A hyperspectral band selection method based on space-spectrum combination graph learning

Abstract

The present disclosure relates to a hyperspectral band selection method based on space-spectrum combined graph learning, which comprises the following steps: firstly, pre-processing a hyperspectral image cube to obtain a hyperspectral image data matrix, and constructing a spatial affinity matrix by using a spatial pixel point set in the hyperspectral image data matrix, and constructing a spectral affinity matrix by using a spectral data point set in the hyperspectral image data matrix; then, embedding the spatial affinity matrix and the spectral affinity matrix into a self-representation model to obtain a graph self-representation model containing a coefficient matrix; finally, processing a neighboring band of the coefficient matrix to obtain a reconstruction target function, and obtaining an optimal band subset. The present disclosure can improve the robustness and effectiveness of the spectral band selection algorithm in the spatial and spectral dimensions, while ensuring the local spatial consistency between the hyperspectral bands.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of hyperspectral remote sensing image processing, and particularly relates to a hyperspectral band selection method based on space-spectrum combined graph learning. BACKGROUND

[0002] The hyperspectral remote sensing technology can collect tens to hundreds of narrow-band ground feature spectral response signals from visible light to near-infrared. The hyperspectral image (HSI) obtained by using an imaging spectrometer can provide rich spectral information and spatial information, and has a wide range of applications in environmental monitoring, precision agriculture, urban regional planning and the like.

[0003] When the hyperspectral image is used to accurately identify and classify the ground objects, the high-dimensional data of the hyperspectral image needs to be reduced. At present, the dimension reduction of the hyperspectral image mainly includes two categories of algorithms, i.e., feature extraction and band selection. Among them, the band selection is to select a suitable band subset from the original band set according to certain rules, so that the information of each band obtained is as rich as possible, and the correlation between the bands is reduced. The band selection is generally divided into two ways, i.e., supervised and unsupervised.

[0004] The unsupervised way is divided into clustering algorithm and sorting algorithm. The clustering algorithm is to divide the bands into different groups, select one or more representative bands from each group to form a new band subset, and then further process. The effectiveness of this kind of algorithm mainly depends on the similarity calculation between the bands. However, due to the uncertainty and complexity of the context information of the HSI, a single band may belong to different groups at the same time, thereby leading to an incorrect clustering result. The sorting algorithm is to quantify the importance of each band according to one or more specific criteria, and then sort the bands according to the quantification result, and finally select a number of bands with high ranking as the representative bands. In recent years, the graph learning algorithm has been applied to the hyperspectral band selection. The graph learning method is to map the correlation between the bands to the relationship between the graphs, which can fully explore the potential relationship between the bands. However, there are two shortcomings in the graph learning method: first, the current graph learning method only considers the spectral characteristics of the HSI, and ignores the spatial information contained in the HSI; second, the global framework of the image is usually used for modeling, so that a suitable graph matrix is obtained, but the spatial distribution difference between different pixels and bands is ignored.

[0005] Therefore, it is necessary to propose a scheme to improve one or more problems in the above-mentioned related technical solutions.

[0006] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present disclosure, and therefore can include information which does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0007] The embodiment of the present disclosure provides a hyperspectral band selection method based on space-spectrum combination graph learning, which comprises the following steps:

[0008] Pretreat a hyperspectral image cube to obtain a hyperspectral image data matrix; the hyperspectral image data matrix comprises a spatial pixel point set and a spectral data point set;

[0009] Divide the spatial pixel point set into multiple regions, wherein the multiple regions comprise multiple homogeneous regions and multiple non-homogeneous regions; calculate pixel affinity values between the multiple homogeneous regions respectively, and thus construct a spatial affinity matrix;

[0010] Set a spectral objective function related to the spectral data point set, and impose multiple constraints in the spectral objective function, and thus construct a spectral affinity matrix;

[0011] Establish a self-representation model, embed the spatial affinity matrix and the spectral affinity matrix in the self-representation model, and introduce a Laplace regularization term, to obtain a graph self-representation model, wherein the graph self-representation model comprises a coefficient matrix;

[0012] Perform a reconstruction objective function processing on multiple adjacent bands corresponding to the coefficient matrix, to obtain an optimal band subset to be selected.

[0013] In an example embodiment of the present disclosure, an expression of the hyperspectral image data matrix comprises:

[0014] X∈R Y×B (1)

[0015] Wherein, X represents a hyperspectral image data matrix; Y represents a spatial pixel point set, Y={y1,y2,...,y N}, B represents a total number of bands of the hyperspectral image, B={b1,b2...b i ,...b j ...b B}; R represents a hyperspectral image data set; Y×B represents a dimension.

[0016] In an example embodiment of the present disclosure, the step of dividing the spatial pixel point set into multiple regions, wherein the multiple regions comprise multiple homogeneous regions and multiple non-homogeneous regions, and calculating pixel affinity values between the multiple homogeneous regions respectively, and thus constructing a spatial affinity matrix comprises:

[0017] The spatial pixel point set is segmented into a plurality of regions by using an entropy rate superpixel segmentation algorithm; similar pixel points in each region are respectively divided into a homogeneous region, and other dissimilar pixel points are respectively divided into a non-homogeneous region; thereby forming a plurality of homogeneous regions and a plurality of non-homogeneous regions.

