Hyperspectral image feature extraction method based on geodesic space-spectrum collaborative graph learning

Abstract

The present invention belongs to the technical field of remote sensing image processing, and relates to a hyperspectral image feature extraction method based on geodesic space-spectrum collaborative graph learning. The method uses a collaborative representation method to learn the global collaborative representation relationship between hyperspectral image pixels, and characterizes the local manifold structure of hyperspectral data through local constraints to improve the discrimination ability of the coefficient matrix. In addition, spatial proximity information and spectral information based on geodesic distance are integrated into the regularization term of the global collaborative representation model constructed above, and a space-spectrum collaborative representation coefficient matrix of geodesic metric constraints is obtained to fully reveal and utilize the space-spectrum proximity structure characteristics of hyperspectral data. On this basis, an unsupervised weighted graph is constructed using the representation coefficient matrix, and the optimal hyperspectral low-dimensional feature projection matrix is ​​derived based on graph embedding theory to map the original hyperspectral image to a low-dimensional feature subspace. Compared with other feature extraction methods, this method can provide more valuable feature information, effectively explore the complex intrinsic characteristics of hyperspectral data, and thus achieve higher classification accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of remote sensing image processing and relates to a hyperspectral image feature extraction method based on geodesic space-spectrum collaborative graph learning. Background Art

[0002] Hyperspectral images are composed of the spectral characteristics of objects reflected by dozens or hundreds of bands received by imaging spectrometers. They have good spectral resolution and spatial resolution, and provide a powerful detection method for fine classification of objects. At present, they have been widely used in agricultural management, atmospheric monitoring, urban planning, mineral exploration and other fields. However, hyperspectral data has the characteristics of large data volume, many bands, and strong correlation between bands. Traditional methods are prone to "dimensionality disaster" problems. Therefore, how to reduce the number of bands and retain useful information as much as possible has become a hot research issue in the field of hyperspectral remote sensing.

[0003] Feature extraction is an effective means to solve the problems of high redundancy, strong correlation between bands and large data volume of hyperspectral images. It uses mapping or transformation to convert the original high-dimensional data information into a low-dimensional feature space. The process is to process, process and optimize the features of the original data according to certain optimization rules, while reducing the data dimension, retaining the valuable information in the data, which is convenient for subsequent classification or other processing processes.

[0004] Researchers have proposed a large number of feature extraction methods, and continue to combine new theories and new technologies to expand the scope of feature extraction methods. However, hyperspectral images not only contain rich spectral information, but also have good spatial information. Feature extraction based only on spectral information may lead to insufficient or over-classification. The feature extraction method based on manifold learning introduces spatial information as compensation for spectral information to facilitate classification tasks. However, the traditional use of spatial information usually utilizes the spatial neighborhood relationship of hyperspectral data in a specific area, while ignoring the influence of spatial information in the construction of the adjacency graph and the spatial and spectral correlation of the entire data, so that the effective information of the hyperspectral image cannot be fully extracted.

[0005] Therefore, designing a feature extraction method for hyperspectral images based on geodesic space-spectrum synergistic graph learning is of great significance for the subsequent processing in the field of hyperspectral image processing. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide a hyperspectral image feature extraction method based on geodesic space-spectrum collaborative graph learning. The collaborative representation method is used to learn the global information of the hyperspectral image, and the local constraint is used to learn the local manifold structure of the hyperspectral data to improve the discrimination ability of the coefficient matrix. In addition, the spatial information and the spectral information are simultaneously merged into the regularization constraint term of the collaborative representation model, and the geodesic spectral information and spatial information of the hyperspectral data are fully utilized. Then, the representation coefficient matrix is ​​obtained to construct an unsupervised weighted graph. After the graph is constructed, the optimal projection matrix is ​​derived using the graph embedding theory to map the original hyperspectral image to a low-dimensional feature subspace.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A feature extraction method for a hyperspectral image based on collaborative representation of spatial-spectral information, the method comprising the following steps:

[0009] Step 1) using collaborative representation method and local constraints to learn the global information and local manifold structure information of the hyperspectral image;

[0010] Step 2) jointly embedding the spatial information and the geodesic-based spectral information into a collaborative representation regularization term;

[0011] Step 3) Based on the obtained geodesic space-spectrum synergy representation coefficients, a geodesic space-spectrum synergy graph is constructed, and then the graph embedding framework is used to solve the generalized eigenvalue decomposition problem to obtain the optimal projection matrix and obtain the low-dimensional feature subspace of the hyperspectral image data.

