A Hyperspectral Band Selection Method Based on Spectral-Spatial Hypergraph Regularization and Sparse Self-Representation

Abstract

This invention relates to a hyperspectral band selection method based on spectral-spatial hypergraph regularized sparse self-representation. To address the insufficient utilization of band adjacency relationships in traditional sparse self-representation models, this method first integrates spectral similarity and spatial proximity to design a comprehensive index for evaluating band correlation. It explores and evaluates adjacency relationships between bands from multiple perspectives, constructing a hypergraph to generate a more complete inter-spectral local structure. Second, based on the aforementioned local band constraints, it supplements this with global band characteristics to jointly guide the optimization process of the sparse self-representation band selection model, obtaining the optimal low-dimensional representation of high-dimensional data and achieving band selection. This method overcomes the limitations of using a single similarity metric for decision-making and fully explores the multi-faceted adjacency relationships between bands, effectively reducing band redundancy, improving the quality of band subsets, and contributing to improved analytical accuracy in subsequent tasks.

Description

Technical Field

[0001] This invention belongs to the field of hyperspectral image dimensionality reduction technology, specifically involving a hyperspectral band selection method based on spectral-space hypergraph regularized sparse self-representation. Background Technology

[0002] Hyperspectral remote sensing images possess numerous spectral bands, dense spectral density, and rich feature information, enabling them to effectively distinguish various ground features and demonstrating great potential in hyperspectral image classification. However, the high dimensionality and band redundancy of hyperspectral data pose significant challenges to data transmission and interpretation. Their high dimensionality greatly reduces data transmission efficiency and increases computational load. More importantly, small sample sizes and high dimensionality make classification susceptible to the Hughes phenomenon, leading to decreased classification accuracy. Therefore, dimensionality reduction of hyperspectral images is necessary.

[0003] Hyperspectral dimensionality reduction techniques include feature extraction and band selection. Band selection can be interpreted as choosing a subset of bands from hyperspectral data that can effectively reduce data dimensionality while preserving key information about ground features. Compared with feature extraction, the reduced data still retains the true physical meaning of ground features, and therefore has been widely studied. In recent years, the development of sparse representation techniques has provided new ideas and methods for band selection. Band selection methods based on sparse representation assume that each band vector can be sparsely represented using only a small number of non-zero coefficients under an appropriate dictionary. For example, band selection can be defined as a sparse problem of each band vector and its corresponding dictionary. By solving an optimization model with constraints on sparsity and reconstruction accuracy, a low-dimensional representation of a high-dimensional image can be obtained. Although existing methods have achieved good dimensionality reduction results, they usually ignore the spatial information between bands and underutilize their local structure.

[0004] Graphs can effectively describe the statistical characteristics and geometric relationships between data samples. Furthermore, graph regularizers can adaptively adjust to changes in sparse representation. Therefore, sparse representation models embedded in graphs can reveal the underlying structural information of the original image, making band selection more robust. However, simple graphs can only measure binary relationships between adjacent bands. In reality, each band may be associated with multiple bands, requiring the exploration of multivariate adjacency relationships between bands. Therefore, simple graphs struggle to handle these complex band structural relationships, thus failing to obtain reasonable local constraint structures.

[0005] The information disclosed in this background section is only intended to enhance the understanding of the background technology of this application, and therefore may include prior art that is not known to those skilled in the art. Summary of the Invention

[0006] To address the aforementioned problems in the prior art, this invention proposes a hyperspectral band selection method based on spectral-space hypergraph regularized sparse self-representation, which solves the technical problem that traditional band selection methods based on sparse self-representation do not make sufficient use of local relationships between bands.

[0007] To achieve the above-mentioned objectives, the present invention employs the following technical solution:

[0008] Step S1: Select a hyperspectral image and convert it into a two-dimensional data matrix;

[0009] Step S2: Construct a hypergraph based on band spectral correlation and spatial proximity;

[0010] Step S3: Combining the hypergraph and sparse self-representation model, construct the spectral band selection model HyGSR with regularized sparse self-representation of the spectral-space hypergraph;

[0011] Step S4: The HyGSR model is optimized and solved using the alternating direction multiplier method to obtain the coefficient matrix, and the band weights are calculated accordingly to achieve band selection.

[0012] Furthermore, a hyperspectral image is selected and converted into a two-dimensional data matrix, denoted by X. L represents the band number. Let N represent the vector of the i-th band, where N is the number of pixels.

