Hyperspectral image classification method based on superpixel and tensor robust principal component analysis

Abstract

The invention relates to the technical field of hyperspectral image classification, in particular to a hyperspectral image classification method based on superpixel and tensor robust principal component analysis, and the method comprises the following steps: 1, carrying out the superpixel segmentation of a hyperspectral image through a superpixel segmentation algorithm, and obtaining an irregular superpixel segmentation image; 2, acquiring envelope cubes of different super-pixel areas corresponding to the super-pixel segmentation image from the original hyperspectral image, and defining the envelope cubes as super-tensors; 3, constructing a local neighborhood preserving graph based on a supertensor; 4, setting a target function, introducing an auxiliary variable, and iteratively solving a low-rank item, an auxiliary item and a noise item of the original hyperspectral image based on an alternating direction multiplier method; and 5, dividing a training set, and classifying the obtained low-rank items by using a multi-class support vector machine algorithm to obtain a final classification result. According to the method, the influence of redundant information and noise in a hyperspectral image classification task is reduced, so that higher ground feature classification precision is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of hyperspectral image classification, and in particular to a hyperspectral image classification method based on superpixel and tensor robust principal component analysis. Background Art

[0002] Hundreds of continuous spectral bands in hyperspectral images (HSI) have rich spectral information, which can realize accurate identification and distinction of objects. Hyperspectral image classification refers to the assignment of each pixel in the image to a predefined category, such as water, building, vegetation, etc. At present, this technology has been widely used in agriculture, forestry monitoring, urban planning, environmental assessment and other fields. However, the highly correlated spectral bands in hyperspectral images also contain a lot of redundant information, which may obscure the important features that determine the pixel category. In addition, the spectral imaging process inevitably generates noise due to various factors (such as sensor defects), resulting in differences in the spectral dimension of pixels that originally belong to the same category, thus affecting the accuracy of classification. In general, redundant information and noise affect the performance of hyperspectral images in classification tasks.

[0003] In recent years, tensor robust principal component analysis has been shown to effectively alleviate the impact of the above problems, but such methods usually rely on the global low-rank assumption, and the inherent differences between different local regions of hyperspectral images often violate this assumption. In addition, such methods cannot fully remove the influence of noise, and the residual noise in low-rank images also limits the further improvement of classification performance. Summary of the invention

[0004] The present invention provides a hyperspectral image classification method based on superpixel and tensor robust principal component analysis. The method uses the local low-rank approximation hypothesis to replace the global low-rank hypothesis, defines the envelope cube of the superpixel block as a supertensor, and constructs a local neighborhood preservation graph constraint based on the supertensor to overcome the technical problem that the existing tensor robust principal component analysis method has low accuracy in the hyperspectral image classification task.

[0005] To achieve the above object, the present invention provides a hyperspectral image classification method based on superpixel and tensor robust principal component analysis, comprising the following steps:

[0006] S1: Use superpixel segmentation algorithm to perform superpixel segmentation on the hyperspectral image to obtain an irregular superpixel segmentation map;

[0007] S2: Obtain the envelope cubes of different superpixel regions corresponding to the superpixel segmentation map from the original hyperspectral image, which is defined as a supertensor;

[0008] S3: Constructing a local neighborhood preserving graph based on supertensors;

[0009] S4: Set up the objective function, introduce auxiliary variables, and iteratively solve the low-rank term, auxiliary term and noise term of the original hyperspectral image based on the alternating direction multiplier method;

[0010] S5: Divide the training set, use the multi-class support vector machine algorithm to classify the obtained low-rank items, and obtain the final classification results.

[0011] Furthermore, the specific implementation of S1 is: using an entropy rate superpixel segmentation algorithm to perform superpixel segmentation on the original hyperspectral image. The entropy rate superpixel segmentation algorithm is an image segmentation method based on graph theory and information entropy theory, which aims to divide the image into several superpixel regions with similar features.