[0012] Furthermore, step 1) includes the following specific contents:

[0013] Assume there is a hyperspectral dataset N represents the number of pixels, d is the number of spectral bands of the hyperspectral image.

[0014] Using collaborative representation to learn the global information of hyperspectral images, for each pixel xi in the dataset X, the typical collaborative representation method can be mathematically expressed as an l2 norm optimization problem:

[0015]

[0016] Among them, X i Does not contain x i A d×(N-1)-dimensional dictionary, λ>0 is a regularization parameter used to balance the remaining terms of the collaborative representation and the regularization term

[0017] In collaborative representation, each pixel is collaboratively represented by all other pixels in all classes, which can reveal the collaborative representation relationship between all pixels, but cannot effectively characterize the local manifold structure of the data. After being projected into a low-dimensional subspace, it cannot maintain its inherent manifold distribution structure and discrimination ability. Therefore, local constraints are introduced in collaborative representation to characterize the local neighborhood structure relationship between different pixels:

[0018]

[0019] In the formula, is the pixel x i If there are k nearest neighbors, the values ​​of the remaining Nk pixels are set to zero, and μ>0 is the regularization parameter.

[0020] Furthermore, step 2) includes the following specific contents:

[0021] The above research only studies hyperspectral images from the perspective of spectral features. However, in addition to spectral features, hyperspectral images also contain rich spatial geometric information. Spatial information is used to characterize the location of objects in the image and the spatial position relationship between different objects. The use of spatial information can enhance the ability to describe and distinguish objects in the image. However, the spectral information and spatial information of hyperspectral images are not independent of each other. Traditional spatial information is usually used to utilize the spatial neighborhood relationship of hyperspectral data in a specific area, while ignoring the influence of spatial information in the construction of the adjacency graph and the spatial and spectral correlation of the entire data. Therefore, in order to make full use of spatial-spectral information, spectral information and spatial information are simultaneously merged into the regularization constraint term of the above collaborative representation framework:

[0022]

[0023] Where S represents the geodesic-based spectral information matrix of the hyperspectral data X, D represents the spatial information matrix, and β is the regularization parameter.

[0024] Construction of D: D contains x i and x j The distance between (i≠j), the corresponding pixel coordinate is (a i , b i ) and (a j , b j ), then the spatial distance between samples is:

[0025] D=[dist((a i , b i ), (a j , b j ))] (4)

[0026] where dist(·) represents the Euclidean distance.

[0027] Construction of S: Under the condition that the neighboring sample points are still neighbors when embedded in the low-dimensional space, the samples that were originally far away from each other are also far away from each other when embedded in the low-dimensional space. Therefore, the geodesic distance is used to represent the shortest spectral distance between two pixels.

[0028] Geodesic distances are measured as follows:

[0029] (1) Calculate x i and x j The Euclidean distance d between x (x i , x j ), if x i is x j The K nearest neighbors of x i and x j The Euclidean distance d between x (x i , x j ) is less than ε, then x i is x j The weight of this edge is d x (x i , x j );

[0030] (2) Calculate the shortest path if x i and x j If there is an edge between them, the shortest path is considered to be d G (x i , x j ) = d x (x i , x j ), if it does not exist, the shortest path is d G (x i , x j )=∞.

[0031] Spectral geodesic distance:

[0032] d G (x i , x j )=min(d G (x i , x j ), d G (x i , x l )+d G (x l , x j )) (5)

[0033] Wherein, l = 1, 2, ..., n;

[0034] (3) We can get the matrix S = {d G (x i , x j )}.