[0013] Furthermore, a hypergraph is constructed based on band spectral correlation and spatial proximity. Here, V and E represent the sets of vertices and hyperedges, respectively. Each band vector... A vertex in the perceived V. This represents a superedge containing vertex k. Based on this, calculate The corresponding weight is

[0014] (1);

[0015] in, For kernel function, For The spectral-empty integral function centered on the center, . For band Its adjacent band Spectral-space similarity between them Defined as:

[0016] (2);

[0017] here, and These are represented as spectral similarity and spatial similarity, respectively:

[0018] (3);

[0019] (4);

[0020] in, and For kernel function, It is the image of the i-th band. The index value. Specifically, if the band and band The more similar the spectra, the better. The larger the value, the higher the band. and band The closer the wavelengths are, the better. The larger the value, the better. It integrates spectral information from multiple adjacent bands within the same hyperedge and comprehensively considers the actual positional relationship between band wavelengths, thus improving the accuracy of similarity measurement.

[0021] Furthermore, construct the weight matrix W, the correlation matrix H, and the vertex degree matrix. and hypermarginality matrix They are respectively:

[0022] (5);

[0023] (6);

[0024] (7);

[0025] (8);

[0026] in, This represents a diagonal matrix. The diagonal elements of the vertex degree matrix are represented as... The diagonal elements in the hypermarginality matrix are defined as follows: Therefore, the normalized Laplace matrix is ​​calculated as follows:

[0027] (9);

[0028] Where I is the identity matrix. Compared with the classic hypergraph model, this hypergraph can effectively mine the spectral-spatial adjacency relationships between adjacent bands, providing more accurate guidance for subsequent band selection.

[0029] Furthermore, the spectral-space hypergraph regularized sparse self-representation model HyGSR is obtained in the following way:

[0030] Assumption This represents a hyperspectral image. This represents a band image containing N pixels. The sparse self-representation model fully utilizes the self-representational properties of data (i.e., each band can be represented by a linear weighted sum of all bands) to reconstruct the hyperspectral image. Its objective function is defined as:

[0031] (10);

[0032] in, Let X be the coefficient matrix. Considering the band redundancy in hyperspectral images, it is more reasonable to approximate the dataset X using as few bands as possible, i.e., dictionary columns. Therefore, we introduce... Norm to constrain coefficient matrix To achieve row sparsity, the model can be further optimized. Among these, For regularization parameters, . As the regression coefficient matrix, its row vector The contribution of each band to the reconstruction of the original image by the i-th band is explained.

[0033] However, (10) did not consider the spatial relationship between bands, so on the basis of the above, the model added hypergraph regularization to constrain the relationship. Combined with the hypergraph A hyperspectral band selection model based on sparse self-representation is constructed using spectral-space hypergraph regularized sparse self-representation. Specifically, the objective function is defined as:

[0034] (11);

[0035] in, and For balancing parameters, For Laplace matrix, This is a trace operation. To avoid finding trivial solutions, i.e. Add constraints in (11) and To facilitate the solution, auxiliary variables are introduced. and The objective function is transformed into:

[0036] (12);

[0037] Furthermore, the Lagrange function is obtained as follows:

[0038] (13);

[0039] in, and For balancing parameters, For penalty parameters, and For Lagrange operators.

[0040] Furthermore, the alternating direction multiplier method is used to solve the model:

[0041] (1) Fixed and , get about The subproblems are:

[0042] (14);

[0043] Introduce a diagonal matrix , , To avoid Factors with a denominator of zero. Therefore, (14) is rewritten as:

[0044] (15);

[0045] make If the derivative is zero, then in the iteration process, the solution for the (n+1)th iteration is... The solution can be obtained from the nth iteration. The calculation yields the following result:

[0046] (16);

[0047] (2) Fixed and Then regarding The function is:

[0048] (17);

[0049] get The update rules are as follows:

[0050] (18);

[0051] (3) Fixed variables and Then regarding The subproblems are:

[0052] (19);

[0053] Solve for:

[0054] (20);

[0055] here, .

[0056] Finally, iterate and update the other variables:

[0057] (twenty one) ;

[0058] (twenty two) ;

[0059] (twenty three) ;

[0060] Until the residual and residual Converging to a set threshold The algorithm ends.

[0061] Furthermore, the coefficient matrix The i-th row Indicates band Reconstruct the contribution of each band in the original data X. In other words, The larger the value, the greater the importance of the band. Therefore, according to... The bands are sorted in descending order of their values, and the top values ​​are selected. One band is used as the final band subset.

