CN109447009B - Hyperspectral image classification method based on subspace nuclear norm regularization regression model - Google Patents

Hyperspectral image classification method based on subspace nuclear norm regularization regression model Download PDF

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CN109447009B
CN109447009B CN201811302039.3A CN201811302039A CN109447009B CN 109447009 B CN109447009 B CN 109447009B CN 201811302039 A CN201811302039 A CN 201811302039A CN 109447009 B CN109447009 B CN 109447009B
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詹天明
孙乐
杨国为
吴泽彬
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NANJING AUDIT UNIVERSITY
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Abstract

The invention discloses a hyperspectral image classification method based on a subspace nuclear norm regularization regression model, which comprises the steps of wave band selection, sample representation, classification model establishment and design optimization algorithm, final classification result output by integrating classification results of all wave bands, wave bands are selected by using a sparse representation model, non-discriminative wave bands are removed, the subsequent classification precision and speed can be improved, the hyperspectral images are classified by establishing the subspace nuclear norm regularization regression model, the classification precision is improved, the hyperspectral image classification method can be used in the fields of geological exploration, agricultural planting statistics and the like, and the hyperspectral image classification method has a good application prospect.

Description

Hyperspectral image classification method based on subspace nuclear norm regularization regression model
Technical Field
The invention relates to the technical field of image processing, in particular to a hyperspectral image classification method based on a subspace nuclear norm regularization regression model.
Background
The hyperspectral imaging technology is that a target area is imaged by a plurality of continuous and subdivided spectral bands in ultraviolet, visible light, near infrared and mid-infrared areas of an electromagnetic spectrum through an imaging spectrometer carried on different platforms, and the spectral information of the target area is acquired while the earth surface image information is captured. Therefore, the abundant information of the spectrum wave band is helpful for distinguishing targets with similar spectrums, so that the hyperspectral image plays a crucial role in remote sensing.
Currently, in ecological science, hyperspectral images are often used to estimate biomass, biodiversity, or to study land cover changes, etc.; in geological science, hyperspectral images are used for detecting mineral components and abundance thereof, and detecting the proportion of water, organic matters and mineralization in soil; in hydrology, the change of wetland characteristics can be determined by utilizing a hyperspectral image, and the water quality, the estuary environment and the coastal zone can also be analyzed; in precision agricultural applications, hyperspectral images are used to classify crops, extract nitrogen content, identify plant species, etc.; in military application, the hyperspectral image is also used for detecting specific military targets and is widely applied.
Although the hyperspectral images are applied in various fields, the application of the hyperspectral images has the precondition that the hyperspectral images are accurately classified, and image classification refers to the fact that pixel points in the images are gathered into different categories, so that the pixels in the same category have similar properties. At present, a plurality of image classification methods are provided, but the high dimension of the hyperspectral images, the small amount of labeled samples and the spatial variability of spectral features all bring challenges to the classification of the hyperspectral images, and in addition, how to express the spatial correlation among pixels in the hyperspectral images and how to express the context prior of the images are still worth deep research.
In the last decade, many scholars have actively studied the problem of classifying hyperspectral images, and many new hyperspectral image classification methods are proposed, which mainly include the following classes:
(1) the hyperspectral image classification method of supervised learning mainly utilizes known samples to train a classification model, and utilizes the classification model to classify samples to be classified;
(2) the method mainly comprises the steps of automatically gathering pixel points with similar properties in an image to achieve the purpose of classification through the similarity of pixel points, wherein the classification precision of the method is lower than that of a supervised hyperspectral image classification method under the conditions of unknown category number and prior loss;
(3) the method mainly aims at the problem that the classification effect of a supervised learning method is poor when the training data volume is small, and the hyperspectral images are classified by using the ideas of self-learning and collaborative learning.
In practical application, when training samples are sufficient, a classification method of supervised learning is selected, but how to solve the problem of spatial correlation and context prior existing in a hyperspectral image so as to further improve the classification accuracy of the hyperspectral image is also a problem to be solved.
Disclosure of Invention
The invention aims to overcome the defects of the existing hyperspectral image classification method. According to the hyperspectral image classification method based on the subspace nuclear norm regularization regression model, the sparse representation model is used for selecting wave bands, non-discriminative wave bands are eliminated, the subsequent classification precision and speed can be improved, the hyperspectral images are classified by establishing the subspace nuclear norm regularization regression model, the classification precision is improved, the hyperspectral image classification method based on the subspace nuclear norm regularization regression model can be used in the fields of geological exploration, agricultural planting statistics and the like, and the hyperspectral image classification method has a good application prospect.
