Hyperspectral image classification method based on multi-frequency high-dimensional feature representation

Abstract

The invention discloses a hyperspectral image classification method based on multi-frequency high-dimensional feature representation. The method comprises the following steps: (1) acquiring an open source data set and preprocessing the open source data set; (2) carrying out space-spectrum fusion feature extraction based on frequency domain components and then carrying out feature segmentation; (3) processing a result obtained in the step (2) through a classification neural network; (4) obtaining a classification result; according to the method, the problems of complex textures and mixed pixels are effectively solved, and the classification precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of hyperspectral image technology, and particularly relates to a hyperspectral image classification method based on multi-frequency high-dimensional feature representation. Background Art

[0002] Currently, the mainstream HSI classification methods can be divided into traditional machine learning methods and convolutional neural network-based methods. Traditional machine learning methods use handcrafted features to train classifiers, which require high domain expertise and engineering skills, and it is difficult to optimize the feature design for different datasets, resulting in difficulty in balancing the robustness and discrimination ability of features. In addition, a single feature is difficult to comprehensively represent image information, and a combination of multiple features is required, and this feature combination depends on artificial design, increasing complexity. To overcome the limitations of traditional methods, CNN-based methods have been proposed to automatically learn features from data in a hierarchical manner and build a model with continuously growing semantic layers until a suitable feature representation is obtained. The CNN architectures for HSI classification are mainly divided into three types: spectral CNN, spatial CNN, and spectral-spatial CNN.

[0003] The limitations of the spectral CNN model are that it mainly focuses on spectral features, ignores spatial context, and is relatively sensitive to changes in spectral features, affecting its robustness in diverse practical scenarios. The limitations of the spatial CNN model are that it utilizes spectral information insufficiently, is prone to overfitting, and has limited generalization ability. The spectral-spatial CNN model depends on the design of local receptive fields and convolutional kernels, which may lead to the loss of spatial information in complex texture and boundary regions, and lacks explicit robust processing of noise and mixed pixels. At the same time, simple convolutional operations cannot fully capture the complexity of spatial-spectral feature interactions and cannot effectively fuse multi-dimensional spectral and spatial information. Summary of the Invention

[0004] Object of the Invention: The object of the present invention is to provide a hyperspectral image classification method based on multi-frequency high-dimensional feature representation, which solves the problem of insufficient extraction of complex texture and boundary information in hyperspectral images; solves the problem of insufficient fusion of spatial and spectral features in neural network-based hyperspectral image classification methods; and solves the problem of robustness of hyperspectral image feature extraction to noise interference and mixed pixel processing.

[0005] Technical Solution: A hyperspectral image classification method based on multi-frequency high-dimensional feature representation according to the present invention includes the following steps:

[0006] (1) Obtain an open-source dataset and perform preprocessing;

[0007] (2) Extract spatial-spectral fusion features based on frequency-domain components and then perform feature segmentation;

[0008] (3) Process the result obtained in step (2) through a classification neural network;

[0009] (4) Obtain the classification result.

[0010] Furthermore, in step (1), the preprocessing is specifically as follows: The principal component analysis technique is used to perform dimensionality reduction preprocessing in the spectral dimension of the original data.

[0011] Furthermore, in step (2), the spatial-spectral fusion feature extraction based on frequency domain components includes the following steps:

[0012] (S21) Let I ∈ R H×W×1 represent a certain wavelength band in the hyperspectral image X′. Each pixel in I is regarded as a discrete sampling of a continuous binary function f(x, y), where (x, y) is the pixel coordinate;

[0013] Use the Fourier embedding function to map the two-dimensional coordinates to a high-dimensional space. Through the combination of sine and cosine functions, each coordinate point generates a high-dimensional feature vector containing spatial position information and frequency information. The formula is as follows:

[0014] For coordinates x and y, the definition of the Fourier embedding function is:

[0015]

[0016] where γ(·): R → R 1×(2n+1) is the Fourier embedding function, which realizes the uniaxial position encoding transformation; n ∈ N is the maximum frequency number of Fourier embedding, and the constant term is used to normalize the amplitude of the embedding vector; map each coordinate x and y to a (2n + 1)-dimensional high-dimensional space;

