Hyperspectral band selection method based on weighted sparse self-representation of kl divergence
By fusing spectral and spatial information in hyperspectral data and using KL divergence to measure the differences between bands, a weighted sparse constraint model is constructed. This solves the problem of insufficient information utilization in sparse self-representation models and improves the representativeness of band selection and classification accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIJING INST OF TECH
- Filing Date
- 2023-02-22
- Publication Date
- 2026-07-21
AI Technical Summary
Existing sparse self-representation models fail to fully utilize spectral and spatial information in the selection of hyperspectral data bands, resulting in high similarity among the selected representative bands and affecting subsequent classification performance.
We employ a weighted sparse self-representation method based on KL divergence. By fusing spectral and spatial information, we use KL divergence to measure the differences between bands and construct a weighted sparse constraint model to select representative bands with large differences.
It improves the classification accuracy of hyperspectral data, reduces information redundancy, and the selected bands are more representative and suitable for subsequent image processing.
Smart Images
Figure CN117409311B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the fields of image processing, data representation, and band selection technology, specifically relating to a hyperspectral band selection method based on weighted sparse self-representation of KL divergence. Background Technology
[0002] Hyperspectral remote sensing technology can simultaneously acquire two-dimensional spatial information describing the distribution of ground features and one-dimensional spectral information describing their spectral characteristics. Compared with traditional panchromatic and multispectral remote sensing images, hyperspectral remote sensing images have high spectral resolution, with each pixel containing tens to hundreds of narrow spectral bands, generating a complete and continuous spectral curve and possessing extremely rich spectral information about ground features. However, its narrow spectral range, large number of bands, and strong correlation between bands also lead to a large data volume, high information redundancy, and susceptibility to problems such as the Hughes phenomenon, affecting subsequent classification performance. Therefore, dimensionality reduction processing of hyperspectral data is of great significance.
[0003] Dimensionality reduction methods for hyperspectral data can be divided into two types: feature extraction and feature selection (also known as band selection). Compared to feature extraction, band selection has the advantage of preserving the physical meaning of the original bands in the dimensionality-reduced image, and therefore it is widely used. Currently, existing band selection methods mainly include algorithms based on theories such as sorting, searching, clustering, and sparse representation, among which band selection algorithms based on sparse self-representation have become a research hotspot.
[0004] According to sparse self-representation theory, each band in a hyperspectral image can be represented as a linear combination of representative bands. This means that when each band is represented using all bands, the representation coefficients exhibit row sparsity. The objective function of the sparse self-representation model is defined as:
[0005] Among them, hyperspectral data matrix Let N be the number of pixels, B be the number of bands, W be the sparse representation coefficient matrix, L(X-XW) be the loss function, R(W) be the regularization term, and λ be the corresponding regularization parameter. The Frobenius norm is typically used to measure the reconstruction error, and the L(X-XW) of W is introduced. 2,1 Norm regularization term ||W|| 2,1 To ensure that the solved coefficient matrix W has row sparsity, that is, all bands are represented as linear combinations of a small number of representative bands as possible. Therefore, the objective function of the traditional sparse self-representation model is defined as: Building upon this, several other improved self-representation models have emerged. For example, the Regularized Self-Representation (RSR) model, taking into account the Frobenius norm's sensitivity to outliers, uses an L... 2,1Norms are used to represent reconstruction errors; Graph Self-Representation Sparse Feature Selection (GSR-SFS) adds graph regularization terms to the self-representation model to preserve the original distribution of the data; Self-representation Hypergraph Low-rank Feature Selection (SHLFS) integrates hypergraph regularization terms and low-rank constraints to enhance the robustness of the model. Although the above methods improve upon traditional models to varying degrees, they all only utilize the band features of hyperspectral data and ignore spatial information. Existing Marginalized Graph Self-Representation (MGSR) methods incorporate spatial information to improve band selection results, but do not constrain the similarity between bands. Without considering this information, the selected representative band subset may contain similar bands. Therefore, it is necessary to select dissimilar bands as much as possible during the band selection process to reduce information redundancy caused by similar bands and further improve the performance of band selection. Summary of the Invention
[0006] The purpose of this invention is to address the problem of insufficient information utilization in existing sparse self-representation models. It proposes a hyperspectral band selection method based on KL divergence for weighted sparse self-representation. This method fuses spectral and spatial information to measure the differences between hyperspectral pixels, uses KL divergence to measure the differences between bands, and applies KL divergence as a weight to impose weighted sparsity constraints on the sparse coefficient matrix. This maximizes the differences between the selected representative bands, providing more reliable data support for subsequent image processing such as classification.