In order to achieve the purpose, the invention adopts the technical scheme that:
a hyperspectral image classification method based on a subspace kernel norm regularization regression model comprises the following steps,
step (A), selecting wave bands of the known hyperspectral images, and constructing new hyperspectral images to be classified;
step (B), according to the new hyperspectral image to be classified, representing the image block of each pixel point in the two-dimensional image on the hyperspectral image to be classified of each wave band as the characteristic of the pixel point on the wave band;
step (C), establishing a subspace nuclear norm regularization regression model, designing an alternative iteration solving algorithm according to an operator classification method, and solving the characteristics of each pixel point in the step (B) on the corresponding wave band to obtain classification results of all the wave bands;
and (D) fusing the classification results of all the wave bands, solving the category of each sample point by using a voting mode, and outputting the classification result of the hyperspectral image.
The hyperspectral image classification method based on the subspace nuclear norm regularization regression model comprises the following steps of (A) selecting the wave bands of the known hyperspectral images to construct new hyperspectral images to be classified,
(A1) extracting training samples of known hyperspectral images and rearranging the training samples into a matrix;
(A2) constructing a feature selection-oriented sparse representation model, obtaining a feature representation coefficient with sparse characteristics by an energy minimization method, and selecting a wave band with the coefficient of 1 from the known hyperspectral images to reconstruct a new hyperspectral image to be classified according to the obtained feature representation coefficient.
In the hyperspectral image classification method based on the subspace nuclear norm regularization regression model, (A1), training samples of known hyperspectral images are extracted and rearranged into a matrix, specifically, the wave spectrums of the training samples are extracted to form a matrix X according to the positions of the training samples in the images,
Figure BDA0001852644700000051
and m is the number of training samples of the hyperspectral data, and d is the number of spectral wave bands of the hyperspectral image.
In the hyperspectral image classification method based on the subspace nuclear norm regularization regression model, (A2), a feature selection-oriented sparse representation model is constructed, a feature representation coefficient with sparse characteristics is obtained by an energy minimization method, and a new hyperspectral image to be classified is reconstructed by selecting a wave band with the coefficient of 1 from known hyperspectral images according to the obtained feature representation coefficient, which comprises the following steps,
(A21) establishing a class mark vector y according to the class of the training sample,
y＝[l(x1)，l(x2)，…，l(xn)]Twhere l denotes the class of the current training sample, xi＝[xi，1，xi，2，…xid]Represents the entire spectral band value of the ith training sample;
(A22) establishing a hyperspectral image characteristic selection sparse representation model,
Figure BDA0001852644700000061
tau is a Lagrange multiplier, w is a vector with sparse characteristics to be solved, and s.t. is a constraint condition;
Figure BDA0001852644700000062
is defined as solving for w, such that
Figure BDA0001852644700000063
The value is minimum;
(A23) solving the minimization of a hyperspectral image feature selection sparse representation model by using a soft threshold iteration method, wherein the process comprises the steps of giving a multiplier lambda, a category label vector y, training a sample matrix X, setting the initial value of each value in a vector w to be 1, iteratively solving, and wt+1＝Proxλ(τwt-(XTy-XTXwt) Prox) is a projection function, which is expressed as follows:
Figure BDA0001852644700000064
wherein C represents an unknown variable;
(A24) judging the termination iteration condition | | wt+1-wtIf the result is less than or equal to 0.0001, if the result meets the requirement of outputting the vector w with the sparse characteristic, if the result does not meet the requirement, continuing the iteration until the condition of stopping the iteration is mett+1-wt||≤0.0001；
(A25) According to the output value of w, if wi(I-1, …, d) is equal to 0, the ith wave band is deleted from the known hyperspectral images, a new hyperspectral image I to be classified is constructed, and the number of the wave bands is dn(ii) a d is the wave band number of the hyperspectral remote sensing image.
The hyperspectral image classification method based on the subspace nuclear norm regularization regression model comprises the following steps of (B) according to a new hyperspectral image to be classified, representing an image block of each pixel point in a two-dimensional image of the hyperspectral image to be classified of each waveband, which is taken from the image, as the characteristic of the pixel point on the waveband,
aiming at constructing each wave band image I in a new hyperspectral image I to be classifiedi(i＝1，…，dn) And selecting an image block with the size of p × q where the pixel point is located to represent the characteristics of the pixel point on the wave band, wherein the image block of the training sample is represented by A, and the image block of the test sample is represented by Y.