[0017] (S22) Calculate to obtain the two-dimensional feature matrix X T Y ∈ R (2n+1)×(2n+1) , and each element in the matrix represents the inner product of Fourier basis functions; the inner product follows the orthogonality principle, that is:

[0018] X T Y = ∫[γ(x)] T [γ(y)]dx dy

[0019] where each element in the matrix is the inner product result of γ(x) and γ(y); each element in the matrix X T Y represents the projection of the binary function on the Fourier basis, that is, the matrix reflects the distribution of the image in the spatial frequency domain;

[0020] Flatten the two-dimensional inner product matrix X T Y into a one-dimensional feature vector to obtain the final position encoding MFF(x, y). The formula is as follows:

[0021] MFF(x, y) = flat(X T Y)

[0022] Wherein, Through the flattening operation, the two-dimensional inner product matrix is converted into a one-dimensional high-dimensional feature vector;

[0023] (S23) Let the spectral information of each pixel be r(x, y) ∈ R C , which is composed of the reflectance values of its respective bands, and the formula is as follows:

[0024] r(x, y) = [r 1 (x, y), r 2 (x, y), …, r C (x, y)]

[0025] By fusing the position encoding and the spectral information, the spatial-spectral feature vector of each pixel is formed; then the spatial-spectral fusion feature vector F(x, y) of the pixel (x, y) in band I is expressed as:

[0026] F(x, y) = r I (x, y) · MFF(x, y)

[0027] Wherein, is the feature vector after spatial-spectral fusion; the feature vectors F(x, y) of all pixels are arranged according to the pixel positions to obtain the spatial-spectral features of the entire band I Then the features of the entire hyperspectral image can be expressed as

[0028] Further, in step (2), the feature segmentation is specifically as follows: Extract the corresponding feature blocks centered around each pixel point. For the edge pixels, zero padding is used before extraction; wherein, the true label of each feature block is determined by the label of the central pixel; Let the size of each segmented feature block be S × S × C(2n + 1) 2 , and the corresponding relationship between the original hyperspectral data and the labels is converted into the corresponding relationship between multiple feature blocks and the labels.

[0029] Further, step (3) is specifically as follows: The classification neural network includes 3 three-dimensional convolutional blocks, 1 two-dimensional convolutional block, 2 fully connected layers, and 1 linear layer; in the three-dimensional convolutional block, first, the three-dimensional convolutional layer processes the features in both the spatial dimension and the spectral dimension, then the batch normalization layer is used to accelerate convergence, and finally, the ReLU activation function is passed through; the structure of the two-dimensional convolutional block is similar to that of the three-dimensional convolutional block, using two-dimensional convolution to process spatial features, flattening the features obtained by convolution into a one-dimensional vector and then inputting it into the fully connected layer, and using dropout to prevent overfitting; finally, a classification score vector of the sample is obtained through 1 linear layer, and then the output is transformed into a probability distribution through the softmax activation function; among them, cross-entropy loss is used as the objective function during training to calculate the difference between the predicted probability and the true label.

[0030] A hyperspectral image classification system based on multi-frequency high-dimensional feature representation according to the present invention includes:

[0031] A preprocessing module: used to obtain an open-source data set and perform preprocessing;

[0032] An extraction and segmentation module: used to perform feature extraction based on the spatial-spectral fusion features of frequency domain components and then perform feature segmentation;

[0033] A classification neural network module: used to process the results obtained in the extraction and segmentation module through a classification neural network;

[0034] A classification result module: used to obtain a classification result.

[0035] Further, in the preprocessing module, the preprocessing is specifically as follows: The principal component analysis technique is used to perform dimensionality reduction preprocessing in the spectral dimension of the original data.

