An adaptive reconstruction method for band-limited graph signals with unknown signal support

Abstract

The present invention discloses an adaptive reconstruction method for a band-limited graph signal with unknown signal support. The method comprises: constructing a corresponding observation graph signal model based on an observation signal affected by impulse noise; establishing an optimization problem model based on the observation graph signal model using the l2 norm and the l0 norm to describe the recovery problem; solving the optimization problem model using an alternating optimization method to obtain a reconstructed signal; and performing an inverse graph Fourier transform on the reconstructed signal to obtain a reconstructed graph signal. The present invention reconstructs observation signals affected by impulse noise by exploiting the sparsity of the graph signal in its frequency domain. This method can effectively process graph signals affected by impulse noise, and even when the signal support is unknown, the reconstructed signal still has very high accuracy.

Description

Technical Field

[0001] The invention relates to an adaptive reconstruction method for a band-limited graph signal with unknown signal support, and belongs to the technical field of signal processing. Background Art

[0002] Classical signal processing is typically used to process signals with regular structures. However, in many practical applications, signals often have complex and irregular structures. Graphs can accurately describe these complex structures. In this context, graph signal processing (GSP) has emerged to effectively process these complex signals.

[0003] Graph signal reconstruction is a crucial technology in the field of GPS. It is based on graph signal sampling. In recent years, the integration of traditional adaptive signal processing with GPS has given rise to the new field of adaptive graph signal processing. However, existing adaptive graph signal processing frameworks are all based on the assumption of Gaussian noise. Therefore, their performance degrades dramatically when encountering impulse noise. In fact, impulse noise is a common occurrence in real-world scenarios, such as underwater communications and power line communications. Summary of the Invention

[0004] Objective: In view of at least one of the above technical problems, the present invention provides an adaptive reconstruction method for a band-limited graph signal with unknown signal support, which reconstructs the observation signal affected by impulse noise by utilizing the sparsity of the graph signal in its frequency domain.

[0005] The technical solution adopted in the present invention is:

[0006] In a first aspect, the present invention provides a method for adaptively reconstructing a band-limited graph signal with unknown signal support, comprising:

[0007] According to the observation signal affected by the impulse noise, a corresponding observation graph signal model is constructed;

[0008] Based on the observation graph signal model, the l2 norm and l0 norm are used to describe the restoration problem and establish an optimization problem model;

[0009] Solving the optimization problem model using an alternating optimization method to obtain a reconstructed signal;

[0010] Perform graph inverse Fourier transform on the reconstructed signal to obtain the reconstructed graph signal.

[0011] In some embodiments, constructing a corresponding observation graph signal model based on an observation signal affected by impulse noise includes:

[0012] The observation signal affected by impulse noise is modeled as a graph signal, and the signal is processed using graph Fourier transform. A sampling strategy based on a greedy algorithm is added to obtain the sampled observation graph signal model, which specifically includes:

[0013] The observed signal affected by impulse noise is expressed as: 0 +v[n],x 0 is the original image signal, n is the time index, and v[n] is the impulse noise;

[0014] The observation signals are mapped to the vertices of the graph, and the relationship between the observation signals is represented by the topological structure of the graph, and the topological structure of the graph is represented by the adjacency matrix; G = (v, ε, A) represents a graph, where v = {v1, v2, ..., v N} represents the vertex set of the graph, ε=(v m ,v n ) is an edge set and v m ,v n ∈v, A is the adjacency matrix of the graph, element a ij ,i,j=1,...,N represents the vertex v of the graph i With another vertex v j relationship;

[0015] The graph signal is a function f: Map the information of each vertex in the vertex set v to a real vector of length N; Laplace matrix L = KA = UΛU T , where K is the degree matrix of the graph signal, U is the eigenvector matrix, and Λ is the eigenvalue matrix, which is a diagonal matrix;

[0016] Define the Fourier transform of the graph as s=U T x, the support of the Fourier transform signal s is F = {i∈{1,...,N}:s i ≠0}, the cardinality |F| of the set F is the bandwidth of the graph signal;

[0017] The observation graph signal model y[n] is:

[0018]

[0019] Where n is the time index, S is the sample set, v[n] is the impulse noise, is a dense component, assuming it conforms to the Gaussian distribution, is the sparse component, D S =diag{1 S}, D S is the vertex restriction operator, which is a sparse matrix.