The hyperspectral image classification method based on the subspace nuclear norm regularization regression model comprises the following steps of (C), establishing a subspace nuclear norm regularization regression model, designing an alternate iteration solving algorithm according to an operator classification method, solving the characteristics of each pixel point in the step (B) on the corresponding wave band, and obtaining the classification results of all the wave bands,
(C1) establishing a sub-dictionary for the training samples in each wave band image according to the categories of the training samples,
Figure BDA0001852644700000071
i＝1，…，dndenotes the ith band, L1, …, L denotes the ith class; p denotes a row of the image block, q denotes a column of the image block;
(C2) for the test sample Y in each band imagei，jWherein j is 1, …, niRepresenting the jth test sample image block, n, in the ith band imageiRepresenting the number of test samples in the ith wave band image, establishing a kernel norm regularization regression model in the subspace of the test samples,
Figure BDA0001852644700000081
wherein,
Figure BDA0001852644700000082
Figure BDA0001852644700000083
represents the test specimen Yi，jThe reconstructed image block in the I-th subspace,
Figure BDA00018526447000000810
is a representation coefficient vector, F is a reconstruction function of the image block;
(C3) optimizing the model according to the operator splitting and alternative iteration method to obtain each test sample Yi，j(j＝1，…，ni) The representation residual in the I-th category specifically comprises the following steps:
(C31) input the sub-dictionary of each category
Figure BDA0001852644700000084
And test specimen Yi，j∈Rp×qModel parameter λ, tolerance error;
(C32) initializing intermediate variables
Figure BDA0001852644700000085
(C33) Calculating
Figure BDA0001852644700000086
Wherein
Figure BDA0001852644700000087
Vec (-) denotes the operator that converts the matrix into a vector;
(C34) calculating
Figure BDA0001852644700000088
Wherein
Figure BDA0001852644700000089
SVD denotes SVD decomposition;
(C35) calculating
Figure BDA0001852644700000091
(C36) Judging whether the iteration is stopped or not, if the following two conditions are met simultaneously, stopping the iteration,
Figure BDA0001852644700000092
Figure BDA0001852644700000093
(C37) the output represents the residual error
Figure BDA0001852644700000094
(C4) Representing residual errors by means of outputs
Figure BDA0001852644700000095
Obtaining Y according to the minimum residual error criterioni，jAnd obtaining classification results of all the wave bands according to the subordination categories.
The hyperspectral image classification method based on the subspace kernel norm regularization regression model comprises the following steps of (D) fusing classification results of all wave bands, solving the classification of each sample point by using a voting mode, and outputting the classification result of a hyperspectral image,
(D1) counting the times of different categories of the jth pixel point in the hyperspectral image in each wave band;
(D2) obtaining the maximum times and the corresponding category thereof, and taking the maximum times and the corresponding category as the final category of the jth pixel point;
(D3) and solving the final category of all the pixel points according to the results of (D1) and (D2), thereby outputting the classification result of the hyperspectral image.
The invention has the beneficial effects that: the hyperspectral image classification method based on the subspace nuclear norm regularization regression model selects wave bands by utilizing the sparse representation model, eliminates non-discriminative wave bands, can improve the subsequent classification precision and speed, classifies hyperspectral images by establishing the subspace nuclear norm regularization regression model, improves the classification precision, can be used in the fields of geological exploration, agricultural planting statistics and the like, has good application prospect, and has the following specific advantages:
(1) selecting the wave bands in the hyperspectral image by using a sparse representation model, and selecting the wave bands with discrimination to classify, so that the calculation amount of subsequent classification is reduced, and the interference of the wave bands without discrimination on classification results is eliminated;
(2) the image block is taken to represent the pixel point characteristics, and the spatial relationship and the context information of the pixel points in the image can be embodied;
(3) a subspace representation method of each category is designed, a kernel norm constraint discrimination model is established in each subspace, the low-rank characteristic of image blocks belonging to the same category under a dictionary is reflected through the kernel norm constraint, an alternative iterative algorithm of model solution is provided based on an operator splitting method, an original problem is converted into iterative solution of a plurality of sub-problems, and each sub-problem has an analytic solution.
Therefore, the hyperspectral image classification method can effectively improve the hyperspectral image classification precision and promote the further excavation of the low-rank characteristic of the hyperspectral image.
