the ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion proposed by the present invention;

[0054] Figure 2 It is the complete two-dimensional ocean sound propagation loss and sampled sound propagation loss map of the reconstructed area;

[0055] Figure 3 is a graph structure that models the row correlation of the two-dimensional ocean sound propagation loss field in the selected region;

[0056] Figure 4 is a graph structure that models the column correlation of the two-dimensional ocean sound propagation loss field in the selected region;

[0057] Figure 5 This is the reconstruction effect of the algorithm proposed in the present invention on the two-dimensional ocean sound propagation loss field. DETAILED DESCRIPTION

[0058] In order to enable a more detailed understanding of the features and technical contents of the embodiments of the present application, the implementation of the embodiments of the present application is described in detail below in conjunction with the accompanying drawings. The attached drawings are for reference only and are not used to limit the embodiments of the present application.

[0059] In the embodiments of the present application, it should be noted that, unless otherwise specified and limited, the term "connection" should be understood in a broad sense. For example, it can be an electrical connection or a connection between two components. It can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to the specific circumstances.

[0060] It should be noted that the terms "first\second\third" involved in the embodiments of the present application are only used to distinguish similar objects, and do not represent a specific order for the objects. It is understandable that the specific order or sequence of "first\second\third" can be interchanged where permitted. It should be understood that the objects distinguished by "first\second\third" can be interchanged where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein.

[0061] The embodiment of the present invention provides an improved graph-guided Bayesian low-rank matrix completion ocean sound propagation loss reconstruction algorithm, such as Figure 1 As shown, the following steps are included:

[0062] Step 1: Extract the sound field data observation matrix of the selected sound field reconstruction area: Perform sound field reconstruction on the selected area as required, and obtain the sound propagation loss observation data matrix in the area through experiments.

[0063] Step 2: Construct row and column graph models based on the sound field data observation matrix: Based on the characteristic that there is spatial correlation between rows and columns of the sound field matrix, the row correlation graph structure and column correlation graph structure are constructed for the observation matrix respectively to obtain the row correlation graph and column correlation graph.

[0064] Step 3: Add the row-by-row and column-by-column regularization terms to the optimization objective function: represent the regularization term of the row-by-row graph using the row-by-row graph Laplace matrix, represent the regularization term of the column-by-column graph using the column-by-column graph Laplace matrix, add the row-column spatial correlation regularization term to the original optimization objective function, and obtain a new optimization objective function.

[0065] Step 4: Solve based on the improved Bayesian method: decompose the input sound field data matrix into the product of two factor matrices. The sparse-promoted Student's t distribution can be obtained through the marginal distribution of the two factor matrices. According to the improved graph-guided Bayesian low-rank matrix completion algorithm, the hyperparameters are automatically learned from the data, and the factor matrix and hyperparameters of the input sound field matrix are continuously updated.

[0066] Step 5: Observe whether the number of iterations reaches the preset number. If it reaches the preset maximum number of iterations, the result of the last iteration is used as the final reconstruction result of the sound field in the selected area as the output result of the algorithm.

[0067] The specific steps are analyzed as follows:

[0068] Step 1: Calculate the sound propagation loss to reconstruct the sound propagation loss observation data matrix of the ocean area.

[0069] An ocean area that needs to be reconstructed for sound propagation loss is selected, and the sound propagation loss observation data matrix obtained is used as the input data matrix of the algorithm of the present invention. Only some elements in the matrix can be observed, and the remaining elements of the matrix are unknown, which are the target elements that the algorithm needs to reconstruct.

[0070] Step 2: Construct the graph structure of the sound propagation loss observation data matrix.

[0071] For the observation data matrix of sound propagation loss in the specified area of ​​the ocean sound field, the matrix is ​​constructed into a graph structure by row, and each row element is used as a node of the graph structure model. In the graph structure model, the edge between two nodes indicates that the corresponding two rows of matrix elements are correlated. A similar graph structure model is constructed for the matrix by column, and each column element is used as a node of the graph structure model. In the graph structure model, the edge between two nodes indicates that the corresponding two columns of matrix elements are correlated. And only undirected graphs are considered.