[0018] Pixel affinity values between all pixel points in the plurality of homogeneous regions are respectively calculated by using a Gaussian kernel function, and pixel affinity values between all pixel points in the plurality of non-homogeneous regions are set to zero; thereby constructing the spatial affinity matrix.

[0019] In an example embodiment of the present disclosure, an expression of the entropy rate superpixel segmentation algorithm comprises:

[0020] min(R(I))+δB(I)) (2)

[0021] wherein R(I) represents an entropy rate function; B(I) represents a balance term; δ represents a weight factor between R(I) and B(I); and min represents minimization.

[0022] An expression of the homogeneous region after segmentation comprises:

[0023]

[0024] wherein H represents a hyperspectral image cube; H1 to H K represent a plurality of homogeneous regions segmented therefrom; and s.t. represents a constraint.

[0025] In an example embodiment of the present disclosure, an expression of the spatial affinity matrix comprises:

[0026]

[0027] wherein A spa represents the spatial affinity matrix, A spa ∈R Y×Y ; y i and y j represent vectors of any two pixels in the H i th homogeneous region; θ represents a parameter of the Gaussian kernel function; and Y×Y represents a dimension. represents an Euclidean distance between y i and y j .

[0028] In an example embodiment of the present disclosure, in the step of setting a spectral objective function related to the spectral data point set and imposing a plurality of constraints in the spectral objective function, an expression of the spectral objective function comprises:

[0029]

[0030] Where B represents the total number of bands in the hyperspectral image; b i b represents the i-th spectral data point; j This represents the j-th spectral data point; Represents spectral data point b i and spectral data point b j Euclidean distance between them; A ij Represents spectral data point b i and spectral data point b j The spectral affinity between them; α represents the value used to adjust the Laplace regularization term. The weight parameters; T represents the transpose of the matrix; A i Represents the columns of a matrix; A i T The 1 in 1 represents a column vector consisting entirely of 1s.

[0031] In an exemplary embodiment of this disclosure, the step of constructing the spectral affinity matrix includes: the expression of the spectral affinity matrix includes:

[0032]

[0033] Among them, A spe Denotes the spectral affinity matrix, A spe ∈R B×B ;, B×B represents dimension; d i,k+1 Indicates the bth i The Euclidean distance from the (k+1)th spectral data point to the (j+1)th spectral data point; j and k represent the j-th and k-th spectral data points, respectively. j <h≤k,d ih Represents spectral data point b i and spectral data point b h The Euclidean distance between them.

[0034] In an exemplary embodiment of this disclosure, the step of establishing a self-representation model involves embedding both the spatial affinity matrix and the spectral affinity matrix into the self-representation model and introducing a Laplace regularization term to obtain a graph self-representation model, wherein the graph self-representation model includes a coefficient matrix.

[0035] The expression of the graph self-representation model includes:

[0036] min||X-(A spa X+XA spe )Z||2+λ1||Z||2+λ2tr(ELE T (7)

[0037] Wherein, X represents a hyperspectral image data matrix; λ1 and λ2 both represent balance parameters; E represents an error matrix; L represents a Laplace matrix; Z represents a coefficient matrix; E T represents the transpose of error matrix E; tr represents the trace of a matrix.

[0038] In an example embodiment of the present disclosure, the step of obtaining the optimal waveband subset to be selected by processing the reconstruction objective function on the plurality of adjacent wavebands corresponding to the coefficient matrix comprises:

[0039] The reconstruction objective function is set, and the plurality of adjacent wavebands corresponding to the coefficient matrix are iteratively optimized and solved by using the reconstruction objective function, and the optimal waveband subset is obtained by using the recursive relationship existing in the optimal solution.

[0040] In an example embodiment of the present disclosure, the expression of the reconstruction objective function comprises:

[0041]

[0042] Wherein, Z j represents the jth waveband of coefficient matrix Z; Z p represents the combination of the left and right adjacent wavebands of the jth waveband of coefficient matrix Z, and respectively represent the adjacent wavebands of the jth waveband of coefficient matrix Z, Bx2 represents the dimension, t represents a variable, and when 1≤j≤B, t satisfies n t ≤j<n t+1 ; W j represents a reconstruction coefficient matrix; B represents the total number of wavebands of a hyperspectral image; n t represents the tth waveband index; n t+1 represents the t+1th waveband index;

[0043] The expression of obtaining the optimal waveband subset comprises:

[0044]

[0045] Wherein, n j represents the optimal waveband subset obtained by using n j represents the optimal solution obtained by using the reconstruction objective function.