[0036] Further, in the extraction and segmentation module, the spatial-spectral fusion feature extraction based on frequency domain components is specifically as follows:

[0037] First, let I ∈ R H×W×1 represent a certain wavelength band in the hyperspectral image X′, and each pixel in I is regarded as a discrete sampling of a continuous binary function f(x, y), where (x, y) is the pixel coordinate;

[0038] The Fourier embedding function is used to map the two-dimensional coordinates to a high-dimensional space. Through the combination of sine and cosine functions, each coordinate point generates a high-dimensional feature vector containing spatial position information and frequency information. The formula is as follows:

[0039] For coordinates x and y, the definition of the Fourier embedding function is:

[0040]

[0041] where γ(·): R → R1×(2n+1) is the Fourier embedding function, which realizes the single-axis position encoding transformation; n∈N is the maximum frequency number of Fourier embedding, the constant term Used to normalize the magnitude of the embedding vector; map each coordinate x and y to a (2n+1)-dimensional high-dimensional space;

[0042] Then, the two-dimensional feature matrix X is calculated T Y∈R (2n+1)×(2n+1) , each element in the matrix represents the inner product of the Fourier basis function; the inner product follows the orthogonality principle, that is:

[0043] X T Y = ∫[γ(x)] T [γ(y)]dxdy

[0044] Each element in the matrix is ​​the inner product of γ(x) and γ(y); the matrix X T Each element in Y represents the projection of a binary function on the Fourier basis, that is, the matrix reflects the distribution of the image in the spatial frequency domain;

[0045] The two-dimensional inner product matrix X T Y is flattened into a one-dimensional feature vector to obtain the final position code MFF(x,y), the formula is as follows:

[0046] MFF(x,y)=flat(X T Y)

[0047] in, Through the flattening operation, the two-dimensional inner product matrix is ​​converted into a one-dimensional high-dimensional feature vector;

[0048] Finally, let the spectral information of each pixel be r(x,y)∈R C , which is composed of the reflectance values ​​of each band, and the formula is as follows:

[0049] r(x,y)=[r 1 (x,y),r 2 (x,y),…,r C (x,y)]

[0050] By fusing the position code and spectral information, the spatial-spectral feature vector of each pixel is formed; then the spatial-spectral fusion feature vector F(x, y) of the pixel (x, y) in band I is expressed as:

[0051] F(x,y)=r I (x,y)·MFF(x,y)

[0052] in, It is the feature vector after spatial-spectral fusion; the feature vectors F(x, y) of all pixels are arranged according to the pixel position to obtain the spatial-spectral characteristics of the entire band I Then the characteristics of the entire hyperspectral image can be expressed as

[0053] Furthermore, in the extraction and segmentation module, the feature segmentation is as follows: extract the corresponding feature block around each pixel point as the center, and extract the edge pixels after filling with zero values; the true value label of each feature block is determined by the label of the center pixel; suppose the size of each feature block after segmentation is S×S×C(2n+1) 2 , the correspondence between the original hyperspectral data and the label is converted into the correspondence between multiple feature blocks and the label.

[0054] Furthermore, in the classification neural network module, the details are as follows: the classification neural network includes 3 three-dimensional convolution blocks, 1 two-dimensional convolution block, 2 fully connected layers and 1 linear layer; in the three-dimensional convolution block, the features are first processed in the spatial dimension and spectral dimension at the same time through the three-dimensional convolution layer, and then the batch normalization layer is used to accelerate the convergence, and finally the ReLU activation function is passed; the structure of the two-dimensional convolution block is similar to the three-dimensional convolution block, and two-dimensional convolution is used to process spatial features, and the features passed through the convolution are flattened into a one-dimensional vector and input into the fully connected layer, and dropout is used to prevent overfitting; finally, the classification score vector of the sample is obtained through a linear layer, and then the output is converted into a probability distribution through a softmax activation function; among them, the cross entropy loss is used as the objective function in training to calculate the difference between the predicted probability and the true label.

[0055] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: Fourier embedding is used to perform multi-frequency encoding on each pixel position of the hyperspectral image, and the original low-dimensional coordinate space is mapped to a high-dimensional space. By capturing information of different frequencies (low frequency reflects the global structure, and high frequency depicts local details), the network's ability to capture texture and edge information is optimized, so that the classification model performs better than existing methods in the edge area of ​​the object. And the combination of multi-frequency information can effectively separate useful signals and noise, and improve the stability of the model under noisy conditions. Feature representation that does not require training, the Fourier embedding process is parameter-free and does not require training, which reduces the computational burden and avoids the parameter adjustment problem in traditional methods. The high-dimensional embedded features are combined with the spectral information of the hyperspectral image to form a unique fusion feature representation. This high-dimensional feature can be used as the input of a deep neural network, which helps to learn complex nonlinear features more efficiently, effectively handle problems with complex textures and mixed pixels, and improve classification accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1It is a schematic diagram of the process of the present invention;