[0012] Furthermore, the specific implementation of S2 is as follows: irregular superpixel blocks are cut out on the original hyperspectral image data according to the superpixel segmentation map, and the irregular superpixel blocks are filled into regular cubes and defined as supertensors, wherein the data points used for filling are the original image pixels.

[0013] Furthermore, the specific implementation of S3 is as follows: construct a local neighborhood preserving graph based on a super tensor, and the weight calculation formula between two points in the graph is as follows:

[0014]

[0015] where exp() refers to the exponential function with the real number e as the base, γ is a positive scalar, and x i and x j Indicates pixel i and pixel j, NB i It represents the neighborhood of pixel i, that is, whether it belongs to the same super tensor as pixel i. The local preservation graph based on the super tensor is defined as G=DW, where D is the diagonal matrix of W.

[0016] Furthermore, the objective function in S4 is defined as:

[0017]

[0018] The constraints of the above formula are Among them, X, L sum , E represent the original hyperspectral image tensor, the low-rank term of the original hyperspectral image tensor and the noise term of the original hyperspectral image tensor respectively, L i represents the low-rank part of the i-th hypertensor, represents the aggregation operation, i∈(1,k), k is the number of supertensors, ∥∥ * represents the nuclear norm, ∥∥ 2,2,1 Represents the tensor l 2,2,1 norm, represents the local neighborhood preserving graph regularization term based on the super tensor. α and β represent positive weight parameters. The subscript symbol (3) represents the modulo 3 expansion of the tensor, that is, the tensor with the original size of n1×n2×n3 is expanded into a 2D matrix of n3×(n1n2). The superscript symbol T represents the matrix transpose. The auxiliary variable Z=L is introduced sum , solve for l sum This can be transformed into an aggregation of low-rank approximations that solve all hypertensors:

[0019]

[0020] where μ is a positive scalar, and Both are Lagrange multipliers, || || F After obtaining the low-rank approximation of all hypertensors, restore them to their initial positions to obtain L sum , repeated pixels are treated as average values. Solving the auxiliary variable Z can be transformed into solving the following sub-problems:

[0021]

[0022] Solving the noise term E can be transformed into solving the following sub-problems:

[0023]

[0024] Furthermore, the convergence condition in S4 is ‖L sum -ZE‖ ∞ ≤∈ and ‖ZE‖ ∞ ≤∈, indicating L sum -The norm values ​​of ZE and ZE are less than ∈, where ∈ is a minimum value.

[0025] The present invention obtains the envelope cube of the superpixel block in the hyperspectral image through superpixel segmentation and defines it as a supertensor. By calculating the low-rank approximation of the supertensor, it is ensured that the local area can obtain a lower rank than the global low-rank approximation, thereby fully reducing redundant information. In addition, based on the tensor l 2,2,1 norm, the present invention can separate the noise in the original hyperspectral image while maintaining local smoothness. The local preservation map based on the hypertensor retains the local manifold structure in the hyperspectral image and enhances the robustness of the model to noise. Experimental results show that the hyperspectral image classification method in the present invention is superior to the existing methods in terms of accuracy and has significant practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0027] Figure 1 A flowchart of a hyperspectral image classification method based on superpixels and tensor robust principal component analysis in an embodiment of the present invention is shown.

[0028] Figure 2 Schematic diagram of obtaining envelope cube supertensors from different superpixel regions in an embodiment of the method of the present invention.

[0029] Figure 3 This is a flow chart of an algorithm for iteratively solving low-rank terms, auxiliary terms and noise terms based on the alternating direction multiplier method described in an embodiment of the method of the present invention. DETAILED DESCRIPTION

[0030] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same symbols represent the same parameters. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and cannot be understood as limiting the present invention.