[0046] ​The high-spectral band selection method based on space-spectrum combined graph learning provided by the present disclosure comprises the following steps: preprocessing a hyperspectral image to obtain a hyperspectral image data matrix, constructing a spatial affinity matrix by using a spatial pixel point set in the hyperspectral image data matrix, and constructing a spectral affinity matrix by using a spectral data point set in the hyperspectral image data matrix; then embedding the spatial affinity matrix and the spectral affinity matrix into a self-representation model to obtain a graph self-representation model containing a coefficient matrix; finally, performing a reconstruction objective function processing on the neighboring bands of the coefficient matrix to obtain an optimal band subset. Thus, the robustness and effectiveness of the spectral band selection algorithm in the spatial and spectral dimensions are improved, and the local spatial consistency between the hyperspectral bands is ensured. BRIEF DESCRIPTION OF DRAWINGS

[0047] The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate embodiments consistent with the present disclosure and, together with the description, further serve to explain the principles of the disclosure. It is to be noted, of course, that the appended drawings illustrate only some embodiments of the disclosure and are therefore not to be considered in a limiting sense, because the embodiments described in connection with the drawings can be implemented in any number of variations as would be understood by those having ordinary skill in the art.

[0048] Figure 1 A step schematic diagram of the hyperspectral band selection method based on space-spectrum combined graph learning in the exemplary embodiment of the present disclosure is shown;

[0049] Figure 2 A flow schematic diagram of the hyperspectral band selection method based on space-spectrum combined graph learning in the exemplary embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0050] Example implementations will now be described more fully with reference to the accompanying drawings. Example implementations may, however, be implemented in many different forms and should not be construed as limited to the implementations set forth herein; rather, these implementations are provided so that this disclosure will be thorough and complete, and will fully convey the inventive concept to those skilled in the art. Additive features, structures, or characteristics described can be combined in any suitable manner in one or more implementations.

[0051] In addition, the accompanying drawings are merely schematic and are not intended to be to scale. Like reference numerals denote like or similar parts throughout the several views, so that repeated description is omitted. Some of the block diagrams shown in the drawings are functional entities that do not necessarily have to correspond to physically or logically independent entities. These functional entities can be implemented in the form of software, or in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0052] The example embodiment provides a hyperspectral band selection method based on spatio-spectral graph learning, as shown in Figure 1 The hyperspectral band selection method includes:

[0053] Step S101: Preprocess the hyperspectral image cube to obtain a hyperspectral image data matrix; the hyperspectral image data matrix includes a spatial pixel point set and a spectral data point set.

[0054] Step S102: Divide the spatial pixel point set into multiple regions, including multiple homogeneous regions and multiple non-homogeneous regions; calculate the pixel affinity value between the multiple homogeneous regions respectively, thereby constructing a spatial affinity matrix.

[0055] Step S103: Set a spectral objective function related to the spectral data point set, and impose multiple constraints in the spectral objective function, thereby constructing a spectral affinity matrix.

[0056] Step S104: Establish a self-representation model, embed both the spatial affinity matrix and the spectral affinity matrix in the self-representation model, and introduce a Laplacian regularization term to obtain a graph self-representation model, which includes a coefficient matrix.

[0057] Step S105: Perform reconstruction objective function processing on the multiple adjacent bands corresponding to the coefficient matrix to obtain an optimal band subset to be selected.

[0058] It should be noted that spatio-spectrum refers to the spatial information and spectral information of the hyperspectral image.

[0059] The hyperspectral band selection method based on spatio-spectral graph learning proposed in the embodiments of the present disclosure, by preprocessing the hyperspectral image to obtain a hyperspectral image data matrix, and using the spatial pixel point set in the hyperspectral image data matrix to construct a spatial affinity matrix, and using the spectral data point set in the hyperspectral image data matrix to construct a spectral affinity matrix; then embedding both the spatial affinity matrix and the spectral affinity matrix in a self-representation model to obtain a graph self-representation model containing a coefficient matrix; finally, performing reconstruction objective function processing on the adjacent bands of the coefficient matrix to obtain an optimal band subset. The present disclosure improves the robustness and effectiveness of the spectral band selection algorithm in both spatial and spectral dimensions, while ensuring the local spatial consistency between the hyperspectral bands.

[0060] In the following, the hyperspectral band selection method based on spatio-spectral graph learning in the example embodiment will be described in more detail. As shown in Figure 2

[0061] ​In step S101, the step is a preprocessing step of constructing a spatial affinity matrix and a spectral affinity matrix. In the embodiment, the step pre-processes a hyper spectral image (HSI) cube to obtain a hyper spectral image data matrix.

[0062] Further, the expression of the hyper spectral image data matrix is:

[0063] X∈R Y×B (1)

[0064] Wherein, X represents the hyper spectral image data matrix; Y represents a spatial pixel point set, Y={y1, y2,..., y N}, B represents the total number of wavebands of the hyper spectral image, B={b1, b2...b i ,...b j ...b B}; R represents a hyper spectral image data set; YxB represents the dimension.