Drawings
FIG. 1 is a schematic flow chart of a hyperspectral image classification method based on a subspace nuclear norm regularization regression model according to the present invention;
FIG. 2 is a schematic illustration of a band selection process of the present invention;
FIG. 3 is an overall flow chart of the hyperspectral image classification of the invention;
FIG. 4 is a flow chart of a subspace nuclear norm regularized regression method of the present invention for classifying individual test samples;
FIG. 5 is a schematic diagram of an optimization process of the subspace nuclear norm regularized regression model of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings.
As shown in FIG. 1, the hyperspectral image classification method based on the subspace kernel norm regularization regression model comprises the following steps,
step (A), selecting wave bands of the known hyperspectral images, and constructing new hyperspectral images to be classified;
step (B), according to the new hyperspectral image to be classified, representing the image block of each pixel point in the two-dimensional image on the hyperspectral image to be classified of each wave band as the characteristic of the pixel point on the wave band;
step (C), establishing a subspace nuclear norm regularization regression model, designing an alternative iteration solving algorithm according to an operator classification method, and solving the characteristics of each pixel point in the step (B) on the corresponding wave band to obtain classification results of all the wave bands;
and (D) fusing the classification results of all the wave bands, solving the category of each sample point by using a voting mode, and outputting the classification result of the hyperspectral image.
Wherein, the step (A) is to select the wave band of the known hyperspectral images and construct new hyperspectral images to be classified, as shown in figure 2, comprising the following steps,
(A1) extracting the training samples of the known hyperspectral images and rearranging the training samples into a matrix, specifically, extracting the whole spectrum of the training samples to form a matrix X according to the positions of the training samples in the images,
Figure BDA0001852644700000121
wherein m is the number of training samples of the hyperspectral data, and d is the number of spectral wave bands of the hyperspectral image;
(A2) constructing a feature selection-oriented sparse representation model, obtaining a feature representation coefficient with sparse characteristics by an energy minimization method, and reconstructing a new hyperspectral image to be classified by selecting a wave band with the coefficient of 1 from the known hyperspectral images according to the obtained feature representation coefficient,
(A21) establishing a class mark vector y according to the class of the training sample,
y＝[l(x1)，l(x2)，…，l(xn)]Twhere l denotes the class of the current training sample, xi＝[xi，1，xi，2，…xid]Represents the entire spectral band value of the ith training sample;
(A22) establishing a hyperspectral image characteristic selection sparse representation model,
Figure BDA0001852644700000131
tau is a Lagrange multiplier, w is a vector with sparse characteristics to be solved, and s.t. is a constraint condition;
Figure BDA0001852644700000132
meaning that, w is calculated to
Figure BDA0001852644700000133
The value is minimum;
(A23) solving the minimization of a hyperspectral image characteristic selection sparse representation model by using a soft threshold iteration method, wherein the process comprises the steps of giving a multiplier lambda, a category label vector y, training a sample matrix X, setting the initial value of each value in the vector w as 1, iteratively solving,
wt+1＝Proxλ(τwt-(XTy-XTXwt) Prox) is a projection function, which is expressed as follows:
Figure BDA0001852644700000134
wherein C represents an unknown variable;
(A24) judging the termination iteration condition | | wt+1-wtIf the result is less than or equal to 0.0001, if the result meets the requirement of outputting the vector w with the sparse characteristic, if the result does not meet the requirement, continuing the iteration until the condition of stopping the iteration is mett+1-wt||≤0.0001；
(A25) According to the output value of w, if wi(I-1, …, d) is equal to 0, the ith wave band is deleted from the known hyperspectral images, a new hyperspectral image I to be classified is constructed, and the number of the wave bands is dn(ii) a d is the wave band number of the hyperspectral remote sensing image;
wherein, the step (B) is to take the image block of each pixel point in the two-dimensional image on the hyperspectral image to be classified of each wave band to express the characteristic of the pixel point on the wave band according to the new hyperspectral image to be classified,
aiming at constructing each wave band image I in a new hyperspectral image I to be classifiedi(i＝1，…，dn) Selecting the image block of p × q size where the pixel point is located to represent the characteristic of the pixel point on the wave band, wherein the image block of the training sample is represented by A, and testing the sample graphThe block is denoted by Y.