[0007] To achieve the above objectives, the present invention adopts the following technical solution.
[0008] The hyperspectral band selection method includes:
[0009] Acquire a 3D hyperspectral image cube and convert it into a 2D spectral matrix;
[0010] Principal component analysis is performed on the three-dimensional hyperspectral image cube to obtain the first principal component. Superpixel segmentation is then applied to the first principal component to generate several partitions of the three-dimensional hyperspectral image cube.
[0011] Construct a neighborhood graph of the two-dimensional spectral matrix, calculate the similarity graph, and then normalize it to obtain a normalized similarity graph;
[0012] The difference in information content between paired bands is calculated based on KL divergence, and the dissimilarity matrix is calculated.
[0013] We construct a weighted sparse self-representation model that integrates spatial spectral information using a normalized similarity graph and a dissimilarity matrix, and then obtain the final value of the coefficient matrix by solving the weighted sparse self-representation model.
[0014] The construction of the weighted sparse self-representation model that integrates spatial spectrum information is specifically achieved by constructing an error term and a constraint term and adding them together;
[0015] The error term is specifically obtained by weighting the original pixels with a normalized similarity map, integrating the spatial and spectral information of the two-dimensional spectral matrix, multiplying it by a coefficient matrix on the right, and then linearly reconstructing the original pixels.
[0016] The constraint term is specifically obtained by constructing a weighted sparse regularization term based on KL divergence and a row sparse constraint term and adding them together;
[0017] The construction of the weighted sparse regularization term based on KL divergence is specifically achieved by multiplying and summing the corresponding elements of the dissimilarity matrix and the coefficient matrix, thereby enhancing the sparsity of the coefficients in the coefficient matrix.
[0018] The construction of row sparse constraint terms is specifically achieved by using L 2,1 The norm regularization term applies row sparsity constraints to the coefficient matrix, thereby reducing the similarity between the paired bands;
[0019] The magnitude of the L2 norm of the row vector of the final value of the coefficient matrix represents the importance of the corresponding band;
[0020] Find the L2 norm of the row vectors of the final value of the coefficient matrix and sort them in descending order. Select the first M bands in descending order as the final band subset.
[0021] Where M is the number of selected bands.
[0022] The calculation of the similarity map is specifically achieved by calculating the Gaussian kernel function of the two-dimensional spectral matrix;
[0023] The three-dimensional hyperspectral image cube has several partitions, the number of which is the same as the set number of superpixel segmentation regions.
[0024] The dissimilarity matrix is the sum of the KL divergences of paired bands of the two-dimensional spectral matrix, which are approximately distributed with respect to the observed distribution.
[0025] The process of constructing a neighborhood graph of the two-dimensional spectral matrix, calculating a similarity graph, and then normalizing it to obtain a normalized similarity graph is as follows:
[0026] S1. Calculate the similarity graph of the two-dimensional spectral matrix; the size of the elements in the similarity graph represents the similarity between corresponding pairs of pixels; if a pair of pixels belongs to the same partition, the corresponding element is 0; otherwise, calculate the Gaussian kernel function of the two-dimensional spectral matrix to obtain the corresponding element.