[0065] In step S102, the step includes the following sub-steps:

[0066] Sub-step S1021: using an entropy rate superpixel segmentation algorithm to segment the spatial pixel point set into multiple regions; similar pixel points contained in each region are respectively divided into a homogeneous region, and other dissimilar pixel points are respectively divided into a non-homogeneous region; thereby forming multiple homogeneous regions and non-homogeneous regions.

[0067] Sub-step S1022: using a Gaussian kernel function to respectively calculate the pixel affinity values between all pixel points in multiple homogeneous regions, and setting the pixel affinity values between all pixel points in multiple non-homogeneous regions to zero; thereby constructing the spatial affinity matrix.

[0068] Further, the expression of the entropy rate superpixel segmentation algorithm includes:

[0069] min(R(I))+δB(I)) (2)

[0070] Wherein, R(I) represents an entropy rate function; B(I) represents a balance term; δ represents a weight factor between R(I) and B(I); min represents minimization.

[0071] Further, the expression of the segmented homogeneous region includes:

[0072]

[0073] Wherein, H represents a hyper spectral image cube; H1 to H Krepresents the constraint.

[0074] In sub-step S1022, the Gaussian kernel function generally refers to a radial basis function, i.e., a real-valued function whose value depends only on the distance from a particular point.

[0075] Further, the expression of the spatial affinity matrix includes:

[0076]

[0077] wherein A spa represents the spatial affinity matrix, A spa ∈R Y×Y ; y i and y j respectively represent vectors of any two pixels in the ith homogeneous region H i ; θ represents parameters of the Gaussian kernel function; Y×Y represents the dimension; represents the Euclidean distance between y i and y j ; the spatial affinity value can be calculated by using equation (4).

[0078] In step S103, in most cases, in order to save efficiency and obtain higher performance, it is generally expected to obtain a sparse spectral affinity matrix, and therefore a spectral objective function related to the set of spectral data points is set. At the same time, multiple constraints are imposed in the spectral objective function to obtain an optimal spectral affinity matrix. That is, the constraint A i T 1=1 is set so that the sum of each column in the set matrix is equal to 1, thereby ensuring that a non-negative normalized affinity matrix is learned. Here, T represents the transpose of the matrix; A i represents a column of the matrix; A i T 1 in the 1 represents a full column vector of 1. The constraint A i >0 is set, wherein A i represents a column vector of the set matrix, thereby ensuring that no negative affinity value occurs. The set spectral objective function problem is converted into a minimization problem: that is, the expression of the spectral objective function is:

[0079]

[0080] wherein B represents the total number of bands of the hyperspectral image; b i represents the ith spectral data point; b j represents the jth spectral data point; represents the Euclidean distance between the spectral data point b i and the spectral data point b j ; Aij spectral affinity value between spectral data points b i and spectral data points b j ; a represents a weight parameter used to adjust the Laplace regularization term ; T represents the transpose of a matrix; A i represents the column of a matrix; A i T 1 in 1 represents a full 1 column vector.

[0081] Further, the expression of the spectral affinity matrix is:

[0082]

[0083] wherein A spe represents the spectral affinity matrix, A spe ∈R B×B ; B x B represents the dimension; d i,k+1 represents the Euclidean distance from the spectral data point b i to the k+1th spectral data point; k represents the number of spectral data points, j < h ≤ k, d ih represents the Euclidean distance between spectral data points b i and spectral data points b h . The spectral affinity value can be calculated by equation (6).

[0084] In step S104, firstly, a self-representation model is constructed, and on the basis of the self-representation model, the spatial affinity matrix and the spectral affinity matrix constructed above are embedded into the self-representation model, so as to ensure that the coefficient matrix obtained has high robustness in both spatial and spectral dimensions; meanwhile, in order to ensure the consistency of the local space between adjacent wave bands, a Laplace regularization term is introduced into the self-representation model. Finally, a graph self-representation model is constructed.

[0085] Further, the expression of the graph self-representation model is:

[0086] min ||X-(A spa X+XA spe )Z||2+λ1||Z||2+λ2tr(ELE T ) (7)

[0087] wherein X represents the hyperspectral image data matrix; λ1 and λ2 both represent balance parameters; E represents the error matrix; L represents the Laplace matrix; Z represents the coefficient matrix; E T represents the transpose of the error matrix E; tr represents the trace of a matrix.

[0088] Step S105 includes the following sub-steps:

[0089] Sub-step S1051: Process the multiple neighboring bands corresponding to the coefficient matrix Z using the reconstruction objective function to obtain a subset of reconstructed bands. This step includes: setting the reconstruction objective function, using the reconstruction objective function to iteratively optimize and solve the multiple neighboring bands corresponding to the coefficient matrix Z to obtain the optimal solution, and using the recursive relationship existing in the optimal solution to obtain the optimal subset of bands.