[0020] In some embodiments, the optimization problem model includes:

[0021]

[0022] Where y[n] is the observation graph signal model, D is the discrete set selected by the constrained sampling strategy, ||·||2 represents the l2 norm, ||·||0 represents the l0 norm, α>0 is the parameter that adjusts the sparsity of the graph Fourier transform signal s, and β>0 is the parameter that adjusts the sparsity of the noise sparse component z; D S is the vertex restriction operator, U is the eigenvector matrix;

[0023] The first term of the optimization problem represents the computational error, the second term ensures the sparsity of the noise sparse component, and the third term ensures the sparsity of the reconstructed signal in the frequency domain.

[0024] In some embodiments, an alternating optimization method is used to solve the optimization problem model to obtain a reconstructed signal;

[0025] Iteratively executing the loop steps until an optimal solution is approached to obtain a reconstructed signal, wherein the loop steps include:

[0026] In a given D S In the case of and s, the non-negative Garotte estimator is used to update the noise sparse component z;

[0027] According to the given D S and the updated noise sparse component z, and use the soft threshold iterative algorithm to update the graph Fourier transform signal s; and calculate the support F of the updated graph Fourier transform signal s;

[0028] According to the obtained noise sparse component z and the support F of the Fourier transform signal s, the vertex restriction operator D is used based on the sampling strategy of the greedy algorithm. S Make an estimate and get the approximate optimal sampling set S.

[0029] Furthermore, in some embodiments, the non-negative Garotte estimator is used to update the noise sparse component z, including:

[0030] In a given D S and s, the optimization problem model is transformed into the optimization problem P1:

[0031]

[0032] Define the fitting error w[n]=y[n]-D S Us, for the optimization problem P1, restrict the operator D at a fixed vertex S The noise sparse component z is updated while Fourier transforming the signal s of the graph of x, so that the outliers are separated from the fitting error;

[0033] For the optimization problem P1, the non-negative Garotte estimator is used to solve it;

[0034]

[0035] The parameter α that adjusts the sparsity of the Fourier transform signal s is determined by the median absolute deviation method. 2 =η·Med(|w[n]|-Med(|w[n]|)), where Med(·) is the sample median operator and η is a parameter used to control the range of the credible interval.

[0036] Furthermore, in some embodiments, the image Fourier transform signal s is updated using a soft threshold iteration algorithm, including:

[0037] According to the given D S And the updated noise sparse component z, the optimization problem model is transformed into the optimization problem P21:

[0038] Using the convex relaxation method, the l1 norm is used instead of the l0 norm to transform the optimization problem P21 into the optimization problem P22:

[0039] The optimization problem P22 is solved using the soft threshold iterative algorithm to update the Fourier transform signal s;

[0040] s[n+1]=T βμ (s[n]+μU T D S [n](y[n]-D S [n]Us-z[n]))

[0041] Among them, μ>0 is the update step size, T λ The functional form of (·) is as follows:

[0042]

[0043] Intermediate parameter k = s[n] + μU T D S [n](y[n]-D S [n]Us-z[n]), intermediate parameter λ=βμ;

[0044] Let h[n]=s[n]+μU T D S [n](y[n]-D S [n]Us-z[n]),

[0045] Then we can conclude

[0046] In some embodiments, the sampling strategy based on the greedy algorithm includes:

[0047] The number of preset sampling points M, the initial sampling set When |S|<M, execute where |·| + Is to find the smallest non-zero eigenvalue of the matrix; U F It is a matrix composed of columns of U indexed by the support F of the graph Fourier transform signal; j is the subscript of the vertex that meets the sampling strategy, j∈v\S.