[0057] Figure 2 It is a schematic diagram of the network structure prototype of the present invention. DETAILED DESCRIPTION

[0058] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0059] like Figure 1 As shown, the embodiment of the present invention provides a hyperspectral image classification method based on multi-frequency high-dimensional feature representation, comprising the following steps:

[0060] (1) Obtain open source datasets and preprocess them. The preprocessing is as follows: Take the Indian Pines dataset, which is a commonly used and public dataset in the field, as an example. The hyperspectral image of this dataset contains 145×145 pixels and 220 spectral bands, recording the information of spectral wavelengths within 400 to 2500nm. After removing the 20 bands destroyed by the water absorption effect, experiments are conducted on the remaining 200 bands. There are 10,249 ground object pixels for classification, including 16 categories. 10% of the pixels in each category are randomly selected as the training set, and the remaining 90% are used as the test set. The principal component analysis technique is used to perform dimensionality reduction preprocessing on the spectral dimension of the original data. The specific process is as follows: Assume that a hyperspectral image X with a given resolution of H×W×B is used as input, where H, W, and B are the height, width, and number of spectral bands, respectively. Because it is a pixel-level classification task, each pixel in X forms a one-dimensional one-hot label vector Y=(y 1 ,y 2 ,…,y N ), where N represents the number of categories. PCA technology is used to reduce the number of bands to C while keeping the spatial dimension unchanged, and the reduced-dimensional hyperspectral image X′ is obtained, and the resolution becomes H×W×C. Hyperspectral data is preprocessed to eliminate redundant bands and retain spatial information that is critical to the classification task.

[0061] (2) Extracting spatial-spectral fusion features based on frequency domain components and then performing feature segmentation; Extracting spatial-spectral fusion features based on frequency domain components includes the following steps: In order to construct a multi-frequency high-dimensional feature representation of the hyperspectral image, use I∈R H ×W×1 Represents a certain band in the hyperspectral image X′, and regards each pixel in I as a discrete sampling of a continuous binary function f(x,y), where (x,y) is the pixel coordinate. The goal is to map each pixel coordinate into a high-dimensional space through Fourier embedding to form a feature representation that can capture spatial and frequency information.

[0062] (S21) Use the Fourier embedding function to map the two-dimensional coordinates to a high-dimensional space. Through the combination of sine and cosine functions, each coordinate point generates a high-dimensional feature vector containing spatial position information and frequency information. The formula is as follows:

[0063] For coordinates x and y, the Fourier embedding function is defined as:

[0064]

[0065] Among them, γ(·):R→R 1×(2n+1) is the Fourier embedding function, which realizes the single-axis position encoding transformation; n∈N is the maximum frequency number of Fourier embedding, the constant term Used to normalize the amplitude of the embedded vector; map each coordinate x and y to a (2n+1)-dimensional high-dimensional space; each dimension in the space corresponds to a frequency component in the Fourier transform, which can capture the periodic structure in the space.

[0066] (S22) Calculate the two-dimensional feature matrix X T Y∈R (2n+1)×(2n+1) , each element in the matrix represents the inner product of the Fourier basis function; due to the orthogonality of the Fourier basis, the inner product follows the orthogonality principle, that is:

[0067] X T Y = ∫[γ(x)] T [γ(y)]dx dy

[0068] Each element in the matrix is ​​the inner product of γ(x) and γ(y). Due to the orthogonality of the Fourier basis, the matrix X T Each element in Y represents the projection of a binary function (e.g., each pixel in the image) on the Fourier basis, i.e., the matrix reflects the distribution of the image in the spatial frequency domain;

[0069] The two-dimensional inner product matrix X T Y is flattened into a one-dimensional feature vector to obtain the final position code MFF(x,y), the formula is as follows:

[0070] MFF(x,y)=flat(X T Y)

[0071] in, Through the flattening operation, the two-dimensional inner product matrix is ​​converted into a one-dimensional high-dimensional feature vector; through the flattening operation, the two-dimensional inner product matrix is ​​converted into a one-dimensional high-dimensional feature vector. The core significance of this operation is to map the input coordinates (x, y) into a high-dimensional space through Fourier embedding, and each coordinate point corresponds to a high-dimensional feature vector. These features not only contain spatial position information, but also contain structural information in the frequency domain, which can help the neural network capture the complex structure of hyperspectral images. The features of each band can be composed of feature vectors of all pixel positions.