[0090] The expression for the reconstruction objective function is:

[0091]

[0092] Among them, Z j Z represents the j-th band of the coefficient matrix Z; p This represents the combination of the left and right adjacent bands of the j-th band in the reconstruction coefficient matrix Z. and Let represent the bands adjacent to the j-th band of the coefficient matrix Z, where B×2 represents the dimension and t represents the variable. When 1≤j≤B, t satisfies n t ≤j <n t+1 W j Let represent the reconstruction coefficient matrix; B represents the total number of bands in the hyperspectral image. Here, t essentially represents that for all 1 ≤ j ≤ B, there exists a variable t that satisfies n t ≤j <n t+1 This makes Z j and and Related; n t n represents the index of the t-th band; t+1 This represents the index of the (t+1)th band.

[0093] Formula (8) is difficult to solve using traditional machine learning methods because it is a combinatorial optimization problem involving the band exponent vector n. Therefore, a special solution to this formula needs to be given here.

[0094] First, define a loss variable T. a,b The loss variable T a,b This represents the reconstructed band vector combination [Z] a+1 Z a+2 ,...,Z b-1 The amount of loss, [Z] a+1 Z a+2 ,...,Z b-1 [ is a subset of the coefficient matrix Z. The loss variable T] is a subset of the coefficient matrix Z. a,b The expression T a,b for:

[0095]

[0096] wherein T a,b represents the loss variable; a represents the sequence number of the a-th waveband; b represents the sequence number of the b-th waveband; represents an arbitrary j value; E j represents the reconstruction error matrix. The minimum norm solution of the expression of the loss variable is:

[0097]

[0098] wherein Z a represents the a-th waveband; Z b represents the b-th waveband; -1 represents the inverse of the matrix; T represents the transpose.

[0099] Secondly, an auxiliary variable M i,j is defined, and the expression of the auxiliary variable M i,j is:

[0100]

[0101] wherein M i,j represents the auxiliary variable; represents the loss variable at the time of reconstructing Z p .

[0102] There are two cases as follows:

[0103] When j > 1, wherein 1≤i≤B+1, 1≤j≤i. i and j represent different wavebands respectively.

[0104] When j = 1, M i,1 = T 0,i .

[0105] Thus, the expression of the optimal waveband subset is obtained as follows:

[0106]

[0107] wherein n j represents the optimal waveband subset obtained by n j ; and represents the optimal solution obtained by the reconstruction objective function.

[0108] The iterative solution is obtained by using the formula (9), the preset adjacent preset waveband number is l, so that n l+1 = B+1. Then, l is substituted into the formula (9), and the l-th waveband index n l is obtained. By analogy, the optimal waveband subset n * is obtained by reverse selection (i.e. from l to 1), n *= {n1, n2,... n j ...n l}.

[0109] Here, n l represents the waveband index corresponding to the first selected waveband, and so on. According to the waveband index, the corresponding waveband subset can be found.

[0110] In order to verify the effectiveness and beneficial effects of the method of the present disclosure, the following simulation experiments are performed.

[0111] The experimental conditions are set as follows:

[0112] The present disclosure is implemented on a processor i7-12700H 2.70GHz CPU, memory is 16G, LegionY9000P, Win11 operating system, using MATLAB2020b programming language for experimental analysis.

[0113] First, the selected comparative algorithm

[0114] In order to evaluate the advantages of the method of the present disclosure, the Adaptive Subspace Partition Strategy (ASPS) algorithm and the Fast Neighborhood Grouping method for hyperspectral Band Selection (FNGBS) algorithm are selected for comparison with the algorithm of the present disclosure, as follows:

[0115] ASPS algorithm: first, the spectral bands are processed in order, then the bands with similar spectral characteristics are adaptively divided into multiple sub-cubes, and finally the band with the smallest noise in each sub-cube is selected as the representative band.

[0116] FNGBS algorithm: the context information on the hyperspectral image is mined through the neighborhood waveband grouping strategy, the importance of each waveband is evaluated using information entropy and local density, and the highest ranked waveband is selected to form the final waveband subset.

[0117] Second, the types of hyperspectral data sets selected for experiments

[0118] Indian Pinas data set: this image data was obtained by AVIRIS sensor in 1992, including 16 ground object categories. After removing the water absorption waveband, there are still 200 wavebands left, and the image cube size is 145x145x220. In addition, after removing the background pixels of no value, 10249 pixels can be used for subsequent applications.

[0119] Pavia University Dataset: This image data was captured by the ROSIS-03 sensor in 2003 and includes 9 land cover categories. After removing bands of no value, 103 bands remain, and the image cube size is 610×340×103. Furthermore, after removing background pixels, 42,776 pixels were used for image processing.

[0120] Botswana dataset: This scene was captured by the NASA EO-1 sensor in 2001 and contains 14 land cover categories. After removing worthless bands, 145 bands remain, and the image cube size is 1475×256×145. Furthermore, after removing background pixels, 3248 pixels are available for image classification.

[0121] The Salinas dataset: This image data, captured by the AVIRIS sensor in California, includes 16 categories. After removing 20 water absorption bands, a total of 224 spectral bands are available for image analysis. Furthermore, after removing background pixels, 54,129 pixels are available for further research.