[0048] In some embodiments, performing an inverse graph Fourier transform on the reconstructed signal to obtain a reconstructed graph signal includes:

[0049] x opt =Us opt

[0050] Among them, x opt is the reconstructed image signal, s opt is the reconstructed signal, and U is the eigenvector matrix.

[0051] In a second aspect, the present invention provides an adaptive reconstruction system for a band-limited graph signal with unknown signal support, comprising a processor and a storage medium;

[0052] The storage medium is used to store instructions;

[0053] The processor is configured to operate according to the instructions to perform the method according to the first aspect.

[0054] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the method described in the first aspect when executed by a processor.

[0055] In a fourth aspect, the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method described in the first aspect when executing the computer program.

[0056] In a fourth aspect, the present invention provides a computer program product, comprising a computer program, which implements the steps of the method described in the first aspect when executed by a processor.

[0057] Beneficial Effects: The adaptive reconstruction method for band-limited graph signals with unknown signal support provided by the present invention has the following advantages: The present invention reconstructs observed signals affected by impulse noise by leveraging the sparsity of the graph signal in its frequency domain. This method can effectively process graph signals affected by impulse noise, demonstrating its applicability in the presence of impulse noise. Furthermore, even when the signal support is unknown, the reconstructed signal still has very high accuracy. The present method is robust and has a wider range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 2 is a flow chart of a method for adaptively reconstructing a band-limited graph signal with unknown signal support according to an embodiment of the present invention;

[0059] Figure 2 Schematic diagram of an original image signal in an observation signal according to an embodiment of the present invention;

[0060] Figure 3 Schematic diagram of a reconstructed image signal obtained according to a method of an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The present invention will be further described below in conjunction with the accompanying drawings and examples. The following examples are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0062] In the description of the present invention, "several" means more than one, "plurality" means more than two, "greater than," "less than," and "exceed" are understood to exclude the number itself, while "above," "below," and "within" are understood to include the number itself. The use of "first" and "second" in the description is solely for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance, implicitly specifying the number of the indicated technical features, or implicitly specifying the order of the indicated technical features.

[0063] In the description of the present invention, reference to terms such as "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples" means that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the exemplary expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0064] Example 1

[0065] like Figure 1 As shown, this embodiment provides an adaptive reconstruction method for a band-limited graph signal with unknown signal support, including:

[0066] S1. Constructing a corresponding observation graph signal model based on the observation signal affected by impulse noise;

[0067] In this embodiment, this step may include: modeling the observation signal affected by impulse noise as a graph signal, processing the signal using a graph Fourier transform, adding a sampling strategy based on a greedy algorithm, and obtaining a sampled observation graph signal model, specifically including:

[0068] Assume that the observed signal affected by impulse noise is expressed as: 0 +v[n],x 0 is the original image signal, n is the time index, and v[n] is the impulse noise. It should be noted that the observed signal is represented as a complex signal with an irregular structure contaminated by impulse noise.

[0069] The observation signals are mapped to the vertices of the graph, and the relationship between the observation signals is represented by the topological structure of the graph, and the topological structure of the graph is represented by the adjacency matrix; G = (v, ε, A) represents a graph, where v = {v1, v2, ..., v N} represents the vertex set of the graph, ε=(v m ,v n ) is an edge set and v m ,v n ∈v, A is the adjacency matrix of the graph, element a ij ,i,j=1,...,N represents the vertex v of the graph i With another vertex v j relationship;

[0070] The graph signal is a function f: Map the information of each vertex in the vertex set v to a real vector of length N; Laplace matrix L = KA = UΛU T , where K is the degree matrix of the graph signal, U is the eigenvector matrix, and Λ is the eigenvalue matrix, which is a diagonal matrix;

[0071] Define the Fourier transform of the graph as s=U T x, the support of the Fourier transform signal s is F = {i∈{1,...,N}:s i ≠0}, the cardinality |F| of the set F is the bandwidth of the graph signal;

[0072] The observation graph signal model y[n] is:

[0073]

[0074] Where n is the time index, S is the sample set, v[n] is the impulse noise, is a dense component, assuming it conforms to the Gaussian distribution, is the sparse component, D S =diag{1 S}, D S is the vertex restriction operator, which is a sparse matrix. Due to the sparsity of the vertex restriction operator, The sparsity of is higher than z[n].