[0035] Then we can solve for a i The values ​​are:

[0036]

[0037] Let A = [a1, a2, ..., a N ], where the diagonal elements of matrix A are 0, and the graph embedding weight matrix is ​​calculated as: W = (A + A T ) / 2.

[0038] Furthermore, step 3) includes the following specific contents:

[0039] The purpose of feature extraction is to find a transformation matrix P∈R d×d′ The high-dimensional data x i ∈R d×1 Mapped to a low-dimensional subspace y i ∈R d′×1 (d′<<d):y i =P T x i .

[0040] In the low-dimensional subspace, according to the graph embedding principle, the vertex index x i and x j The similarity relationship between , its objective function can be expressed as:

[0041]

[0042] Among them, B is a constraint matrix to avoid trivial solutions. It can be a scale-normalized diagonal matrix or a penalty graph G P The Laplace matrix L P .

[0043] Therefore, the optimal projection matrix can be solved as:

[0044]

[0045] The above formula can be solved by generalized eigenvalue decomposition problem:

[0046] XL T P=ΛXL P X T P (9)

[0047] In summary, Λ is a diagonal eigenmatrix, and the projection matrix P consists of eigenvectors corresponding to the d′ smallest non-zero eigenvalues, thus obtaining a low-dimensional subspace

[0048] Compared with the prior art, the beneficial effect of the present invention is that the present invention combines the spectral information of the hyperspectral image with the spatial information, and the neighbors in the spatial domain and the feature space make more contributions in the collaborative representation of the test sample, thereby generating a more accurate representation coefficient matrix. Compared with other feature extraction methods, this method can provide more valuable feature information, effectively explore the complex intrinsic characteristics of hyperspectral data, and thus achieve higher classification accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0050] Figure 1 It is a schematic flow chart of the method of the present invention. DETAILED DESCRIPTION

[0051] The present invention will be further described below in conjunction with the accompanying drawings.

[0052] like Figure 1 The figure is a flow chart of the method of the present invention. The method comprises the following steps: step 1) using the collaborative representation method and local constraints to learn the global information and local manifold structure information of the hyperspectral image; 2) jointly embedding the spatial information and the spectral information based on the geodesic into the collaborative representation regularization term; 3) based on the obtained geodesic space-spectrum collaborative representation coefficient, constructing a geodesic space-spectrum collaborative graph, and then using the graph embedding framework, by solving the generalized eigenvalue decomposition problem, obtaining the optimal projection matrix, and obtaining the low-dimensional feature subspace of the hyperspectral image data.

[0053] The specific method is as follows:

[0054] First, input a hyperspectral dataset N represents the number of pixels, d is the number of spectral bands of the hyperspectral image. The collaborative representation is used to learn the global information of the hyperspectral image. For each pixel x in the dataset X i , the typical collaborative representation method can be mathematically expressed as an l2 norm optimization problem:

[0055]

[0056] Among them, X i Does not contain x i A d×(N-1)-dimensional dictionary, λ>0 is a regularization parameter used to balance the remaining terms of the collaborative representation and the regularization term

[0057] In collaborative representation, each pixel is collaboratively represented by all other pixels in all classes, which can reveal the collaborative representation relationship between all pixels, but cannot effectively characterize the local manifold structure of the data. After being projected into a low-dimensional subspace, it cannot maintain its inherent manifold distribution structure and discrimination ability. Therefore, local constraints are introduced in collaborative representation to characterize the local neighborhood structure relationship between different pixels:

[0058]

[0059] In the formula, is the pixel x i If there are only k nearest neighbors, the values ​​of the remaining Nk pixels are set to zero, and μ>0 is a regularization parameter.