[0027] S2. Normalize the similar graph to obtain a normalized similar graph. This is achieved by left-multiplying the similar graph matrix with self-loops by the square root of the inverse of the degree matrix.
[0028] The similarity graph matrix with self-loops is the sum of the identity matrix and the similarity graph, and is used to add the node's own information to the similarity graph by adding self-loops.
[0029] The degree matrix is a diagonal matrix whose diagonal elements are the sum of the corresponding rows of the similarity graph matrix.
[0030] The dimension of the three-dimensional hyperspectral image cube is w×h×B, where B represents the number of bands in the image; N = w×h represents the number of pixels in the image; N×B is the dimension of the two-dimensional spectral matrix; w and h represent the dimensions of the image spatial dimension, with the width of the image spatial dimension being w pixels and the height of the image spatial dimension being h pixels.
[0031] The calculation of the difference in information content between paired bands based on KL divergence and the calculation of the dissimilarity matrix are specifically as follows:
[0032] The paired bands are denoted as: band y u and band y v The expressions are as follows:
[0033] y u =(x u1 ,...,x ul ,...x uN ) and y v =(x v1 ,...,x vl ,...x vN ), x ul and x vl These are the spectral values of the l-th pixel in the u-th and v-th band vectors, respectively, with l ranging from 1 to N; u and v ranging from 1 to B; the KL divergence is defined as follows:
[0034] Where k ranges from 1 to N, and P = (P(1),...,P(N)) and Q = (Q(1),...,Q(N)) are the bands y u and y v Normalized probability distribution; As can be seen from the previous equation, the KL divergence does not satisfy symmetry, so it is not suitable for direct measurement of the information content difference between bands. In order to improve the symmetry of the dissimilarity measurement between bands, the dissimilarity matrix of the two-dimensional spectral matrix is calculated after the original KL divergence is improved.
[0035] The calculation of the dissimilarity matrix of the two-dimensional spectral matrix is specifically achieved by adding the original KL divergence to the KL divergence calculated after swapping the paired bands.
[0036] The final value of the coefficient matrix is obtained by solving the weighted sparse self-representation model, specifically as follows:
[0037] By taking the derivative of the objective function and setting it equal to 0, we obtain the expression for the coefficient matrix.
[0038] Set the convergence threshold and the regularization parameter for the coefficient matrix expression;
[0039] Initialize the coefficient matrix and iteratively update the coefficient matrix according to the coefficient matrix expression until the value of the objective function is less than the convergence threshold.
[0040] Beneficial effects
[0041] This application proposes a hyperspectral band selection method based on weighted sparse self-representation using KL divergence, which has the following advantages compared with existing sparse self-representation models:
[0042] 1. The hyperspectral band selection method replaces the original pixels with a weighted combination of surrounding similar pixels, which integrates the spatial information of the original data and is beneficial for subsequent classification. It also uses KL divergence to measure the dissimilarity between bands and adopts a weighted sparse regularization term based on KL divergence to constrain the coefficient matrix, so as to avoid selecting similar bands and make the selected bands more representative.
[0043] 2. Experiments were conducted on two sets of real hyperspectral datasets. Compared with existing band selection algorithms, the experimental results show that the proposed hyperspectral band selection method can achieve higher classification accuracy for most of the selected bands, indicating that the selected representative bands are beneficial to subsequent classification. Attached Figure Description
[0044] Figure 1 This is a schematic diagram of the algorithm flow of the weighted sparse self-representation hyperspectral image band selection method based on KL divergence described in this invention.
[0045] Figure 2 This is a pseudo-color image of the Botswana dataset in this embodiment of the invention;
[0046] Figure 3 This is a pseudo-color image of the Indian Pines dataset in this embodiment of the invention;
[0047] Figure 4 These are the classification results of various algorithms after band selection, tested on the Botswana dataset;
[0048] Figure 5These are the classification results after band selection by various algorithms tested on the Indian Pines dataset. Detailed Implementation
[0049] The hyperspectral image band selection method based on weighted sparse self-representation of KL divergence described in this invention will be further described below with reference to the accompanying drawings and embodiments.