[0075] S2. Based on the observation graph signal model, using the l2 norm and l0 norm to describe the restoration problem, and establishing an optimization problem model;

[0076] It should be noted that, considering that in real applications, the support of a bounded graph signal is not always known a priori, since the graph signal may change in different aspects over time.

[0077] In this embodiment, assuming that the support of the graph signal is unknown, the optimization problem model includes:

[0078]

[0079] Where y[n] is the observation graph signal model, D is the discrete set selected by the constrained sampling strategy, ||·||2 represents the l2 norm, ||·||0 represents the l0 norm, α>0 is the parameter that adjusts the sparsity of the graph Fourier transform signal s, and β>0 is the parameter that adjusts the sparsity of the noise sparse component z; D S is the vertex restriction operator, U is the eigenvector matrix;

[0080] The first term of the optimization problem model represents the computational error, the second term ensures the sparsity of the noise sparse component, and the third term ensures the sparsity of the reconstructed signal in the frequency domain.

[0081] S3, solving the optimization problem model using an alternating optimization method to obtain a reconstructed signal;

[0082] In this step, considering the non-convex nature of the above optimization problem model, the alternating optimization method is used to optimize z, s, and D respectively. S Please help.

[0083] In this embodiment, this step may include:

[0084] Iteratively executing the loop steps until an optimal solution is approached to obtain a reconstructed signal, wherein the loop steps include:

[0085] S31, given D S In the case of and s, the non-negative Garotte estimator is used to update the noise sparse component z;

[0086] In some embodiments, S31 may include:

[0087] In a given DS and s, the optimization problem model is transformed into the optimization problem P1:

[0088]

[0089] Define the fitting error w[n]=y[n]-D S Us, for the optimization problem P1, restrict the operator D at a fixed vertex S The noise sparse component z is updated while Fourier transforming the signal s of the graph of x, so that the outliers are separated from the fitting error;

[0090] For the optimization problem P1, the non-negative Garotte estimator is used to solve it;

[0091]

[0092] The parameter α that adjusts the sparsity of the Fourier transform signal s is determined by the median absolute deviation method. 2 =η·Med(|w[n]|-Med(|w[n]|)), where Med(·) is the sample median operator and η is a parameter used to control the range of the credible interval. In some embodiments, it is generally 2<η<5.

[0093] S32, according to the given D S and the updated noise sparse component z, and use the soft threshold iterative algorithm (ISTA algorithm) to update the graph Fourier transform signal s; and calculate the support F of the updated graph Fourier transform signal s;

[0094] In some embodiments, S32 may include:

[0095] According to the given D S And the updated noise sparse component z, the optimization problem model is transformed into the optimization problem P21:

[0096] Using the convex relaxation method, the l1 norm is used instead of the l0 norm to transform the optimization problem P21 into the optimization problem P22:

[0097] The optimization problem P22 is solved using the soft threshold iterative algorithm to update the Fourier transform signal s;

[0098] s[n+1]=T βμ (s[n]+μU T D S [n](y[n]-D S [n]Us-z[n]))

[0099] Among them, μ>0 is the update step size, T λ The functional form of (·) is as follows:

[0100]

[0101] Intermediate parameter k = s[n] + μU T D S [n](y[n]-D S [n]Us-z[n]), intermediate parameter λ=βμ;

[0102] Let h[n]=s[n]+μU T D S [n](y[n]-D S [n]Us-z[n]),

[0103] Then we can conclude

[0104] S33, according to the noise sparse component z obtained by solving, the support F of the Fourier transform signal s of the graph, based on the sampling strategy of the greedy algorithm, the vertex restriction operator D S Make an estimate and get the approximate optimal sampling set S.