[0060] The above research only studies hyperspectral images from the perspective of spectral features. However, in addition to spectral features, hyperspectral images also contain rich spatial geometric information. Spatial information is used to characterize the location of objects in the image and the spatial position relationship between different objects. The use of spatial information can enhance the ability to describe and distinguish objects in the image. However, the spectral information and spatial information of hyperspectral images are not independent of each other. Spatial information usually uses the spatial neighborhood relationship of hyperspectral data in a specific area, while ignoring the influence of spatial information in the construction of the adjacency graph and the spatial and spectral correlation of the entire data. Therefore, in order to make full use of spatial-spectral information, spectral information and spatial information are simultaneously merged into the regularization constraint term of the above collaborative representation framework:

[0061]

[0062] Where S represents the geodesic-based spectral information matrix of the hyperspectral data X, D represents the spatial information matrix, and β is the regularization parameter.

[0063] Construction of D: D contains x i and x j The distance between (i≠j), the corresponding pixel coordinate is (a i , b i ) and (a j , b j ), then the spatial distance between samples is:

[0064] D=[dist((a i , b i ), (a j , b j ))] (4)

[0065] dist(·) represents the Euclidean distance.

[0066] Construction of S: Under the condition that the neighboring sample points are still neighbors when embedded in the low-dimensional space, the samples that were originally far away from each other are also far away from each other when embedded in the low-dimensional space. Therefore, the geodesic distance is used to represent the shortest spectral distance between two pixels.

[0067] Geodesic distances are measured as follows:

[0068] (1) Calculate x i and x j The Euclidean distance d between x (x i , x j ), if x i is x j The K nearest neighbors of x i and x j The Euclidean distance d between x (x i , x j ) is less than ε, then x i is x j The weight of this edge is d x (x i , x j );

[0069] (2) Calculate the shortest path if x i and x j If there is an edge between them, the shortest path is considered to be d G (x i , x j ) = d x (x i , x j ), if it does not exist, the shortest path is d G (x i , x j )=∞.

[0070] Spectral geodesic distance:

[0071] d G (x i , x j )=min(d G (x i , x j ), d G (x i , x l )+d G (x l , x j )) (5)

[0072] Wherein, l = 1, 2, ..., n;

[0073] (3) We can get the matrix S = {d G (x i , x j )}.

[0074] Then we can solve for a i The values ​​are:

[0075]

[0076] Let A = [a1, a2, ..., a N ], where the diagonal elements of matrix A are 0, and the graph embedding weight matrix is ​​calculated as: W = (A + A T ) / 2.

[0077] The purpose of feature extraction is to find a transformation matrix P∈R d×d′ The high-dimensional data x i ∈R d×1 Mapping to a lower dimensional subspace y i =P T x i .

[0078] In the low-dimensional subspace, according to the graph embedding principle, the vertex index x i and x j The similarity relationship between , its objective function can be expressed as:

[0079]

[0080] Among them, B is a constraint matrix to avoid trivial solutions. It can be a scale-normalized diagonal matrix or a penalty graph G P The Laplace matrix L P .

[0081] Therefore, the optimal projection matrix can be solved as:

[0082]

[0083] The above formula can be solved by generalized eigenvalue decomposition problem:

[0084] XL T P=ΛXL P X T P (9)

[0085] In summary, Λ is a diagonal eigenmatrix, and the projection matrix P consists of eigenvectors corresponding to the d′ smallest non-zero eigenvalues, thus obtaining a low-dimensional subspace

[0086] By executing the above content, image feature information containing rich spectral information and spatial information can be obtained, and then the optimal low-dimensional feature subspace can be obtained, thereby achieving higher classification accuracy in image classification.

[0087] Finally, it is noted that the above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Those skilled in the art should understand that the technical solutions of the present invention can be modified, replaced by equivalents, improved, etc. without departing from the purpose and scope of the technical solutions, which should be included in the scope of the claims of the present invention.