[0050] Example 1
[0051] This embodiment illustrates the specific implementation of the hyperspectral image band selection method based on KL divergence weighted sparse self-representation described in this invention. The method is illustrated using publicly available hyperspectral remote sensing datasets—Botswana and Indian Pines—as examples. It is understood that this method can also be applied to other hyperspectral images. Hyperspectral images are obtained using hyperspectral imaging technology, possessing high spectral resolution and multiple narrow bands. They can originate from fields such as food safety, medical diagnosis, and aerospace remote sensing, but are not limited to these. Furthermore, besides applying this method to SVM classification of hyperspectral images as listed in this embodiment, it can also be applied to other subsequent processing of hyperspectral images. For example, when applying it to hyperspectral image classification, the classifier can also be KNN, SRC, decision trees, and logistic regression, etc. It is understood that this method retains the main information of the hyperspectral image after band selection, reducing the subsequent data volume and computational burden. Therefore, it can also be applied to other applications besides classification, such as remote sensing data processing and interpretation, which this application does not limit. In this embodiment, the method is as follows... Figure 1 As shown, it includes the following steps:
[0052] Acquire a 3D hyperspectral image cube and convert it into a 2D spectral matrix;
[0053] The dimension of the three-dimensional hyperspectral image cube is w×h×B, where B represents the number of bands in the image; the two-dimensional spectral matrix is denoted as: X∈R N×B N = w × h represents the number of pixels in the image; N × B is the dimension of the two-dimensional spectral matrix and the two-dimensional spectral matrix contains B bands; w and h represent the dimensions of the image spatial dimension, and the width of the image spatial dimension is w pixels and the height of the image spatial dimension is h pixels.
[0054] Principal component analysis was performed on the cube of the three-dimensional hyperspectral image to obtain its first principal component;
[0055] The first principal component is denoted as: I f ∈R w×h ;
[0056] The principal component analysis, or PCA, is used to reduce the dimensionality of a 3D hyperspectral image cube, extracting the first principal component of the cube while removing noise to facilitate subsequent data processing and prevent noise bands from affecting band selection.
[0057] Set the number of superpixel segmentation regions and apply superpixel segmentation on the first principal component to generate several partitions of a three-dimensional hyperspectral image cube;
[0058] The number of superpixel segmentation regions is the same as the number of partitions, denoted as K, and the features of pixels within the same partition are similar, with no overlap between different partitions;
[0059] The number of superpixel segmentation regions is set in the first principal component I. f Superpixel segmentation is applied.
[0060] The superpixel segmentation, or Entropy Rate Superpixel Segmentation (ERS), is used to divide the three-dimensional hyperspectral image cube into regions. The segmented regions are homogeneous, which makes it easy to make full use of the spatial information of the three-dimensional hyperspectral image cube. Moreover, its computational complexity is very low, which effectively improves the band selection efficiency of this embodiment.
[0061] The process of generating several partitions of a three-dimensional hyperspectral image cube by applying superpixel segmentation on the first principal component is achieved by the following formula:
[0062] Among them, H k Represents the k-th partition;
[0063] Construct a neighborhood graph of the two-dimensional spectral matrix, calculate the similarity graph, and then normalize it to obtain a normalized similarity graph; specifically:
[0064] The neighborhood graph is denoted as G(V,E); the nodes V of the graph represent pixels, and the edges E of the graph represent pairs of pixels x. i ,x j Similarities between them;
[0065] S1: Calculate the similarity graph of the two-dimensional spectral matrix;
[0066] The similarity diagram is denoted as: A;
[0067] The similarity graph for calculating the two-dimensional spectral matrix is achieved using the following formula:
[0068]
[0069] Among them, Aij Let be the element in the i-th row and j-th column of similar graph A, representing the weight of the edge in the similar graph. exp() represents an exponential function with the natural constant as the base. If pixel x... i and x j If they belong to the same partition, use the Gaussian kernel function. The similarity between two points is represented by σ; otherwise, the similarity is 0, and σ is the standard deviation in the Gaussian function. It can be understood that pixels more similar on the first principal component have greater weights on edges in the similarity graph.