[0122] Third, the classifier settings in the experiment

[0123] To verify the effectiveness of the proposed method, this disclosure selects two mainstream classifiers: Support Vector Machine (SVM) and k-Nearest Neighbors (KNN) for classification experiments. Furthermore, to compare the performance of various algorithms, the same classifier parameters are used throughout the experiments. Specifically, for all classification validation experiments on KNN, the nearest neighbor parameter k is set to 5, and the distance metric is Euclidean distance. For the SVM classifier, a Gaussian radial basis function (RBF) is used as the kernel function, and the initialization of the penalty factor C and the RBF coefficient gamma is set to 10. 4 And 0.5. Because both classifiers are supervised, for each dataset, 10% of the samples are randomly selected to train the classifier, while the remaining 90% are used for the test task. In addition, all experiments are run 5 times individually to reduce the impact of randomness on classification accuracy, and the average of the results is taken as the final classification result.

[0124] Fourth, establish evaluation criteria.

[0125] To evaluate the performance of different algorithms in obtaining band subsets, two commonly used evaluation metrics were employed to analyze classification accuracy: overall accuracy (OA) and average overall accuracy (AOA). For both metrics, higher values ​​indicate better classification performance.

[0126] Fifth, set the number of bands to select.

[0127] To evaluate the influence of different number of bands on the classification accuracy, the set of selected number of bands is set to {5, 7, 10, 12, 15, 20, 25, 30, 40, 50}.

[0128] After setting the above experimental conditions, the algorithm of the present disclosure, the ASPS algorithm and the FNGBS algorithm are respectively used for experiment comparison, and the following experimental results are obtained:

[0129] Table 1: Overall accuracy (%) of SVM classifier on Indian Pinas dataset for three algorithms

[0130]

[0131]

[0132] Table 2: Overall accuracy (%) of KNN classifier on Indian Pinas dataset for three algorithms

[0133] 5 7 10 12 15 20 25 30 40 50 The present invention 64.71 67.82 66.11 68.96 67.97 70.15 70.56 70.22 69.05 68.19 ASPS 65.98 65.86 69.46 70.65 69.92 69.42 70.57 69.98 69.65 69.27 FNGBS 63.34 66.01 67.77 66.70 68.27 67.22 69.18 69.13 68.15 68.38

[0134] From Table 1 and Table 2, it can be seen that on the Indian Pinas dataset, the present disclosure has certain performance advantages, especially when the selected number of bands is small, the overall accuracy is higher than other algorithms. Although when the number of selected bands is large, the ASPS algorithm and the FNGBS algorithm are higher than the present disclosure, but this does not affect the advantages of the method of the present disclosure.

[0135] Table 3: Overall accuracy (%) of SVM classifier on Pavia University dataset for three algorithms

[0136] 5 7 10 12 15 20 25 30 40 50 The present invention 85.13 89.27 90.83 91.96 92.52 93.35 93.52 93.42 93.50 93.86 ASPS 83.62 85.71 88.16 88.40 89.97 91.58 92.63 92.81 93.38 93.64 FNGBS 81.64 85.48 88.33 89.17 91.02 92.37 92.68 93.18 93.10 93.83

[0137] Table 4: Overall accuracy (%) of KNN classifier on Pavia University dataset for three algorithms

[0138] 5 7 10 12 15 20 25 30 40 50 The present invention 84.80 86.09 87.45 89.14 88.27 88.93 88.94 89.16 88.43 88.10 ASPS 83.94 84.76 85.71 85.71 86.14 86.52 86.55 86.55 87.06 87.50 FNGBS 82.68 84.03 85.56 84.48 85.17 85.80 86.16 86.85 85.78 86.28

[0139] From Table 3 and Table 4, it can be seen that on the Pavia University dataset, the present disclosure has excellent performance advantages, especially when the selected number of bands is small, the overall accuracy is 2%~3% higher than other algorithms.

[0140] Table 5: Overall accuracy (%) of SVM classifier on Botswana dataset for three algorithms

[0141] 5 7 10 12 15 20 25 30 40 50 The present invention 86.21 88.58 89.03 89.44 89.36 90.16 90.09 90.64 91.15 92.80 ASPS 78.76 85.63 87.18 88.30 88.18 89.27 90.08 90.55 90.52 90.95 FNGBS 79.36 83.44 86.70 86.01 87.76 87.35 89.51 89.33 91.15 91.98

[0142] Table 6: Overall accuracy (%) of KNN classifier for three algorithms on Botswana dataset

[0143] 5 7 10 12 15 20 25 30 40 50 The present invention 82.96 84.43 85.05 84.77 83.61 83.85 84.71 85.46 85.56 85.97 ASPS 75.03 82.21 83.07 83.82 83.59 84.93 85.14 85.11 85.28 84.58 FNGBS 76.52 79.74 83.13 81.28 82.86 82.07 85.02 84.61 84.78 85.22

[0144] From Table 5 and Table 6, it can be seen that the present disclosure has good performance on Botswana dataset, and also has superior performance on SVM classifier and KNN classifier when the number of selected bands is small, and the classification accuracy is not much different as the number of selected bands increases.