[0062] Compared with existing technologies, the advantages and positive effects of this invention are as follows: Based on a spectral-spatial hypergraph regularized sparse self-representation band selection method, this invention first jointly evaluates band correlation by combining spectral similarity and spatial proximity between hyperspectral image bands, and leverages the advantages of hypergraphs to mine multivariate adjacency relationships between bands, constructing a more complete local spatial structure. Secondly, the spectral local constraints obtained from the hypergraph are introduced into the sparse self-representation model, integrating the self-expressiveness and sparsity of hyperspectral data, and jointly optimizing model learning from both local and global perspectives, obtaining the optimal solution for the coefficient matrix through the alternating direction multiplier method. Finally, the contribution of each band to reconstructing the original data is calculated based on the coefficient matrix, thereby obtaining the optimal band subset. This method effectively mines complex adjacency relationships between bands, significantly reduces band redundancy, and provides strong technical support for subsequent rapid and refined classification.

[0063] This invention constructs a spectral-space hypergraph using band spectral correlation and spatial proximity. Compared to existing technologies that use a dual-stream automatic preservation mechanism to extract "one-to-one" adjacency relationships between bands, the proposed spectral-space hypergraph... Figure 1 On the one hand, the supergraph was used to explore the multi-dimensional adjacency relationship between bands, making the local structure of the bands more consistent with the actual situation of hyperspectral images. On the other hand, the band spectral correlation and spatial proximity were used to calculate the adjacency degree between bands, avoiding the one-sidedness caused by using only a single decision index to express the proximity degree.

[0064] This invention proposes a spectral-space hypergraph regularized sparse self-representation model. The model introduces spectral local constraints based on the hypergraph, which guides the sparse coefficient matrix to more reasonably reflect the complex adjacency relationships of each band in the alternating iterative optimization, avoids the simultaneous selection of highly correlated bands, and effectively reduces the redundancy of band subsets.

[0065] Other features and advantages of the present invention will become clearer after reading the detailed embodiments of the invention in conjunction with the accompanying drawings. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 A flowchart of the band selection method for spectral-space hypergraph regularization sparse self-expression;

[0068] Figure 2(a) shows a pseudo-color image of the Indian Pines hyperspectral dataset used in the embodiment;

[0069] Figure 2(b) shows the land cover category labels of the Indian Pines hyperspectral dataset used in the example;

[0070] Figure 3(a) is a comparison of the average accuracy of each band selection method in the embodiment on the Indian Pines dataset;

[0071] Figure 3(b) is a comparison of the overall accuracy of each band selection method in the embodiment on the Indian Pines dataset; Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0073] In the description of this invention, it should be noted that the terms "upper," "lower," "left," and "right," etc., indicate the orientation or positional relationship based on the positional relationship shown in the accompanying drawings, with the direction closer to the center of the cover being "inner," and the opposite being "outer." These terms are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation; therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance; features defined with "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0074] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0075] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0076] The following disclosure provides many different embodiments or examples for implementing various structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. These are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed. In addition, examples of various specific processes and materials are provided, but those skilled in the art will recognize the application of other processes and / or the use of other materials.

[0077] like Figure 1The flowchart shown is for the spectral-spatial hypergraph regularized sparse self-representation method. The specific steps include:

[0078] Step 101: Construct a hypergraph based on band spectral correlation and spatial proximity. Here, V and E represent the sets of vertices and hyperedges. Each band vector A vertex in the perceived V. Represented by vertex For a hyperedge containing vertex k at its center, Based on this, calculate The corresponding weights are:

[0079] (1);

[0080] in, For kernel function, For The spectral-empty integral function centered on the center, . For band Its adjacent band Spectral-space similarity between them Defined as:

[0081] (2);

[0082] here, and These are represented as spectral similarity and spatial similarity, respectively:

[0083] (3);

[0084] (4);

[0085] in, and For kernel function, It is the image of the i-th band. The index value. Specifically, if the band and band The more similar the spectra, the better. The larger the value, the higher the band. and band The closer the wavelengths are, the better. The larger the value, the better. It integrates spectral information from multiple adjacent bands within the same hyperedge and comprehensively considers the actual positional relationship between band wavelengths, thus improving the accuracy of similarity measurement.