[0072] (S23) Each pixel of the hyperspectral image not only has spatial coordinate information, but also contains spectral information of multiple bands; let the spectral information of each pixel be r(x,y)∈R C , which is composed of the reflectance values ​​of each band, and the formula is as follows:

[0073] r(x,y)=[r 1 (x,y),r 2 (x,y),…,r C (x,y)]

[0074] In order to combine spatial information and spectral information, the spatial-spectral feature vector of each pixel is formed by fusing the position encoding and spectral information. Then the spatial-spectral fusion feature vector F(x, y) of the pixel (x, y) in band I is expressed as:

[0075] F(x,y)=r I (x,y)·MFF(x,y)

[0076] in, It is the feature vector after space-spectrum fusion; in this way, the spatial position information is combined with the spectral reflectance information to obtain a feature vector with rich space-frequency structure information.

[0077] Arrange the feature vectors F(x,y) of all pixels according to the pixel position to obtain the spatial-spectral characteristics of the entire band I Then the characteristics of the entire hyperspectral image can be expressed as

[0078] The feature segmentation is as follows: In order to reduce the computational burden and facilitate neural network classification, the present invention adopts a feature segmentation strategy in the spatial dimension, that is, to divide the feature F into multiple feature blocks of the same size and overlap each other. Specifically, the corresponding feature block is extracted around each pixel point as the center, and the edge pixels are extracted after being filled with zero values. The true value label of each feature block is determined by the label of its central pixel, which effectively avoids the risk of test data leakage. The size of each feature block after segmentation is S×S×C(2n+1) 2, the correspondence between the original hyperspectral data and the label is converted into the correspondence between multiple feature blocks and labels, so as to use the subsequent neural network for classification.

[0079] (3) Processing the result obtained in step (2) by a classification neural network; specifically, Figure 2 As shown in the figure, the entire classification network includes 3 3D convolution blocks, 1 2D convolution block, 2 fully connected layers and 1 linear layer. In the 3D convolution block, the features are first processed in both the spatial and spectral dimensions by the 3D convolution layer, and then the batch normalization (BN) layer is used to accelerate the convergence speed, and finally the ReLU activation function is passed. The structure of the 2D convolution block is similar to that of the 3D convolution block, and 2D convolution is used to process spatial features. The features that pass through the convolution are flattened into a one-dimensional vector and input into the fully connected layer, and dropout is used to improve the generalization performance of the model and further prevent overfitting. Finally, the classification score vector of the sample is obtained through a layer of linear layer, and the output is converted into a probability distribution through the softmax activation function. In training, the cross-entropy loss (Cross-Entropy Loss) is used as the objective function to calculate the difference between the predicted probability and the true label. The formula is as follows:

[0080]

[0081] Where N represents the total number of classification categories; y i is the one-hot encoding of the true label. If the sample belongs to the i-th category, then y i =1, otherwise y i =0; is the probability of the i-th class predicted by the model.

[0082] (4) Obtain classification results.

[0083] The embodiment of the present invention further provides a hyperspectral image classification system based on multi-frequency high-dimensional feature representation, comprising:

[0084] Preprocessing module: used to obtain open source data sets and perform preprocessing; the preprocessing is as follows: principal component analysis technology is used to perform dimension reduction preprocessing on the spectral dimension of the original data.