[0072] Step 3: Update the optimization objective function.

[0073] The row space correlation regularization term is expressed as a matrix:

[0074]

[0075] Among them, the matrix A represents the I*J-dimensional adjacency matrix composed of 0 and 1, x i and x k They represent the i-th row data and the k-th row data of the input ocean sound propagation loss observation data matrix, X represents the obtained sound propagation loss reconstruction data matrix, and L r represents the Laplacian matrix of the row-by-row graph, where L r =DA, where D is called the degree matrix, D i，j =∑ k Ai，k .

[0076] The column space correlation regularization term is expressed as a matrix:

[0077]

[0078] Among them, the matrix A represents the I*J-dimensional adjacency matrix composed of 0 and 1, x i and x k They represent the i-th column data and the k-th column data of the input ocean sound propagation loss observation data matrix, X represents the obtained sound propagation loss reconstruction data matrix, and L c Represents the Laplacian matrix of the column-wise graph.

[0079] The original optimization objective function is:

[0080]

[0081] Replacing the value function with the nuclear norm and relaxing the constraints to regularization terms, while adding row-column spatial correlation regularization terms, we get the new optimization problem:

[0082]

[0083] Among them, λ, γ r , γ c are all hyperparameters.

[0084] Step 4: The input sound propagation loss observation data matrix X is decomposed into the product of two factor matrices, which is regarded as the sum of the outer products of the columns in the factor matrices U and V:

[0085]

[0086] Among them, u k and v k are the kth column vectors of the factor matrices U and V, respectively, and X is the obtained ocean sound propagation loss reconstruction data matrix, which is regarded as the sum of the outer products of the columns in U and V. The sparse enhanced Student's distribution can be obtained by integrating the marginal distributions of U and V. Using the gamma distribution as the prior distribution of the columns in U and V, most columns will be guided to zero during the learning process. The sparsity of the columns in the factor matrices U and V can be improved by means of posterior probability distribution to achieve low-rank modeling.

[0087] The above-mentioned embodiment of the present invention addresses the problem that the local interpolation method of the ocean sound propagation loss field cannot fully utilize the global information and has poor resistance to noise. The present invention chooses to use the inherent low-rank structure of the data to fill in the missing values, which helps to discover the hidden structure of the sound propagation loss observation data matrix, makes more full use of global and local information, and has good noise resistance.

[0088] The above embodiments of the present invention aim at the low global computational efficiency and high computational resource usage of ocean sound propagation loss reconstruction methods such as Kriging interpolation method or Gaussian process regression method. The ocean sound propagation loss reconstruction algorithm proposed in the present invention has much higher computational efficiency.

[0089] The present invention discloses an ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion. It utilizes the inherent low-rank structure of the two-dimensional ocean sound propagation loss field and predicts the low-rank matrix, i.e., the two-dimensional ocean sound propagation loss field, based on improved information using a guided Bayesian method, and finally obtains a complete two-dimensional ocean sound propagation loss field in the selected area.

[0090] (1) Extracting the sound field data observation matrix of the selected sound field reconstruction area: The sound field reconstruction area is selected according to the needs, and the sound propagation loss observation data matrix in the area is obtained through experiments.

[0091] The specific process is as follows: first, select the area where the ocean sound propagation loss field is to be reconstructed, obtain its sound velocity profile, seabed bottom quality and other related parameter information, specify the location, depth and frequency information of the transmitting sound source, and then use the parabolic equation model to construct the sound field to obtain the following: Figure 2 The complete two-dimensional ocean sound propagation loss data matrix X of the specified area is shown in (a). Then, the sound field calculated by the parabolic equation model is randomly sampled according to the specified sampling probability p, where the sampling matrix is ​​a matrix Ω with exactly the same size as the sound field data matrix of the selected area and only elements are 0 or 1, and the result is as follows Figure 2 In (b), the randomly sampled sound field is the sound propagation loss observation data matrix Y, which is used as the input of the subsequent process of the algorithm. Therefore, the sound propagation loss optimization problem is modeled as:

[0092]

[0093] Among them, X is the I*J dimension matrix to be completed; Y is the I*J dimension observation matrix, Ω is a matrix of dimension I*J composed of 0 and 1, where 0 represents that the point is not observed and 1 represents that the point is observed; * represents the Hadamard product. The rank function is highly non-convex, and its minimization is an NP problem. In order to solve this problem, a convex function is used to relax the rank function constraint, among which the nuclear norm is the most commonly used replacement norm. Replace the rank function with the nuclear norm, and the problem becomes:

[0094]

[0095] Among them, ||·|| * represents the nuclear norm. Considering noise modeling, the above constraints are relaxed to regularization terms. At this time, the problem is redefined as:

[0096]

[0097] (2) Constructing row and column graph models based on the sound field data observation matrix: Based on the characteristic that there is spatial correlation between the rows and columns of the sound field matrix, the row correlation graph structure and the column correlation graph structure are constructed for the observation matrix respectively to obtain the row correlation graph and the column correlation graph.

[0098] The specific process is 2: The sound field is continuous in adjacent areas, so there is a spatial correlation between the rows and columns of the matrix, and this correlation can be represented by a graph structure. A graph is a data structure consisting of vertices and edges connecting the vertices. If there is at most one edge connecting a given pair of vertices and there is no loop (that is, no edge connecting the vertices themselves), the graph is called a simple graph; if each edge has a direction, the graph is directed. If the data values ​​at adjacent positions in the matrix are continuous, this correlation can be modeled. The row correlation graph structure is shown in 3. Considering that the sound field data matrix X is I*J dimensional, each row of the matrix is ​​recorded as x i , in the graph structure {x 1 , x 2 , ..., x l} represents a node, ε=(x i x k , i=1,...I,k=1,...,I,i≠k} represents an edge connecting two nodes. i x k ∈ε, then the adjacency matrix A i,k =1, otherwise 0.

[0099] Similarly, the same operation is performed on the column graph to obtain the column correlation graph structure as follows Figure 4 shown.

[0100] (3) Adding row-by-row and column-by-column regularization terms to the optimization objective function: The regularization term of the row-by-row graph is represented by the row-by-row graph Laplace matrix, and the regularization term of the column-by-column graph is represented by the column-by-column graph Laplace matrix. The row-column spatial correlation regularization term is added to the original optimization objective function to obtain a new optimization objective function.

[0101] The specific process is: define the adjacency matrix A as an I*J dimensional matrix consisting of elements 0 and 1. If row i has spatial correlation, then A ij =1, otherwise A ij = 0. If rows i and j have spatial correlation, then x i ≈x j , then the row-by-row graph regularization term Should be small. Introduce the row-by-row graph Laplacian matrix L r =DA, where D is called the degree matrix, D i，j =∑k A i，k , then this regularization term can be expressed in matrix form as:

[0102]

[0103] In the above regularization term, the row-by-row graph Laplacian matrix L r is the only term related to the row-by-row graph structure. By minimizing this graph regularization term, rows with spatial correlation will be guided to have similar values, in this way, the implicit spatial correlation between the rows of the matrix can be embedded in the row-by-row graph. Similarly, the spatial correlation between the columns of the matrix can be treated in the same way, and the column spatial correlation regularization term is obtained as:

[0104]

[0105] Add the row-column spatial correlation regularization term to the formula The new optimization problem is:

[0106]

[0107] (4) Based on the improved Bayesian method, the input sound field data matrix is ​​decomposed into the product of two factor matrices. The sparse promoted Student's t distribution can be obtained through the marginal distribution of the two factor matrices. According to the improved graph-guided Bayesian low-rank matrix completion algorithm, the hyperparameters are automatically learned from the data, and the factor matrix and hyperparameters of the input sound field matrix are continuously updated.