[0086] Furthermore, a weight matrix for the hypergraph is generated based on the weights of the hyperedges, and the Laplacian matrix of the spectral-space-linked hypergraph is constructed. The weight matrix W, the incidence matrix H, and the vertex degree matrix are constructed. and hypermarginality matrix They are respectively:

[0087] (5);

[0088] (6);

[0089] (7);

[0090] (8);

[0091] in, This represents a diagonal matrix. The diagonal elements of the vertex degree matrix are represented as... The diagonal elements in the hypermarginality matrix are defined as follows: Therefore, the normalized Laplace matrix is ​​calculated as follows:

[0092] (9);

[0093] Where I is the identity matrix. Compared with the classic hypergraph model, this hypergraph can effectively mine the spectral-spatial adjacency relationships between adjacent bands, providing more accurate guidance for subsequent band selection.

[0094] Step 102: Based on the hypergraph and sparse self-representation model, construct the spectral-space hypergraph regularized sparse self-representation hyperspectral band selection model HyGSR. Self-representation refers to the fact that each band can be represented using a linear weighted average of the entire band. This model effectively utilizes the characteristics of self-representation to model the data itself. The spectral-space hypergraph regularized sparse self-representation model HyGSR is obtained as follows:

[0095] Assumption This represents a hyperspectral image. This represents a band image containing N pixels. The sparse self-representation model fully utilizes the self-representational properties of data (i.e., each band can be represented by a linear weighted sum of all bands) to reconstruct the hyperspectral image. Its objective function is defined as:

[0096] (10);

[0097] in, Let X be the coefficient matrix. Considering the band redundancy in hyperspectral images, it is more reasonable to approximate the dataset X using as few bands as possible, i.e., dictionary columns. Therefore, we introduce... Norm to constrain coefficient matrix To achieve row sparsity, the model can be further optimized. Among these, For regularization parameters, . As the regression coefficient matrix, its row vector The contribution of each band to the reconstruction of the original image by the i-th band is explained.

[0098] However, (10) did not consider the spatial relationship between bands, so on the basis of the above, the model added hypergraph regularization to constrain the relationship. Combined with the hypergraph A hyperspectral band selection model based on sparse self-representation is constructed using spectral-space hypergraph regularized sparse self-representation. Specifically, the objective function is defined as:

[0099] (11);

[0100] in, and For balancing parameters, For Laplace matrix, This is a trace operation. To avoid finding trivial solutions, i.e. Add constraints in (11) and To facilitate the solution, auxiliary variables are introduced. and The objective function is transformed into:

[0101] (12);

[0102] Furthermore, the Lagrange function is obtained as follows:

[0103] (13);

[0104] in, and For balancing parameters, For penalty parameters, and Let be the Lagrange operator. The above model is solved using the alternating direction multiplier method, yielding the following result. , and The corresponding update formula.

[0105] Step 103: Solve the model using the alternating direction multiplier method:

[0106] (1) Fixed and , get about The subproblems are:

[0107] (14);

[0108] Introduce a diagonal matrix , , To avoid Factors with a denominator of zero. Therefore, (14) is rewritten as:

[0109] (15);

[0110] make If the derivative is zero, then in the iteration process, the solution for the (n+1)th iteration is... The solution can be obtained from the nth iteration. The calculation yields the following result:

[0111] (16);

[0112] (2) Fixed and Then regarding The function is:

[0113] (17);

[0114] get The update rules are as follows:

[0115] (18);

[0116] (3) Fixed variables and Then regarding The subproblems are:

[0117] (19);

[0118] Solve for:

[0119] (20);

[0120] here, .

[0121] Finally, iterate and update the other variables:

[0122] (twenty one);

[0123] (twenty two);

[0124] (twenty three);

[0125] Until the residual and residual Converging to a set threshold The algorithm ends.

[0126] Step 104, Coefficient Matrix The i-th row Indicates band Reconstruct the contribution of each band in the original data X. In other words, The larger the value, the greater the importance of the band. Therefore, according to... The bands are sorted in descending order of their values, and the top values ​​are selected. One band is used as the final band subset.

[0127] The specific steps of the hyperspectral band selection method based on spectral-space hypergraph regularization sparse self-representation in this embodiment are as follows:

[0128] A. Sample data source: The hyperspectral data is from the Indian Pines Experimental Area in Indiana, USA. This data contains 220 bands and is [size missing]. It contains 16 target features, with a total of 10249 target pixels. Table 1 shows the number of samples for each target feature category. Its false-color composite image and feature category label are shown in Figure 2(a) and (b).