[0070] S2: Perform a normalization operation on the similarity graph to obtain a normalized similarity graph;
[0071] The normalized similarity graph is denoted as
[0072] The normalization operation on the similarity graph is performed to obtain a normalized similarity graph, which is achieved by the following formula:
[0073]
[0074] in, It is a similarity matrix with self-loops, I N It is an identity matrix with dimensions N×N; by adding self-loops, the self-information of the nodes is added to the similarity graph A; degree matrix It is a diagonal element A diagonal matrix.
[0075] The difference in information content between paired bands is calculated based on KL divergence, and the dissimilarity matrix is calculated.
[0076] The paired bands are denoted as: y s and y t These correspond to the s-th and t-th bands in the two-dimensional spectral matrix, respectively, and are denoted as y. s =(x s1 ,...,x sl ,...x sN ) and y t =(x t1 ,...,x tl ,...x tN And the values of s and t range from 1 to B; x sl and x tl These are the spectral values of the l-th pixel in the s-th and t-th band vectors, respectively; the value of l ranges from 1 to N.
[0077] The dissimilarity matrix is denoted as C;
[0078] The definition of the KL divergence is:
[0079] Where P = (P(1),...,P(N)) and Q = (Q(1),...,Q(N)) are the band y s and y t Normalized probability distribution; where KL divergence does not satisfy symmetry, so it is not suitable for direct measurement of information content differences between bands. In order to achieve symmetry in the measurement of dissimilarity between bands, the original definition is improved and then the dissimilarity matrix of the two-dimensional spectral matrix is defined based on KL.
[0080] The dissimilarity matrix of the two-dimensional spectral matrix defined based on KL divergence is realized by the following formula:
[0081] C st =KL(y s Py t )+KL(y t Py s );
[0082] Among them, C st Let be the element in the s-th row and t-th column of the dissimilarity matrix C, representing the paired band y. s ,y t The differences between them; the values of s and t range from 1 to B;
[0083] A weighted sparse self-representation model incorporating spatial spectral information is constructed using a normalized similarity graph and a dissimilarity matrix. The final value of the coefficient matrix is obtained by solving the weighted sparse self-representation model.
[0084] Specifically, any band of a hyperspectral image can be approximated by a linear combination of other bands, thereby obtaining a coefficient matrix. The magnitude of the non-zero coefficients in the coefficient matrix represents the corresponding weight when the corresponding band is linearly represented by the other bands.
[0085] The weighted sparse self-representation model includes an error term and a constraint term;
[0086] The error term is used to linearly reconstruct the original pixel by weighting it with the neighboring pixels of the surrounding space of the original pixel and integrating the spatial and spectral information of the two-dimensional spectral matrix.
[0087] The constraint terms include a weighted sparse regularization term based on KL divergence and a row sparse constraint term.
[0088] The weighted sparse regularization term based on KL divergence is used to enhance the sparsity of the coefficients in the coefficient matrix, and the row sparse constraint term is used to reduce the similarity between selected bands.