[0108] The specific process is: decompose the matrix X into factor matrix X = UV T , each factor matrix U and V is considered to be normally distributed, where the row precision matrix is ​​the graph Laplacian matrix and the column precision matrix is ​​the diagonal matrix Λ = diag(λ), so:

[0109]

[0110] Among them, the parameter λ=[λ 1 ,λ 2 , ..., λ K ] T The prior distribution is modeled by gamma distribution as:

[0111]

[0112] Among them, c 0 d 0is a hyperparameter. By integrating the marginal distributions of U and V, we can find that their marginal distributions are Student's t distributions with enhanced sparsity. That is, using the gamma distribution as the prior distribution of the columns in U and V, most columns are guided to all zeros during the learning process. Since X = UV T , the rank of X is less than the number of non-zero columns of U and V. Therefore, the sparsity of the columns in the factor matrices U and V can be enhanced by means of posterior probabilities to achieve low-rank modeling.

[0113] (5) Observe whether the number of iterations reaches the preset number. If it reaches the preset maximum number of iterations, the result of the last iteration is used as the final reconstruction result of the sound field in the selected area as the output result of the algorithm. The final result is as follows: Figure 5 shown.

[0114] The technical solutions described in the embodiments of the present application can be combined arbitrarily without conflict.

[0115] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. An ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion, characterized in that: include: Step 1, extracting the sound field data measurement matrix of the selected sound field reconstruction area; Step 2, constructing a row graph and a column graph model according to the sound field data observation matrix; Step 3, adding row-by-row graph and column-by-column graph regularization terms to the optimization objective function; Step 4, solving using the Bayesian method based on the improvement; Step 5, observe whether the number of iterations reaches a preset number. If it reaches a preset maximum number of iterations, the result of the last iteration is used as the final reconstruction result of the sound field in the selected area as the output result of the algorithm.

2. The ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion according to claim 1, characterized in that: The step 1, extracting the sound field data measurement matrix of the selected sound field reconstruction area, comprises: According to the selected area where the sound field needs to be reconstructed, the observation data matrix of sound propagation loss in the area is obtained through experiments.

3. The ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion according to claim 2, characterized in that: The acoustic field reconstruction area is selected according to the need, and the acoustic propagation loss observation data matrix in the area is obtained through experiments, including: Select the area where the ocean sound propagation loss field is to be reconstructed, obtain relevant parameter information such as its sound velocity profile and seabed bottom quality, and specify the location, depth and frequency information of the transmitting sound source; The parabolic equation model is used to construct the sound field and obtain the complete two-dimensional ocean sound propagation loss data matrix X in the specified area; According to the specified sampling probability p, the sound field calculated by the parabolic equation model is randomly sampled, where the sampling matrix is ​​a matrix Ω with exactly the same size as the sound field data matrix of the selected area and only elements of 0 or 1, and the randomly sampled sound field, that is, the sound propagation loss observation data matrix Y, is obtained. This matrix is ​​used as the input of the subsequent process of the algorithm; The acoustic propagation loss optimization problem is modeled as: Where X is the I*J dimension matrix to be completed, Y is the I*J dimension observation matrix, Ω is an I*J dimension matrix composed of 0 and 1, 0 represents that the point is not observed, 1 represents that the point is observed, and * represents the Hadamard product; Replacing the rank function with the nuclear norm, the problem becomes: in,‖·‖ * Represents the nuclear norm, considers noise modeling, relaxes the constraints to regularization terms, and the problem is redefined as:

4. The ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion according to claim 3, characterized in that: The step 2, constructing a row graph and a column graph model according to the sound field data observation matrix, comprises: According to the characteristic of spatial correlation between rows and columns of the sound field matrix, a row correlation graph structure and a column correlation graph structure are constructed for the measurement matrix respectively to obtain a row correlation graph and a column correlation graph.