[0031] See also Figure 1 The present invention provides a hyperspectral image classification method based on superpixel and tensor robust principal component analysis, comprising the following steps:

[0032] S1: Use superpixel segmentation algorithm to perform superpixel segmentation on the hyperspectral image to obtain an irregular superpixel segmentation map;

[0033] S2: Obtain the envelope cubes of different superpixel regions corresponding to the superpixel segmentation map from the original hyperspectral image, which is defined as a supertensor;

[0034] S3: Constructing a local neighborhood preserving graph based on supertensors;

[0035] S4: Set up the objective function, introduce auxiliary variables, and iteratively solve the low-rank term, auxiliary term and noise term of the original hyperspectral image based on the alternating direction multiplier method;

[0036] S5: Divide the training set, use the multi-class support vector machine algorithm to classify the obtained low-rank items, and obtain the final classification results.

[0037] The following is a further explanation based on the specific implementation steps:

[0038] See also Figure 1 and Figure 2The specific implementation of steps S1 and S2 is as follows: the input hyperspectral image is segmented using the entropy rate superpixel algorithm The segmentation results in a two-dimensional superpixel segmentation map with a size of n1×n2. The envelope cube of the corresponding superpixel block on the original image is selected according to the map. In this embodiment, the number of supertensors k is set to 32.

[0039] See also Figure 1 , the specific implementation of step S3 is: the weight calculation formula between any two points on X is as follows:

[0040]

[0041] Where exp() refers to an exponential function with the real number e as the base, and γ is a positive scalar whose value in this embodiment is 1. i and x j Indicates pixel i and pixel j, NB i Indicates the neighborhood of pixel i, that is, whether it belongs to the same super tensor as pixel i. In the embodiment, the local preservation graph is defined as G=DW, where D is the diagonal matrix of W.

[0042] See also Figure 1 , the objective function of step S4 is as follows:

[0043]

[0044] The constraints of the above formula are Where L i is defined as a low-rank approximation of each supertensor block, L sum is the aggregation of all L i Get the low-rank part of the hyperspectral image of the original size, i∈(1,k), represents the aggregation operation between supertensors, ||L sum || * Indicates L sum The nuclear norm of ||E|| 2,2,1 The tensor l representing E 2,2,1 norm, represents the local neighborhood graph regularization term based on the super tensor, and Tr() represents the trace of the matrix. The subscript symbol (3) represents the modulo 3 expansion of the tensor, that is, the original tensor of size n1×n2×n3 is expanded to a 2D matrix of size n3×(n1n2). The superscript symbol T represents the matrix transpose, and α and β represent positive weight parameters, which are set to 1 and 10 respectively in this embodiment. Define the auxiliary variable Z=L sum , based on the alternating direction multiplier method, iteratively solve L sum , Z and E.

[0045] Solving for L sum The formula is transformed into solving subproblems:

[0046]

[0047] Solving the formula for the auxiliary variable Z is transformed into solving the subproblem:

[0048]

[0049] The formula for solving E is transformed into solving subproblems:

[0050]

[0051] Where μ is a positive scalar, and its initial value in this embodiment is 10 -3 . and Both are Lagrange multipliers.

[0052] See also Figure 3 , solve the low-rank term L in step S4 sum It can be transformed into an aggregation of solving low-rank approximations of all hypertensors, where the low-rank approximation of a single hypertensor can be solved by the following formula:

[0053]

[0054] Where L i represents the low-rank approximation of the i-th supertensor, tsvt represents the tensor singular value contraction algorithm, N i is to solve for L i The intermediate variables introduced, The symbol represents the operation of obtaining the envelope cube (hypertensor) from the original image size, N i Size L i same. represents the aggregation operation of the low-rank approximation of the super tensor. Finally, all the low-rank approximations of the super tensor are aggregated into the low-rank part L of the original image. sum .

[0055] See also Figure 3 , the auxiliary variable Z in step S4 can be solved by the following formula:

[0056]

[0057] Where I represents the identity matrix. fold3 represents the tensor modulo 3 folding operation, which restores the two-dimensional matrix n3×(n1n2) to the original three-dimensional tensor n1×n2×n3.