[0089] The weighted sparse self-representation model that integrates spatial spectral information is constructed as shown in the following equation:
[0090]
[0091] Where F(W) is the objective function, γ and λ are regularization parameters, W is the coefficient matrix, and C st and W st The elements in the s-th row and t-th column of C and W, respectively, are weighted sparse regularization terms. C st The larger the |W|, the smaller the correlation between bands. st |The smaller;||W|| 2,1 L is the coefficient matrix W 2,1 Norm;
[0092] The final value of the coefficient matrix is obtained by solving the weighted sparse self-representation model, specifically as follows:
[0093] Taking the derivative of the objective function and setting it equal to 0, we obtain the coefficient matrix expression, as shown in the following equation: Wherein, the diagonal optimization matrix Q∈R B×B Given a diagonal matrix, the diagonal elements and the elements in the s-th row and t-th column of the off-diagonal optimized matrix P are calculated using equation Q. ss =(2||w s ||2) -1 and P st =|C st |·sgn(W st ) to achieve; where w s Let ||w| be the row vector corresponding to the s-th row of W. s ||2 is a vector w s The L2 norm;
[0094] Where sgn(x) is the sign function, i.e.
[0095] Set the convergence threshold and λ and γ in the coefficient matrix expression;
[0096] Initialize the diagonal optimization matrix Q = I B Select sgn(C) st ) replaces sgn(W st P is initialized as the initial value of the result of the symbolic function;
[0097] Among them, I B It is an identity matrix with dimension B×B;
[0098] According to the formula respectively Q ss =(2||w s ||2) -1 and P st =|C st |·sgn(W stUpdate W, the diagonal optimization matrix Q, and the off-diagonal optimization matrix P sequentially until the value of the objective function is less than the convergence threshold;
[0099] Find the L2 norm of the row vectors of the final value of the coefficient matrix and sort them in descending order. Select the first M bands in descending order as the final band subset.
[0100] Specifically, the L2 norm of the row vectors of the final value of the coefficient matrix represents the importance of the corresponding bands. After sorting them in descending order, the bands corresponding to the first M indices are selected as the final band subset, where M is the number of selected bands.
[0101] Thus, from S1 to S7, the hyperspectral band selection method based on weighted sparse self-representation of KL divergence was completed.
[0102] The beneficial effects of the method described in this invention are further illustrated by the following experimental simulations on real hyperspectral datasets:
[0103] 1. Simulation conditions and parameters.
[0104] The simulation experiments of this invention were compiled and completed on MATLAB R2020b. The data required for the experiment came from two publicly available hyperspectral datasets—Botswana data and Indian Pines data.
[0105] (1) Botswana dataset
[0106] The Botswana dataset is a series of data acquired by the Hyperion sensor aboard NASA's EO-1 satellite in the Botswana Delta between 2001 and 2004. The images consist of 1476×256 pixels and 242 bands, with a spectral range of 400-2500 nm, a spectral resolution of 10 nm, and a spatial resolution of 30 m. The pseudo-color images of this dataset are shown below. Figure 2 As shown, there are 14 identified categories. Uncalibrated and noisy bands covering the moisture absorption area were removed, and the remaining 145 bands (10-55, 82-97, 102-119, 134-164, 187-220) were selected as the final bands for use.
[0107] (2) Indian Pines dataset
[0108] The Indian Pines dataset was acquired in 1992 at the Indian Pine Test Site in northwestern Indiana, USA, by the Airborne Visible Infrared Imaging Spectroradiometer (AVRIS) sensor at NASA's Jet Propulsion Laboratory. The images consist of 145×145 pixels and 224 bands, of which 220 bands provide continuous imaging of ground features. The spectral range is 400–2500 nm, and the spatial resolution is 20 m. The pseudo-color images of this dataset are shown below. Figure 3 As shown, it includes 16 crop categories. Twenty bands (104-108, 150-163, 220) covering the water absorption area were removed, and the remaining 200 bands were used as the final bands.
[0109] Simulation experiments: Band selection for hyperspectral datasets was performed using the method proposed in this invention, and compared with three existing band selection algorithms: Marginalized Graph Self-Representation (MGSR), Maximum Variance PCA (MVPCA), and Scalable Self-Representation (SOPSRL). Support Vector Machine (SVM) was used to classify the experimental data, and the classification performance of the selected band subsets by the band selection algorithm was quantitatively evaluated based on the classification results. The kernel function was set as the Gaussian Radial Basis Function (RBF).