[0105] In this embodiment, the sampling strategy based on the greedy algorithm includes:

[0106] The number of preset sampling points M, the initial sampling set When |S|<M, execute S←S∪{s}; where |·| + Is to find the smallest non-zero eigenvalue of the matrix; U F It is a matrix composed of columns of U indexed by the support F of the Fourier transform signal of the graph; j is the subscript of the vertex that meets the sampling strategy, j∈v\S;

[0107] Therefore, the greedy algorithm is expressed as maximizing for all j∈v\S The smallest non-zero eigenvalue of .

[0108] The final updated Fourier transform signal s is used as the reconstructed signal s opt .

[0109] S4. Perform inverse Fourier transform on the reconstructed signal to obtain a reconstructed graph signal.

[0110] According to the definition of graph Fourier transform, in this embodiment, the inverse graph Fourier transform is performed on the reconstructed signal, including:

[0111] x opt =Us opt

[0112] Among them, x opt is the reconstructed image signal, s opt is the reconstructed signal, and U is the eigenvector matrix.

[0113] Simulation Example: This simulation simulates a sensor network subject to impulse noise. The sensor network is modeled as a graph, and the signals on the sensors are graph signals. The bandwidth of the signal is 10, the number of vertices N = 50, and the number of sample sets selected M = 10. βμ = 0.05, η = 3, and the number of iterations is set to 150.

[0114] Figure 2 Schematic diagram of the original image signal in the observation signal of this embodiment; Figure 3 Schematic diagram of the reconstructed image signal obtained by the adaptive reconstruction method of this embodiment. Figure 2 and Figure 3 The results show that the method of the present invention can effectively process the image signal affected by impulse noise, proving the applicability of the method in the case of impulse noise, and when the signal support is unknown, the reconstructed signal still has very high accuracy.

[0115] Example 2

[0116] Based on Example 1, this embodiment provides an adaptive reconstruction system for a band-limited graph signal with unknown signal support, including a processor and a storage medium;

[0117] The storage medium is used to store instructions;

[0118] The processor is configured to operate according to the instructions to execute the steps of the method according to embodiment 1.

[0119] Example 3

[0120] Based on Example 1, this embodiment provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method described in Example 1 are implemented.

[0121] Example 4

[0122] Based on Example 1, this embodiment provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method described in Example 1 when executing the computer program.

[0123] Example 5

[0124] Based on Example 1, this embodiment provides a computer program product, including a computer program. When the computer program is executed by a processor, the steps of the method described in Example 1 are implemented.

[0125] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0126] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0127] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0128] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0129] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. An adaptive reconstruction method for a band-limited graph signal with unknown signal support, characterized in that: include: According to the observation signal affected by impulse noise, the corresponding observation graph signal model is constructed, including: modeling the observation signal affected by impulse noise as a graph signal, processing the signal with graph Fourier transform, adding a sampling strategy based on the greedy algorithm, and obtaining the observation graph signal model after sampling, specifically including: the observation signal affected by impulse noise is expressed as: x 0 +v[n],x 0 is the original graph signal, n is the time index, and v[n] is the impulse noise; the observation signal is mapped to the vertices of the graph, and the relationship between the observation signals is represented by the topological structure of the graph, and the topological structure of the graph is represented by the adjacency matrix; G = (v, ε, A) represents a graph, where v = {v1, v2, ..., v N } represents the vertex set of the graph, ε=(v m ,v n ) is an edge set and v m ,v n ∈v, A is the adjacency matrix of the graph, element a ij ,i,j=1,...,N represents the vertex v of the graph i With another vertex v j The relationship between the graph signal is a function Map the information of each vertex in the vertex set v to a real vector of length N; Laplace matrix L = KA = UΛU T , where K is the degree matrix of the graph signal, U is the eigenvector matrix, Λ is the eigenvalue matrix, which is a diagonal matrix; the Fourier transform of the graph is defined as s=U T x, the support of the Fourier transform signal s is F = {i∈{1,...,N}:s i ≠0}, the cardinality |F| of the set F is the bandwidth of the graph signal; the observed graph signal model y[n] is: Where n is the time index, S is the sample set, v[n] is the impulse noise, is a dense component, assuming it conforms to the Gaussian distribution, is the sparse component, D S =diag{1 S }, D S is the vertex restriction operator, which is a sparse matrix; Based on the observation graph signal model, the l2 norm and l0 norm are used to describe the restoration problem and an optimization problem model is established; the optimization problem model includes: Where y[n] is the observation graph signal model, D is the discrete set selected by the constrained sampling strategy, ||·||2 represents the l2 norm, ||·||0 represents the l0 norm, α>0 is the parameter that adjusts the sparsity of the graph Fourier transform signal s, and β>0 is the parameter that adjusts the sparsity of the noise sparse component z; D S is the vertex restriction operator, U is the eigenvector matrix; the first term of the optimization problem represents the calculation error, the second term ensures the sparsity of the noise sparse component, and the third term ensures the sparsity of the reconstructed signal in the frequency domain; The optimization problem model is solved by an alternating optimization method to obtain a reconstructed signal, including: iteratively executing a loop step until the optimal solution is approached to obtain a reconstructed signal; wherein the loop step includes: S and s, the non-negative Garotte estimator is used to update the noise sparse component z; according to the given D S And the updated noise sparse component z, use the soft threshold iterative algorithm to update the graph Fourier transform signal s; and calculate the support F of the updated graph Fourier transform signal s; according to the solved noise sparse component z and the support F of the graph Fourier transform signal s, based on the sampling strategy of the greedy algorithm, the vertex restriction operator D is S Make an estimate and obtain the approximate optimal sampling set S; Perform graph inverse Fourier transform on the reconstructed signal to obtain the reconstructed graph signal.