[0058] See also Figure 3 , the noise term in step S4 can be solved by the following formula:

[0059]

[0060] in It can be expressed as:

[0061]

[0062] in Finally, the original matrix E is converted into (3) Restored to the noise term E.

[0063] See also Figure 3 , the convergence condition in step S4 is ‖L sum -ZE‖ ∞ ≤∈ and ‖ZE‖ ∞ ≤∈, indicating L sum -The norm values ​​of ZE and ZE are less than the minimum value ∈, and the value of ∈ in the embodiment is 10 -4 In addition, the number of iterations in the embodiment reaches about 160 times before convergence.

[0064] In order to verify the effectiveness of the proposed hyperspectral image classification method based on superpixel and tensor robust principal component analysis, the real dataset Indian Pines is used to test the method of the present invention in this embodiment. The public dataset Indian Pines was acquired by the AVIRIS hyperspectral sensor system over the Indian Pines test site in Indiana, USA. The size of the dataset is 145 pixels × 145 pixels, covering 16 types of ground objects. After removing the noise interference bands and water absorption bands, the remaining 200 spectral bands are used for subsequent classification tasks. Three typical objective evaluation indicators, OA (overall accuracy), AA (average accuracy) and Kappa coefficient, were used to evaluate the performance of different algorithms. The compared algorithms included robust principal component analysis (RPCA), tensor robust principal component analysis (TRPCA) and an efficient and adaptive reconstructive homogeneous block-based local tensor robust pca for feature extraction of hyperspectral images (SPRB-TRPCA).

[0065] In the Indian Pines dataset, the number of training samples for each type of land object is 10% of the total number of samples. The objective evaluation indicators of the three hyperspectral image classification methods (RPCA, TRPCA, SPRB-TRPCA) and the method proposed in this embodiment on the Indian Pines dataset are shown in Table 1. Referring to Table 1, it can be seen that the method of this embodiment has obtained the highest values ​​in the three objective evaluation indicators of OA, AA and Kappa coefficient, that is, the method of this embodiment can achieve the best recognition accuracy, which is about 2.86 to 14.5 percentage points higher than other comparison methods. The hyperspectral image classification method in the present invention proposes a local low-rank approximation hypothesis to replace the global low-rank hypothesis in the traditional tensor robust principal component analysis, and uses the super tensor as the minimum unit for calculating the low-rank approximation, ensuring that each part of the original image can obtain a lower rank. In addition, the local neighborhood preservation graph constraint based on the super tensor ensures the compactness and consistency of the data in each super tensor. The experimental results show that the hyperspectral image recognition method in the present invention can obtain higher land object classification accuracy.

[0066] Table 1: Objective performance indicators of the method in this embodiment and three advanced hyperspectral image methods on the Indian Pines dataset.

[0067]

[0068] What is disclosed above is only a preferred embodiment of the present invention, and it certainly cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of the above embodiment and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A hyperspectral image classification method based on superpixel and tensor robust principal component analysis, characterized in that: The following steps are involved: S1: Use superpixel segmentation algorithm to perform superpixel segmentation on the hyperspectral image to obtain an irregular superpixel segmentation map; S2: Obtain the envelope cubes of different superpixel regions corresponding to the superpixel segmentation map from the original hyperspectral image, which is defined as the supertensor; S3: Constructing a local neighborhood preserving graph based on supertensors; S4: Set up the objective function, introduce auxiliary variables, and iteratively solve the low-rank term, auxiliary term and noise term of the original hyperspectral image based on the alternating direction multiplier method; S5: Divide the training set and use the multi-class support vector machine algorithm to classify the obtained low-rank items to obtain the final classification results.

2. The hyperspectral image classification method based on superpixel and tensor robust principal component analysis as claimed in claim 1, characterized in that: The specific implementation of S1 is: Hyperspectral images The principal component map is segmented by entropy rate superpixel to obtain a superpixel segmentation map of size n1×n2, where the superpixel segmentation map consists of multiple irregular superpixel regions.