Claims

1. A hyperspectral image feature extraction method based on geodesic space-spectrum collaborative graph learning, characterized in that: The method comprises the following steps: Step 1: Use collaborative representation methods and local constraints to learn the global information and local manifold structure information of hyperspectral images; Step 2: Combine spatial information with geodesic-based spectral information Embedded in the collaborative representation regularization term, where S represents the geodesic-based spectral information matrix of the hyperspectral data X, D represents the spatial information matrix, and β is the regularization parameter; Construction of D: D contains x i and x j The distance between them is i≠j, and the corresponding pixel coordinates are and Then the spatial distance between samples is: dist(﹒) represents the Euclidean distance; Construction of S: Under the condition that the neighboring sample points are still neighbors when embedded in the low-dimensional space, the samples that were originally far away from each other are also far away from each other when embedded in the low-dimensional space; therefore, the geodesic distance is used to represent the shortest spectral distance between two pixels; Geodesic distances are measured as follows: (1) Calculate x i and x j The Euclidean distance d between x (x i ,x j ), if x i is x j The K nearest neighbors of x i and x j The Euclidean distance d between x (x i ,x j ) is less than ε, then x i is x j The weight of this edge is d x (x i ,x j ); (2) Calculate the shortest path if x i and x j If there is an edge between them, the shortest path is considered to be d G (x i ,x j ) = d x (x i ,x j ), if it does not exist, the shortest path is d G (x i ,x j )=∞; Spectral geodesic distance: d G (x i ,x j )=min(d G (x i ,x j ),d G (x i ,x l )+d G (x l ,x j )) (2) Where, l = 1, 2, ..., n; (3) We can get the matrix S = {d G (x i ,x j )}; Then solve for a i The values ​​are: Among them, X i Does not contain x i A d×(N-1)-dimensional dictionary, λ>0 is a regularization parameter, is the pixel x i k nearest neighbors, the values ​​of the remaining Nk pixels are set to zero, and μ>0 is the regularization parameter; Let A=[a1,a2,…,a N ], where the diagonal elements of matrix A are 0, and the graph embedding weight matrix is ​​calculated as: W = (A + A T ) / 2; Step 3: Based on the obtained geodesic space-spectrum synergy representation coefficients, a geodesic space-spectrum synergy graph is constructed, and then the graph embedding framework is used to obtain the optimal projection matrix by solving the generalized eigenvalue decomposition problem to obtain the low-dimensional feature subspace of the hyperspectral image data.

2. The method according to claim 1, characterized in that The step 1 includes the following specific contents: first, the global information of the hyperspectral image is learned by using collaborative representation; for each pixel x in the dataset X i , the typical collaborative representation method can be mathematically expressed as an l2 norm optimization problem: Among them, X i Does not contain x i A d×(N-1)-dimensional dictionary, λ>0 is a regularization parameter used to balance the remaining terms of the collaborative representation and the regularization term In collaborative representation, each pixel is collaboratively represented by all other pixels in all classes, which can reveal the collaborative representation relationship between pixels, but cannot effectively characterize the local manifold structure of the data. After being projected into a low-dimensional subspace, it cannot maintain its inherent manifold distribution structure and discrimination ability. Therefore, local constraints are introduced in collaborative representation to characterize the local neighborhood structure relationship between different pixels: In the formula, is the pixel x i If there are k nearest neighbors, the values ​​of the remaining Nk pixels are set to zero, and μ>0 is the regularization parameter.

3. The method according to claim 1, further characterized in that: The step 3 includes the following specific contents: The purpose of feature extraction is to find a transformation matrix P∈R d×d′ The high-dimensional data x i ∈R d×1 Mapped to a low-dimensional feature subspace y i ∈R d′×1 (d′<<d):y i =P T x i ; In the low-dimensional feature subspace, according to the graph embedding principle, the x with the vertex as the index i and x j The similarity relationship between , its objective function can be expressed as: Among them, B is the constraint matrix, which is to avoid trivial solutions. It can be a scale-normalized diagonal matrix or a penalty graph G P The Laplace matrix L P ; Therefore, the optimal projection matrix can be solved as: The above formula can be solved by generalized eigenvalue decomposition problem: XLX T P=ΛXL P X T P (8) In summary, Λ is a diagonal feature matrix, and the projection matrix P is composed of eigenvectors corresponding to the d′ smallest non-zero eigenvalues, thus obtaining a low-dimensional feature subspace

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