Wherein, in the step (C), a subspace nuclear norm regularization regression model is established, a solving algorithm of alternative iteration is designed according to an operator classification method, the characteristics of each pixel point in the step (B) on the corresponding wave band are solved, and the classification results of all the wave bands are obtained, as shown in figure 3, the method comprises the following steps,
(C1) establishing a sub-dictionary for the training samples in each wave band image according to the categories of the training samples,
Figure BDA0001852644700000151
i＝1，…，dndenotes the ith band, L1, …, L denotes the ith class; p denotes a row of the image block, q denotes a column of the image block;
(C2) for the test sample Y in each band imagei，jWherein j is 1, …, niRepresenting the jth test sample image block, n, in the ith band imageiRepresenting the number of test samples in the ith wave band image, establishing a kernel norm regularization regression model in the subspace of the test samples,
Figure BDA0001852644700000152
wherein,
Figure BDA0001852644700000153
Figure BDA0001852644700000154
represents the test specimen Yi，jThe reconstructed image block in the I-th subspace,
Figure BDA0001852644700000155
representing coefficient vectors, wherein F is a reconstruction function of the image block;
(C3) optimizing the model according to the operator splitting and alternative iteration method to obtain each test sample Yi，j(j＝1，…，ni) The representation residuals in the I-th category, as shown in fig. 4, specifically includes the following steps:
(C31) input the sub-dictionary of each category
Figure BDA0001852644700000156
And test specimen Yi，j∈Rp×qModel parameter λ, tolerance error;
(C32) initializing intermediate variables
Figure BDA0001852644700000161
Whether the intermediate variable has a specific meaning or not;
(C33) calculating
Figure BDA0001852644700000162
Wherein
Figure BDA0001852644700000163
Vec (-) denotes the operator that converts the matrix into a vector;
(C34) calculating
Figure BDA0001852644700000164
Wherein
Figure BDA0001852644700000165
SVD denotes SVD decomposition;
(C35) calculating
Figure BDA0001852644700000166
(C36) Judging whether the iteration is stopped or not, if the following two conditions are met simultaneously, stopping the iteration,
Figure BDA0001852644700000167
Figure BDA0001852644700000168
(C37) the output represents the residual error
Figure BDA0001852644700000169
(C4) Representing residual errors by means of outputs
Figure BDA00018526447000001610
Obtaining Y according to the minimum residual error criterioni，jAnd obtaining classification results of all the wave bands according to the subordination categories.
Wherein, the step (D) integrates the classification results of all wave bands, uses the voting mode to calculate the category of each sample point, outputs the classification result of the hyperspectral image, as shown in figure 5, comprises the following steps,
(D1) counting the times of different categories of the jth pixel point in the hyperspectral image in each wave band;
(D2) obtaining the maximum times and the corresponding category thereof, and taking the maximum times and the corresponding category as the final category of the jth pixel point;
(D3) and solving the final category of all the pixel points according to the results of (D1) and (D2), thereby outputting the classification result of the hyperspectral image.
In summary, the hyperspectral image classification method based on the subspace nuclear norm regularization regression model of the invention selects the wave bands by using the sparse representation model, eliminates the non-discriminative wave bands, can improve the subsequent classification precision and speed, classifies the hyperspectral images by establishing the subspace nuclear norm regularization regression model, improves the classification precision, can be used in the fields of geological exploration, agricultural planting statistics and the like, has good application prospects, and has the following specific advantages:
(1) selecting the wave bands in the hyperspectral image by using a sparse representation model, and selecting the wave bands with discrimination to classify, so that the calculation amount of subsequent classification is reduced, and the interference of the wave bands without discrimination on classification results is eliminated;
(2) the image block is taken to represent the pixel point characteristics, and the spatial relationship and the context information of the pixel points in the image can be embodied;
(3) a subspace representation method of each category is designed, a kernel norm constraint discrimination model is established in each subspace, the low-rank characteristic of image blocks belonging to the same category under a dictionary is reflected through the kernel norm constraint, an alternative iterative algorithm of model solution is provided based on an operator splitting method, an original problem is converted into iterative solution of a plurality of sub-problems, and each sub-problem has an analytic solution.