[0110] In the experiment, the regularization parameters λ and γ of the method, as well as the penalty coefficient in the SVM classifier and the parameter gamma in the RBF, were obtained through cross-validation. The number of bands selected ranged from 5 to 50, with a step size of 5. When performing SVM classification, 30% of the samples from each class in both datasets were randomly selected as training samples. Considering that Grass / Pasture-mowed and Oats are minor classes in the Indian pines dataset, we randomly selected 10 samples as training samples.
[0111] The classification results for different band selection numbers, simulated using all algorithms on two sets of public datasets, are as follows: Figure 4 and Figure 5 As shown, Tables 1 and 2 record the specific classification accuracy values, where MGSRDW represents the method described in this invention. Overall classification accuracy (OA) is used to measure classification performance.
[0112] Table 1 shows the specific classification results of the Botswana dataset.
[0113]
[0114] Table 2 shows the specific classification results of the Indian Pines dataset.
[0115]
[0116] Analysis of the simulation results shows that, compared with other comparative algorithms, the hyperspectral band selection method based on weighted sparse self-representation of KL divergence in this invention achieves better classification accuracy for most band selection numbers. Although the classification results of the method described in this invention are slightly lower than the SOPSRL algorithm when the number of band selections is 30 and 45 on the Indian Pines dataset, the effectiveness of the method described in this invention is still demonstrated overall.
[0117] To illustrate the content and implementation method of this invention, a specific embodiment is provided in this specification. The details introduced in the embodiment are not intended to limit the scope of the claims, but rather to aid in understanding the method described in this invention. Those skilled in the art will understand that various modifications, variations, or substitutions to the steps of the preferred embodiment are possible without departing from the spirit and scope of this invention and its appended claims. Therefore, this invention should not be limited to the content disclosed in the preferred embodiment and the accompanying drawings.
Claims
1. A hyperspectral band selection method based on weighted sparse self-representation of KL divergence, characterized in that, include: Acquire a 3D hyperspectral image cube and convert it into a 2D spectral matrix; Principal component analysis is performed on the three-dimensional hyperspectral image cube to obtain the first principal component. Superpixel segmentation is then applied to the first principal component to generate several partitions of the three-dimensional hyperspectral image cube. Construct a neighborhood graph of the two-dimensional spectral matrix, calculate the similarity graph, and then normalize it to obtain a normalized similarity graph; The difference in information content between paired bands is calculated based on KL divergence, and the dissimilarity matrix is calculated. We construct a weighted sparse self-representation model that integrates spatial spectral information using a normalized similarity graph and a dissimilarity matrix, and then obtain the final value of the coefficient matrix by solving the weighted sparse self-representation model. The construction of the weighted sparse self-representation model that integrates spatial spectrum information is specifically achieved by constructing an error term and a constraint term and adding them together; The error term is specifically obtained by weighting the original pixels with a normalized similarity map, integrating the spatial and spectral information of the two-dimensional spectral matrix, multiplying it by a coefficient matrix on the right, and then linearly reconstructing the original pixels. The constraint term is specifically obtained by constructing a weighted sparse regularization term based on KL divergence and a row sparse constraint term and adding them together; The construction of the weighted sparse regularization term based on KL divergence is specifically achieved by multiplying and summing the corresponding elements of the dissimilarity matrix and the coefficient matrix, thereby enhancing the sparsity of the coefficients in the coefficient matrix. The construction of row sparse constraint terms is specifically achieved by using L 2,1 The norm regularization term applies row sparsity constraints to the coefficient matrix, thereby reducing the similarity between the paired bands; The magnitude of the L2 norm of the row vector of the final value of the coefficient matrix represents the importance of the corresponding band; Find the L2 norm of the row vectors of the final value of the coefficient matrix and sort them in descending order. Select the first M bands in descending order as the final band subset. Where M is the number of selected bands.