3. The hyperspectral image classification method based on superpixel and tensor robust principal component analysis as claimed in claim 1, characterized in that: The specific implementation of S2 is: According to the superpixel segmentation map, irregular superpixel blocks are cut out from the original hyperspectral image data, which are filled into regular cubes and defined as supertensors, where the data points used for filling are the original image pixels.

4. The hyperspectral image classification method based on superpixel and tensor robust principal component analysis as claimed in claim 1, characterized in that: The specific implementation of S3 is as follows: Construct a local neighborhood preserving graph based on the hypertensor. The weight calculation formula between two points in the graph is: where exp() refers to the exponential function with the real number e as the base, γ is a positive scalar, and x i and x j Indicates pixel i and pixel j, NB i Represents the neighborhood of pixel i, that is, whether it belongs to the same superpixel block as pixel i. The local neighborhood preservation graph based on the supertensor is defined as G=DW, where D is the diagonal matrix of W.

5. The hyperspectral image classification method based on superpixel and tensor robust principal component analysis as claimed in claim 1, characterized in that: The specific implementation method in S4 is: The objective function is defined as: The constraints of this formula are Where L sum is the low-rank part of the original size hyperspectral image, E is the noise part, and L i is a low-rank approximation of the ith hypertensor, i∈(1,k), represents the aggregation operation, k represents the number of super tensors; an auxiliary variable Z = L is introduced sum , the augmented Lagrangian function of the objective function can be defined as: where ∥L sum ∥ * Indicates L sum The nuclear norm of 2,2,1 The tensor L representing the solution to E 2,2,1 norm, represents the local neighborhood preserving graph regularization term based on the super tensor. The subscript symbol (3) represents the modulo 3 expansion of the tensor, that is, the tensor of the original size of n1×n2×n3 is expanded into a 2D matrix of b3×(n1n2). The superscript symbol T represents the transpose of the matrix. α and β represent positive weight parameters. μ is a positive scalar. and Both are Lagrange multipliers; L in the above formula is sum , Z and E can be solved iteratively by the alternating direction multiplication method to solve L sum The formula can be obtained by aggregating the low-rank approximation of all hypertensors, which is specifically expressed as: where ∥L i ∥ * Indicates L i The nuclear norm of Represents the square of the F norm. After obtaining the low-rank approximation of all super tensors, they are aggregated according to their initial positions to obtain L sum , where repeated pixels are treated as average values; solving the auxiliary variable Z can be transformed into solving the following sub-problems: Solving the noise term E can be expressed as solving the following sub-problems: where ‖E‖ 2,2,1 l represents E 2,2,1 norm; the final convergence condition is ‖L sum -ZE‖ ∞ ≤∈ and ‖ZE‖ ∞ ≤∈, indicating L sum -The norm values ​​of ZE and ZE are less than ∈, where ∈ is a minimum value.

6. The method for solving L according to claim 5 sum , characterized in that, L sum It can be obtained by solving the aggregation of low-rank approximations of all hypertensors, where the specific formula for solving the low-rank approximation of the i-th hypertensor is: Where L i represents the low-rank approximation of the i-th supertensor, tsvt represents the tensor singular value contraction algorithm, N i is to solve for L i The introduced intermediate variables can be expressed as: in The symbol represents the operation of obtaining the envelope cube (hypertensor) from the original image size, each N i Size and L i Same, finally all L i Polymerization to obtain L sum .

7. The method for solving the auxiliary variable Z according to claim 5, characterized in that: Solving the auxiliary variable Z can be transformed into solving the following formula: Where I represents the identity matrix, and fold3 represents the tensor modulo 3 folding operation, that is, restoring the two-dimensional matrix n3×(n1n2) to the original three-dimensional tensor n1×n2×n3.

8. The method for solving the noise term E according to claim 5, wherein: Solving the noise term can be transformed into solving the following equation: in It can be expressed as: in

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