5. The ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion according to claim 4, characterized in that: According to the characteristic that there is spatial correlation between each row and column of the sound field matrix, a row correlation graph structure and a column correlation graph structure are constructed for the measurement matrix respectively to obtain a row correlation graph and a column correlation graph, including: The row-by-row correlation graph is modeled to obtain a row correlation graph. The sound field data matrix X is I*J dimensional, and each row of the matrix is ​​denoted as x i , in the graph structure {x1,x2,…,x l } represents a node, ε={x i x k ,i=1,…I,k=1,…,I,i≠k} represents an edge connecting two nodes. If x i x k ∈ε, then the adjacency matrix A i,k =1, otherwise 0; Similarly, the column-by-column graph is operated to obtain the column correlation graph.

6. The ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion according to claim 5, characterized in that: The step 3, adding row-by-row graph and column-by-column graph regularization terms to the optimization objective function, includes: The regularization term of the row-by-row graph is represented by the row-by-row graph Laplace matrix, the regularization term of the column-by-column graph is represented by the column-by-column graph Laplace matrix, and the row-column spatial correlation regularization term is added to the original optimization objective function to obtain a new optimization objective function.

7. The ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion according to claim 6, characterized in that: The regularization term of the row-by-row graph is expressed by a row-by-row graph Laplace matrix, the regularization term of the column-by-column graph is expressed by a column-by-column graph Laplace matrix, and the row-column spatial correlation regularization term is added to the original optimization objective function to obtain a new optimization objective function, including: The adjacency matrix A is defined as an I*J dimensional matrix consisting of elements 0 and 1. If row i has spatial correlation, then A ij =1, otherwise A ij =0; If rows i and j have spatial correlation, then x i ≈x j , introduce the row-by-row graph Laplacian matrix L r =DA, where D is called the degree matrix, D i,j =∑ k A i,k , this regularization term is expressed as: The column space correlation regularization term is: Add the row-column spatial correlation regularization term to the formula The new optimization problem is:

8. The ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion according to claim 7, characterized in that: The step 4, based on the improved Bayesian method, includes: The input sound field data matrix is ​​decomposed into the product of two factor matrices. The sparse promoted Student's t distribution is obtained through the marginal distribution of the two factor matrices. According to the improved graph-guided Bayesian low-rank matrix completion algorithm, the hyperparameters are automatically learned from the data, and the factor matrix and hyperparameters of the input sound field matrix are continuously updated.

9. The ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion according to claim 8, characterized in that: The input sound field data matrix is ​​decomposed into the product of two factor matrices, and a sparse promoted Student's t distribution is obtained through the marginal distribution of the two factor matrices. According to the improved graph-guided Bayesian low-rank matrix completion algorithm, hyperparameters are automatically learned from the data, and the factor matrix and hyperparameters of the input sound field matrix are continuously updated, including: Decompose the matrix X into the factor matrix X = UV T , each factor matrix U and V is considered to be normally distributed, where the row precision matrix is ​​the graph Laplacian matrix and the column precision matrix is ​​the diagonal matrix Λ = diag(λ), so: Among them, parameter λ = [λ1, λ2,…,λ k ] T The prior distribution is modeled by gamma distribution as: Among them, c0 and d0 are hyperparameters, and gamma distribution is used as the prior distribution of columns in U and V.

10. The ocean sound propagation loss reconstruction algorithm based on improved graph-guided Bayesian low-rank matrix completion according to claim 9, characterized in that: The input sound field data matrix is ​​decomposed into the product of two factor matrices, and a sparse promoted Student's t distribution is obtained through the marginal distribution of the two factor matrices. The hyperparameters are automatically learned from the data according to the improved graph-guided Bayesian low-rank matrix completion algorithm, and the factor matrix and hyperparameters of the input sound field matrix are continuously updated. The method also includes: Low-rank modeling is achieved by enhancing the sparsity of columns in the factor matrices U and V in the form of posterior probabilities.

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