2. The hyperspectral band selection method according to claim 1, characterized in that, The calculation of the similarity map is specifically achieved by calculating the Gaussian kernel function of the two-dimensional spectral matrix; The three-dimensional hyperspectral image cube has several partitions, the number of which is the same as the set number of superpixel segmentation regions.
3. The hyperspectral band selection method according to claim 1, characterized in that, The dissimilarity matrix is the sum of the KL divergences of paired bands of the two-dimensional spectral matrix, which are approximately distributed with respect to the observed distribution.
4. The hyperspectral band selection method according to claim 1, characterized in that, The process of constructing a neighborhood graph of the two-dimensional spectral matrix, calculating a similarity graph, and then normalizing it to obtain a normalized similarity graph is as follows: S1. Calculate the similarity graph of the two-dimensional spectral matrix; the size of the elements in the similarity graph represents the similarity between corresponding pairs of pixels; if a pair of pixels belongs to the same partition, the corresponding element is 0; otherwise, calculate the Gaussian kernel function of the two-dimensional spectral matrix to obtain the corresponding element. S2. Normalize the similar graph to obtain a normalized similar graph. This is achieved by left-multiplying the similar graph matrix with self-loops by the square root of the inverse of the degree matrix.
5. The hyperspectral band selection method according to claim 4, characterized in that, The similarity graph matrix with self-loops is the sum of the identity matrix and the similarity graph, and is used to add the node's own information to the similarity graph by adding self-loops.
6. The hyperspectral band selection method according to claim 4, characterized in that, The degree matrix is a diagonal matrix whose diagonal elements are the sum of the corresponding rows of the similarity graph matrix.
7. The hyperspectral band selection method according to claim 1, characterized in that, The dimension of the three-dimensional hyperspectral image cube is w×h×B, where B represents the number of bands in the image; N = w×h represents the number of pixels in the image; N×B is the dimension of the two-dimensional spectral matrix; w and h represent the dimensions of the image spatial dimension, with the width of the image spatial dimension being w pixels and the height of the image spatial dimension being h pixels. The calculation of the difference in information content between paired bands based on KL divergence and the calculation of the dissimilarity matrix are specifically as follows: The paired bands are denoted as: band y u and band y v The expressions are as follows: y u =(x u1 ,...,x ul ,...x uN ) and y v =(x v1 ,...,x vl ,...x vN ), x ul and x vl These are the spectral values of the l-th pixel in the u-th and v-th band vectors, respectively, with l ranging from 1 to N; u and v ranging from 1 to B; the KL divergence is defined as follows: Where k ranges from 1 to N, and P = (P(1),...,P(N)) and Q = (Q(1),...,Q(N)) are the bands y u and y v Normalized probability distribution; As can be seen from the previous equation, the KL divergence does not satisfy symmetry, so it is not suitable for direct measurement of the information content difference between bands. In order to improve the symmetry of the dissimilarity measurement between bands, the dissimilarity matrix of the two-dimensional spectral matrix is calculated after the original KL divergence is improved.
8. The hyperspectral band selection method according to claim 1, characterized in that, The calculation of the dissimilarity matrix of the two-dimensional spectral matrix is specifically achieved by adding the original KL divergence to the KL divergence calculated after swapping the paired bands.
9. The hyperspectral band selection method according to claim 1, characterized in that, The final value of the coefficient matrix is obtained by solving the weighted sparse self-representation model, specifically as follows: By taking the derivative of the objective function and setting it equal to 0, we obtain the expression for the coefficient matrix. Set the convergence threshold and the regularization parameter for the coefficient matrix expression; Initialize the coefficient matrix and iteratively update the coefficient matrix according to the coefficient matrix expression until the value of the objective function is less than the convergence threshold.