2. The method according to claim 1, characterized in that The non-negative Garotte estimator is used to update the noise sparse component z, including: In a given D S and s, the optimization problem model is transformed into the optimization problem P1: Define the fitting error w[n]=y[n]-D S Us, for the optimization problem P1, restrict the operator D at a fixed vertex S The noise sparse component z is updated while Fourier transforming the signal s of the graph of x, so that the outliers are separated from the fitting error; For the optimization problem P1, the non-negative Garotte estimator is used to solve it; The parameter α that adjusts the sparsity of the Fourier transform signal s is determined by the median absolute deviation method. 2 =η·Med(|w[n]|-Med(|w[n]|)), where Med(·) is the sample median operator and η is a parameter used to control the range of the credible interval.

3. The method according to claim 1, characterized in that The soft threshold iterative algorithm is used to update the Fourier transform signal s, including: According to the given D S And the updated noise sparse component z, the optimization problem model is transformed into the optimization problem P21: Using the convex relaxation method, the l1 norm is used instead of the l0 norm to transform the optimization problem P21 into the optimization problem P22: The optimization problem P22 is solved using the soft threshold iterative algorithm to update the Fourier transform signal s; s[n+1]=T βμ (s[n]+μU T D S [n](y[n]-D S [n]Us-z[n])) Among them, μ>0 is the update step size, T λ The functional form of (·) is as follows: Intermediate parameter k = s[n] + μU T D S [n](y[n]-D S [n]Us-z[n]), intermediate parameter λ=βμ; Let h[n] = s[n] + μU T D S [n](y[n] - D S [n]Us - z[n]), Then we can conclude 4. The method according to claim 1, wherein Sampling strategies based on greedy algorithms include: The number of preset sampling points M, the initial sampling set When |S|<M, execute S←S∪{s}; where |·| + Is to find the smallest non-zero eigenvalue of the matrix; U F It is a matrix composed of columns of U indexed by the support F of the graph Fourier transform signal; j is the subscript of the vertex that meets the sampling strategy, j∈v\S.

5. The method according to claim 1, characterized in that Perform inverse Fourier transform on the reconstructed signal to obtain the reconstructed graph signal, including: x opt =Us opt Among them, x opt is the reconstructed image signal, s opt is the reconstructed signal, and U is the eigenvector matrix.

6. An adaptive reconstruction system for a band-limited graph signal with unknown signal support, characterized in that: including processors and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 5.

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

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