[0145] Table 7: Overall accuracy (%) of SVM classifier for three algorithms on Salinas dataset

[0146] 5 7 10 12 15 20 25 30 40 50 The present invention 90.07 91.12 91.17 91.38 91.87 92.42 92.46 92.25 92.78 92.53 ASPS 83.73 86.03 90.16 91.13 91.79 92.24 92.41 92.62 93.03 93.23 FNGBS 87.32 89.35 91.17 91.14 91.57 91.45 91.73 92.15 92.30 92.70

[0147] Table 8: Overall accuracy (%) of KNN classifier for three algorithms on Salinas dataset

[0148] 5 7 10 12 15 20 25 30 40 50 The present invention 88.55 88.51 88.74 89.03 88.82 88.87 89.37 89.30 89.16 89.28 ASPS 83.36 84.55 87.96 88.30 88.20 88.16 88.31 89.25 89.04 89.15 FNGBS The present invention ASPS FNGBS 85.83 86.70 88.32 88.13 88.20 88.33 88.40 88.70 89.01 89.06

[0149] From Table 7 and Table 8, it can be seen that the present disclosure has good performance on Salinas dataset, and the method of the present disclosure has certain advantages on SVM classifier and KNN classifier compared with other algorithms as the number of bands increases.

[0150] Table 9: Average overall accuracy (%) of SVM classifier for three algorithms on three datasets

[0151]

[0152] Table 10: Average overall accuracy (%) of KNN classifier for three algorithms on three datasets

[0153]

[0154] From Table 9 and Table 10, it can be seen that the average overall accuracy of the present disclosure on each dataset is better than the other two algorithms whether it is KNN classifier or SVM classifier. This fully shows the effectiveness and robustness of the method of the present disclosure, and further proves that the method of the present disclosure fully considers the advantages of spatial and spectral information of hyperspectral images.

[0155] The present disclosure proposes a hyperspectral band selection method based on space-spectrum combined graph learning, which utilizes the correlation between pixels and bands contained in the hyperspectral image to construct a spatial affinity matrix and a spectral affinity matrix, thereby reasonably capturing the structural information of the hyperspectral image. The method models in the spatial and spectral dimensions, which is conducive to the subsequent band subset generation task. At the same time, in order to ensure the local spatial consistency between bands, a Laplace regularization term related to the error matrix is introduced in the self-representation model. In addition, the current subset generation strategy is to sort each band by calculating the cumulative contribution value or to obtain the final band subset by regarding the band selection as a clustering task. These methods often only consider the information amount of the band, so that the correlation between the bands is high. To solve this problem, the present disclosure also adopts a neighboring band reconstruction strategy to obtain the final band subset, thereby effectively evaluating the importance of each band.

[0156] It should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise" and the like in the above description indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the embodiments of the present disclosure and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the embodiments of the present disclosure.

[0157] In addition, the terms "first", "second" are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more of the features. In the description of the embodiments of the present disclosure, the meaning of "multiple" is two or more, unless otherwise explicitly specified and limited.

[0158] In the embodiments of the present disclosure, unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connection", "fixing" and the like should be understood in a broad sense, for example, can be fixedly connected, or can be detachably connected, or can be integrated; can be mechanically connected, or can be electrically connected; can be directly connected, or can be indirectly connected through an intermediate medium; can be the internal communication of two elements or the interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in the present disclosure can be understood according to the specific circumstances.

[0159] In the embodiments of the present disclosure, unless specifically defined and limited otherwise, "on" or "under" of a first feature to a second feature can include that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, "on", "above" and "over" of a first feature to a second feature include that the first feature is directly above and obliquely above the second feature, or only indicates that the first feature is higher than the second feature in horizontal height. "Under", "below" and "underneath" of a first feature to a second feature include that the first feature is directly below and obliquely below the second feature, or only indicates that the first feature is lower than the second feature in horizontal height.

[0160] In the description of the specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example" or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present disclosure. In the specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the specification.