[0085] Extraction and segmentation module: used for spatial-spectral fusion feature extraction based on frequency domain components and then feature segmentation; the spatial-spectral fusion feature extraction based on frequency domain components is as follows:

[0086] First, the Fourier embedding function is used to map the two-dimensional coordinates to a high-dimensional space. Through the combination of sine and cosine functions, a high-dimensional feature vector containing spatial position information and frequency information is generated for each coordinate point. The formula is as follows:

[0087] For coordinates x and y, the Fourier embedding function is defined as:

[0088]

[0089] Among them, γ(·):R→R 1×(2n+1) is the Fourier embedding function, which realizes the single-axis position encoding transformation; n∈N is the maximum frequency number of Fourier embedding, the constant term Used to normalize the magnitude of the embedding vector; map each coordinate x and y to a (2n+1)-dimensional high-dimensional space;

[0090] Then, the two-dimensional feature matrix X is calculated T Y∈R (2n+1)×(2n+1) , each element in the matrix represents the inner product of the Fourier basis function; the inner product follows the orthogonality principle, that is:

[0091] X T Y = ∫[γ(x)] T [γ(y)]dx dy

[0092] Each element in the matrix is ​​the inner product of γ(x) and γ(y); the matrix X T Each element in Y represents the projection of a binary function on the Fourier basis, that is, the matrix reflects the distribution of the image in the spatial frequency domain;

[0093] The two-dimensional inner product matrix X T Y is flattened into a one-dimensional feature vector to obtain the final position code MFF(x,y), the formula is as follows:

[0094] MFF(x,y)=flat(X T Y)

[0095] in, Through the flattening operation, the two-dimensional inner product matrix is ​​converted into a one-dimensional high-dimensional feature vector;

[0096] Finally, let the spectral information of each pixel be r(x,y)∈R C , which is composed of the reflectance values ​​of each band, and the formula is as follows:

[0097] r(x,y)=[r 1 (x,y),r 2 (x,y),…,r C (x,y)]

[0098] By fusing the position code and spectral information, the spatial-spectral feature vector of each pixel is formed; then the spatial-spectral fusion feature vector F(x, y) of the pixel (x, y) in band I is expressed as:

[0099] F(x,y)=rI (x,y)·MFF(x,y)

[0100] in, It is the feature vector after spatial-spectral fusion; the feature vectors F(x, y) of all pixels are arranged according to the pixel position to obtain the spatial-spectral characteristics of the entire band I Then the characteristics of the entire hyperspectral image can be expressed as

[0101] The feature segmentation is as follows: extract the corresponding feature block around each pixel point as the center, and extract the edge pixels after filling with zero values; the true value label of each feature block is determined by the label of the central pixel; suppose the size of each feature block after segmentation is S×S×C(2n+1) 2 , the correspondence between the original hyperspectral data and the label is converted into the correspondence between multiple feature blocks and the label.

[0102] Classification neural network module: used to process the results obtained in the extraction and segmentation module through a classification neural network; specifically, the classification neural network includes 3 three-dimensional convolution blocks, 1 two-dimensional convolution block, 2 fully connected layers, and 1 linear layer; in the three-dimensional convolution block, the features are first processed in both the spatial and spectral dimensions through a three-dimensional convolution layer, and then a batch normalization layer is used to accelerate convergence, and finally a ReLU activation function is used; the structure of the two-dimensional convolution block is similar to that of the three-dimensional convolution block, and two-dimensional convolution is used to process spatial features, and the features passed through the convolution are flattened into a one-dimensional vector and then input into the fully connected layer, and dropout is used to prevent overfitting; finally, a classification score vector of the sample is obtained through a linear layer, and then the output is converted into a probability distribution through a softmax activation function; in training, cross entropy loss is used as the objective function to calculate the difference between the predicted probability and the true label.

[0103] Classification result module: used to obtain classification results.

Claims

1. A hyperspectral image classification method based on multi-frequency high-dimensional feature representation, characterized in that: The following steps are involved: (1) Obtain open source datasets and preprocess them; (2) Extract spatial-spectral fusion features based on frequency domain components and then perform feature segmentation; (3) Processing the results obtained in step (2) through a classification neural network; (4) Obtain classification results.

2. The hyperspectral image classification method based on multi-frequency high-dimensional feature representation according to claim 1 is characterized in that: In step (1), the preprocessing is specifically as follows: principal component analysis technology is used to perform dimension reduction preprocessing on the spectral dimension of the original data.