[0129] Table 1

[0130]

[0131] B. Experimental Setup: Six methods were selected to verify the effectiveness of the proposed HyGSR (ERS-BS) method: Uniform Band Selection (UBS), Maximum Variance Principal Component Analysis (MVPCA), Enhanced Fast Density Peak Clustering (E-FDPC), Optimal Clustering Framework (OCF), Sequential Band Selection (SQ), and Optimal Neighborhood Reconstruction (ONR). The number of bands selected in the experiment ranged from [missing information]. arrive Ten percent of the images were randomly selected as training samples, and a support vector machine was used to classify the images. The experiment was repeated a total of [number missing]. Finally, the classification results are quantified using the average accuracy (AA) and overall accuracy (OA) to evaluate the performance of each band selection method.

[0132] C. Parameter Analysis: HyGSR has three parameters. , , Adjustments are needed. The number of vertices contained in the superedge. The range of values ​​is Regularization parameters and All from The parameters were selected from the available parameters. For parameter determination, the experiment first obtained the optimal parameter set for different band numbers to optimize HyGSR performance; then, the cumulative score of multiple optimal parameter sets was calculated, and the parameter combination with the highest score was ultimately used for HyGSR. For the Indian Pines data, the final values ​​of the three parameters are shown in Table 2.

[0133] Table 2

[0134]

[0135] D. Experimental Results: Figures 3(a) and 3(b) show the AA and OA corresponding to the selected band subsets of each method under different numbers of bands, respectively. It can be observed that the performance of MVPCA, E-FDPC, SQ, and OCF is at the lower end. UBS is stable but not outstanding. ONR performs well with fewer bands, but its performance gradually decreases as the number of bands increases. When the number of bands is small, the curve corresponding to the proposed method HyGSR is ERS-BS, and the AA and OA obtained from this curve are in the middle. When the number of bands exceeds 30, ERS-BS begins to outperform other methods, showing outstanding performance. Furthermore, except for using a small number of bands, ERS-BS outperforms the classification effect using the entire band, indicating that ERS-BS can indeed select information bands that are helpful for hyperspectral image classification. In summary, the method proposed in this embodiment has stable performance in the band selection task, outperforming many competing techniques.

[0136] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions claimed by the present invention.

Claims

1. A method for hyperspectral band selection based on spectral-spatial hypergraph regularized sparse self-representation, characterized in that, The method includes: Step S1: Select a hyperspectral image and convert it into a two-dimensional data matrix; Step S2, constructing a hypergraph according to the waveband spectral correlation and spatial proximity ; wherein V and E represent the set of vertices and hyper-edges, each waveband vector is regarded as a vertex in V, represents a hyper-edge containing k vertices centered on vertex , ; accordingly, the calculation corresponding to the weight is: (1)； in, For kernel function, For The spectral-empty integral function centered on the center, , Representative band Its adjacent band Spectral-space similarity between them It is defined as: (2)； here, and These are represented as spectral similarity and spatial similarity, respectively: (3)； (4)； in, and For kernel function, It is the image of the i-th band. The index value; if the band and band The more similar the spectra, the better. The larger the value; the band and band The closer the wavelengths are, the better. The larger the value; Construct the weight matrix W, the incidence matrix H, and the vertex degree matrix. and hypermarginality matrix for: (5)； (6)； (7)； (8)； In the formula, Represents a diagonal matrix; each diagonal element in the vertex degree matrix is ​​represented as The diagonal elements in the hypermarginality matrix are defined as follows: Therefore, the normalized Laplace matrix is ​​calculated as follows: (9)； Where I is the identity matrix; Step S3, combined with the hypergraph obtained And a sparse self-representation model, constructing a spectral-space hypergraph regularized sparse self-representation hyperspectral band selection model HyGSR: defining the objective function as: (10)； in, and For balancing parameters, For Laplace matrix, This is a trace operation; to avoid finding trivial solutions, i.e. Constraints were added in (10). and ; Step S4: The HyGSR model is optimized and solved using the alternating direction multiplier method to obtain the coefficient matrix, and the band priority is calculated accordingly to achieve band selection.

2. The method according to claim 1, characterized in that, Step S4 introduces auxiliary variables. and The objective function is optimized and solved, and then transformed into: (11)； Furthermore, the Lagrange function is obtained as follows: (12)； in, and For balancing parameters, For penalty parameters, and The Lagrange operator is used; the alternating direction multiplier method is employed to solve the above model, yielding the variables. , and The corresponding update formula is: (13)； (14)； (15)； in, , To avoid factors with a denominator of zero; Represents the coefficient matrix The i-th row is used to reflect the i-th band. Reconstruct the contribution of each band in the original data X; The larger the value, the higher the importance of the band, according to... The bands are sorted in descending order of their values, and the top values ​​are selected. One band is used as the final band subset.

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