[0161] Other embodiments of the present disclosure will be apparent to those skilled in the art upon consideration of the specification and practice of the applications disclosed. The present application is intended to cover any variations, uses or adaptive changes of the present disclosure following the general principles of the present disclosure and including known or customary practices in the art not disclosed in the present disclosure. The specification and examples are only regarded as illustrative, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A hyperspectral band selection method based on spatial-spectral combination graph learning, characterized in that, The hyperspectral band selection method includes: The hyperspectral image cube is preprocessed to obtain a hyperspectral image data matrix; the hyperspectral image data matrix includes a set of spatial pixels and a set of spectral data points. The expression for the hyperspectral image data matrix includes: （1） in, X Represents a hyperspectral image data matrix; Y Represents a set of spatial pixels. , B This indicates the total number of bands in a hyperspectral image. ; R Represents a collection of hyperspectral image data; Y × B Indicates dimension; The spatial pixel set is divided into multiple regions, including multiple homogeneous regions and multiple non-homogeneous regions; the pixel affinity values ​​between the multiple homogeneous regions are calculated respectively, thereby constructing a spatial affinity matrix; The step of dividing the spatial pixel set into multiple regions, including multiple homogeneous regions and multiple non-homogeneous regions, and calculating the pixel affinity values ​​between the multiple homogeneous regions to construct a spatial affinity matrix includes: The spatial pixel set is divided into multiple regions using an entropy rate superpixel segmentation algorithm; similar pixels in each region are assigned to a homogeneous region, and dissimilar pixels are assigned to a non-homogeneous region; thus forming multiple homogeneous regions and multiple non-homogeneous regions. The pixel affinity values ​​between all pixels in the multiple homogeneous regions are calculated using the Gaussian kernel function, and the pixel affinity values ​​between all pixels in the multiple non-homogeneous regions are set to zero; thus constructing the spatial affinity matrix. The expression for the entropy rate superpixel segmentation algorithm includes: （2） in, Represents the entropy rate function; Indicates the balancing term; express and Weighting factors between them; Indicates minimization; The expressions for the homogeneous regions after segmentation include: （3） in, H Represents a hyperspectral image cube; to These represent the multiple homogeneous regions into which the data has been divided. Indicates constraint; A spectral objective function is set to be associated with the set of spectral data points, and multiple constraints are imposed on the spectral objective function to construct a spectral affinity matrix. A self-representation model is established by embedding the spatial affinity matrix and the spectral affinity matrix into the self-representation model and introducing a Laplace regularization term to obtain a graph self-representation model, which includes a coefficient matrix. The objective function is reconstructed for multiple neighboring bands corresponding to the coefficient matrix to obtain the optimal subset of bands to be selected.

2. The hyperspectral band selection method based on spatial-spectral combination graph learning according to claim 1, characterized in that, The expression for the spatial affinity matrix includes: （4） in, Represents the spatial affinity matrix. ; and They represent the first The vector of any two pixels in a homogeneous region; The parameters represent the Gaussian kernel function; Y × Y Indicates dimension; express and The Euclidean distance between them.

3. The hyperspectral band selection method based on spatial-spectral combination graph learning according to claim 2, characterized in that, In the step of setting a spectral objective function associated with the set of spectral data points and applying multiple constraints to the spectral objective function, the expression of the spectral objective function includes: （5） in, B This indicates the total number of bands in a hyperspectral image; Indicates the first i 1 spectral data point; Indicates the first 1 spectral data point; Represents spectral data points and spectral data points The Euclidean distance between them; Represents spectral data points and spectral data points Spectral affinity between them; This indicates the term used to adjust the Laplace regularization. Weight parameters; T Represents the transpose of a matrix; Represents the columns of a matrix; The 1 in the vector represents a column vector consisting entirely of 1s.

4. The hyperspectral band selection method based on spatial-spectral combination graph learning according to claim 3, characterized in that, The step of constructing the spectral affinity matrix includes: the expression of the spectral affinity matrix includes: （6） in, Represents the spectral affinity matrix. ;, B × B Indicates dimension; Indicates the first From the spectral data point to the _ _ k +1 Euclidean distance of spectral data points; , k They represent the first The spectral data point and the k 1 spectral data point, , , , Represents spectral data points and spectral data points The Euclidean distance between them.

5. The hyperspectral band selection method based on spatial-spectral combination graph learning according to claim 4, characterized in that, The step of establishing a self-representation model involves embedding both the spatial affinity matrix and the spectral affinity matrix into the self-representation model and introducing a Laplace regularization term to obtain a graph self-representation model, wherein the graph self-representation model includes a coefficient matrix. The expression of the graph self-representation model includes: （7） in, X Represents a hyperspectral image data matrix; and All represent equilibrium parameters; Represents the error matrix; Represents the Laplace matrix; Represents the coefficient matrix; Representing the error matrix transpose; tr Represents the trace of a matrix.

6. The hyperspectral band selection method based on spatial-spectral combination graph learning according to claim 5, characterized in that, The step of reconstructing the objective function of multiple neighboring bands corresponding to the coefficient matrix to obtain the optimal subset of bands to be selected includes: The reconstruction objective function is set, and the reconstruction objective function is used to iteratively optimize and solve multiple neighboring bands corresponding to the coefficient matrix. The optimal band subset is obtained by using the recursive relationship in the optimal solution.

7. The hyperspectral band selection method based on spatial-spectral combination graph learning according to claim 6, characterized in that, The expression for the reconstruction objective function includes: （8） in, Represents the coefficient matrix The One band; Represents the coefficient matrix The The combination of the left and right adjacent bands of a band. , and Represent the coefficient matrix respectively The The bands adjacent to each other, B ×2 represents the dimension. Represents a variable, when hour, satisfy ; Represents the reconstructed coefficient matrix; B This indicates the total number of bands in a hyperspectral image; Indicates the first Individual wave indexes; Indicates the first +1 band index; The expression for obtaining the optimal band subset includes: （9） in, Indicates the use of Obtain the optimal band subset; This represents the optimal solution obtained by reconstructing the objective function.

Images