3. The hyperspectral image classification method based on multi-frequency high-dimensional feature representation according to claim 1 is characterized in that: In step (2), the spatial-spectral fusion feature extraction based on the frequency domain component includes the following steps: (S21) Let I∈R H×W×1 Represents a certain band in the hyperspectral image X′, and regards each pixel in I as a discrete sampling of the continuous binary function f(x, y), where (x, y) is the pixel coordinate; the two-dimensional coordinates are mapped to a high-dimensional space using the Fourier embedding function, and a high-dimensional feature vector containing spatial position information and frequency information is generated for each coordinate point through the combination of sine and cosine functions. The formula is as follows: For coordinates x and y, the Fourier embedding function is defined as: Among them, γ(·):R→R 1×(2n+1) is the Fourier embedding function, which realizes the single-axis position encoding transformation; n∈N is the maximum frequency number of Fourier embedding, the constant term Used to normalize the magnitude of the embedding vector; map each coordinate x and y to a (2n+1)-dimensional high-dimensional space; (S22) Calculate the two-dimensional feature matrix X T Y∈R (2n+1)×(2n+1) , each element in the matrix represents the inner product of the Fourier basis function; the inner product follows the orthogonality principle, that is: X T Y=∫[γ(x)] T [γ(y)]dx to Each element in the matrix is ​​the inner product of γ(x) and γ(y); T Each element in Y represents the projection of a binary function on the Fourier basis, that is, the matrix reflects the distribution of the image in the spatial frequency domain; The two-dimensional inner product matrix X T Y is flattened into a one-dimensional feature vector to obtain the final position code MFF(x,y), the formula is as follows: MFF(x,y)=flat(X T Y) in, Through the flattening operation, the two-dimensional inner product matrix is ​​converted into a one-dimensional high-dimensional feature vector; (S23) Let the spectral information of each pixel be r(x,y)∈R C , which is composed of the reflectance values ​​of each band, and the formula is as follows: r(x,y)=[r1(x,y),r2(x,y),…,r C (x,y)] By fusing the position code and spectral information, the spatial-spectral feature vector of each pixel is formed; then the spatial-spectral fusion feature vector F(x, y) of the pixel (x, y) in band I is expressed as: F(x,y)=r I (x,y)·MFF(x,y) in, It is the feature vector after spatial-spectral fusion; the feature vectors F(x, y) of all pixels are arranged according to the pixel position to obtain the spatial-spectral characteristics of the entire band I Then the characteristics of the entire hyperspectral image can be expressed as 4. The hyperspectral image classification method based on multi-frequency high-dimensional feature representation according to claim 1 is characterized in that: In step (2), the feature segmentation is as follows: extract the corresponding feature block around each pixel point as the center, and extract the edge pixels after filling with zero values; the true value label of each feature block is determined by the label of the center pixel; suppose the size of each feature block after segmentation is S×S×C(2n+1) 2 , the correspondence between the original hyperspectral data and the label is converted into the correspondence between multiple feature blocks and the label.

5. The hyperspectral image classification method based on multi-frequency high-dimensional feature representation according to claim 1 is characterized in that: Step (3) is as follows: the classification neural network includes 3 three-dimensional convolution blocks, 1 two-dimensional convolution block, 2 fully connected layers and 1 linear layer; in the three-dimensional convolution block, the features are first processed simultaneously in the spatial dimension and the spectral dimension through the three-dimensional convolution layer, and then the batch normalization layer is used to accelerate the convergence, and finally the ReLU activation function is passed; the structure of the two-dimensional convolution block is similar to the three-dimensional convolution block, and the spatial features are processed by two-dimensional convolution, and the features passed through the convolution are flattened into a one-dimensional vector and then input into the fully connected layer, and dropout is used to prevent overfitting; finally, the classification score vector of the sample is obtained through a linear layer, and then the output is converted into a probability distribution through a softmax activation function; wherein, the cross entropy loss is used as the objective function in the training to calculate the difference between the predicted probability and the true label.

6. A hyperspectral image classification system based on multi-frequency high-dimensional feature representation, characterized in that: include: Preprocessing module: used to obtain open source data sets and perform preprocessing; Extraction and segmentation module: used for spatial-spectral fusion feature extraction based on frequency domain components and then feature segmentation; Classification neural network module: used to process the results obtained in the extraction and segmentation module through the classification neural network; Classification result module: used to obtain classification results.

7. The hyperspectral image classification system based on multi-frequency high-dimensional feature representation according to claim 6 is characterized in that: In the preprocessing module, the preprocessing is as follows: principal component analysis technology is used to perform dimension reduction preprocessing on the spectral dimension of the original data.

8. The hyperspectral image classification system based on multi-frequency high-dimensional feature representation according to claim 6 is characterized in that: In the extraction and segmentation module, the spatial-spectral fusion feature extraction based on the frequency domain component is as follows: First, let I∈R H×W×1 Represents a certain band in the hyperspectral image X′, and regards each pixel in I as a discrete sampling of a continuous binary function f(x, y), where (x, y) is the pixel coordinate; Use the Fourier embedding function to map the two-dimensional coordinates to a high-dimensional space. Through the combination of sine and cosine functions, each coordinate point generates a high-dimensional feature vector containing spatial position information and frequency information. The formula is as follows: For coordinates x and y, the Fourier embedding function is defined as: Among them, γ(·):R→R 1×(2n+1) is the Fourier embedding function, which realizes the single-axis position encoding transformation; n∈N is the maximum frequency number of Fourier embedding, the constant term Used to normalize the magnitude of the embedding vector; map each coordinate x and y to a (2n+1)-dimensional high-dimensional space; Then, the two-dimensional feature matrix X is calculated T Y∈R (2n+1)×(2n+1) , each element in the matrix represents the inner product of the Fourier basis function; the inner product follows the orthogonality principle, that is: X T Y=∫[γ(x)] T [γ(y)]dx to Each element in the matrix is ​​the inner product of γ(x) and γ(y); the matrix X T Each element in Y represents the projection of a binary function on the Fourier basis, that is, the matrix reflects the distribution of the image in the spatial frequency domain; The two-dimensional inner product matrix X T Y is flattened into a one-dimensional feature vector to obtain the final position code MFF(x,y), the formula is as follows: MFF(x,y)=flat(X T Y) in, Through the flattening operation, the two-dimensional inner product matrix is ​​converted into a one-dimensional high-dimensional feature vector; Finally, let the spectral information of each pixel be r(x,y)∈R C , which is composed of the reflectance values ​​of each band, and the formula is as follows: r(x,y)=[r1(x,y),r2(x,y),…,r C (x,y)] By fusing the position code and spectral information, the spatial-spectral feature vector of each pixel is formed; then the spatial-spectral fusion feature vector F(x, y) of the pixel (x, y) in band I is expressed as: F(x,y)=r I (x,y)·MFF(x,y) in, It is the feature vector after spatial-spectral fusion; the feature vectors F(x, y) of all pixels are arranged according to the pixel position to obtain the spatial-spectral characteristics of the entire band I Then the characteristics of the entire hyperspectral image can be expressed as 9. The hyperspectral image classification system based on multi-frequency high-dimensional feature representation according to claim 6, characterized in that: In the extraction and segmentation module, the feature segmentation is as follows: extract the corresponding feature block around each pixel point as the center, and extract the edge pixels after filling with zero values; the true value label of each feature block is determined by the label of the center pixel; suppose the size of each feature block after segmentation is S×S×C(2n+1) 2 , the correspondence between the original hyperspectral data and the label is converted into the correspondence between multiple feature blocks and the label.

10. The hyperspectral image classification system based on multi-frequency high-dimensional feature representation according to claim 6, characterized in that: In the classification neural network module, the details are as follows: the classification neural network includes 3 three-dimensional convolution blocks, 1 two-dimensional convolution block, 2 fully connected layers and 1 linear layer; in the three-dimensional convolution block, the features are first processed in the spatial dimension and spectral dimension at the same time through the three-dimensional convolution layer, and then the batch normalization layer is used to accelerate convergence, and finally the ReLU activation function is passed; the structure of the two-dimensional convolution block is similar to the three-dimensional convolution block, and two-dimensional convolution is used to process spatial features. The features passed through the convolution are flattened into a one-dimensional vector and then input into the fully connected layer, and dropout is used to prevent overfitting; finally, the classification score vector of the sample is obtained through a linear layer, and then the output is converted into a probability distribution through the softmax activation function; among them, the cross entropy loss is used as the objective function in training to calculate the difference between the predicted probability and the true label.

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