Therefore, the hyperspectral image classification method can effectively improve the hyperspectral image classification precision and promote the further excavation of the low-rank characteristic of the hyperspectral image.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (4)

1. The hyperspectral image classification method based on the subspace nuclear norm regularization regression model is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
step (A), selecting wave bands of the known hyperspectral images, and constructing new hyperspectral images to be classified;
step (B), according to the new hyperspectral image to be classified, representing the image block of each pixel point in the two-dimensional image on the hyperspectral image to be classified of each wave band as the characteristic of the pixel point on the wave band;
step (C), establishing a subspace nuclear norm regularization regression model, designing an alternative iteration solving algorithm according to an operator classification method, and solving the characteristics of each pixel point in the step (B) on the corresponding wave band to obtain classification results of all the wave bands;
step (D), fusing the classification results of all the wave bands, solving the category of each pixel point by using a voting mode, and outputting the classification result of the hyperspectral image;
wherein, the step (A) of selecting the wave bands of the known hyperspectral images and constructing a new hyperspectral image to be classified comprises the following steps,
(A1) extracting the training samples of the known hyperspectral images and rearranging the training samples into a matrix, specifically, extracting the whole spectrum of the training samples to form a matrix X according to the positions of the training samples in the images,
Figure FDA0002750158190000011
wherein m is the number of training samples of the hyperspectral data, and d is the number of spectral wave bands of the hyperspectral image;
(A2) constructing a feature selection-oriented sparse representation model, obtaining a feature representation coefficient with sparse characteristics by an energy minimization method, and reconstructing a new hyperspectral image to be classified by selecting a wave band with the coefficient of 1 from the known hyperspectral images according to the obtained feature representation coefficient,
(A21) establishing a class mark vector y according to the class of the training sample,
y＝[l(x1),l(x2),…,l(xn)]Twhere l denotes the class of the current training sample, xi＝[xi,1,xi,2,…xid]Represents the entire spectral band value of the ith training sample;
(A22) establishing a hyperspectral image characteristic selection sparse representation model,
Figure FDA0002750158190000021
tau is a Lagrange multiplier, w is a vector with sparse characteristics to be solved, and s.t. is a constraint condition;
Figure FDA0002750158190000022
the meaning of (A) is: ask for w so that
Figure FDA0002750158190000023
The value is minimum;
(A23)，solving the minimization of a hyperspectral image feature selection sparse representation model by using a soft threshold iteration method, wherein the process comprises the steps of giving a multiplier lambda, a category label vector y, training a sample matrix X, setting the initial value of each value in a vector w to be 1, iteratively solving, and wt+1＝Proxλ(τwt-(XTy-XTXwt) Prox) is a projection function, which is expressed as follows:
Figure FDA0002750158190000024
wherein C represents an unknown variable;
(A24) judging the termination iteration condition | | wt+1-wtIf the result is less than or equal to 0.0001, if the result meets the requirement of outputting the vector w with the sparse characteristic, if the result does not meet the requirement, continuing the iteration until the condition of stopping the iteration is mett+1-wt||≤0.0001；
(A25) According to the output value of w, if wi(I-1, …, d) is equal to 0, the ith wave band is deleted from the known hyperspectral images, a new hyperspectral image I to be classified is constructed, and the number of the wave bands is dn(ii) a d is the wave band number of the hyperspectral remote sensing image.
2. The hyperspectral image classification method based on the subspace kernel norm regularization regression model according to claim 1 is characterized in that: step (B), according to the new hyperspectral image to be classified, the image block of each pixel point in the two-dimensional image on the hyperspectral image to be classified of each wave band is taken from the image and expressed as the characteristic of the pixel point on the wave band,
aiming at constructing each wave band image I in a new hyperspectral image I to be classifiedi(i＝1,…,dn) And selecting an image block with the size of p × q where the pixel point is located to represent the characteristics of the pixel point on the wave band, wherein the image block of the training sample is represented by A, and the image block of the test sample is represented by Y.
3. The hyperspectral image classification method based on the subspace kernel norm regularization regression model according to claim 2 is characterized in that: step (C), establishing a subspace nuclear norm regularization regression model, designing an alternative iteration solving algorithm based on an operator classification method, solving the characteristics of each pixel point in the step (B) on the corresponding wave band to obtain the classification results of all the wave bands, and comprises the following steps,
(C1) establishing a sub-dictionary for the training samples in each wave band image according to the categories of the training samples,
Figure FDA0002750158190000031
denotes the ith band, L1, …, L denotes the ith class; p denotes a row of the image block, q denotes a column of the image block;
(C2) for the test sample Y in each band imagei,jWherein j is 1, …, niRepresenting the jth test sample image block, n, in the ith band imageiRepresenting the number of test samples in the ith wave band image, establishing a kernel norm regularization regression model in the subspace of the test samples,
Figure FDA0002750158190000041
wherein,
Figure FDA0002750158190000042
Figure FDA0002750158190000043
represents the test specimen Yi,jThe reconstructed image block in the l-th subspace,
Figure FDA0002750158190000044
is a representation coefficient vector, F is a reconstruction function of the image block;
(C3) optimizing the model according to the operator splitting and alternative iteration method to obtain each test sample Yi,j(j＝1,…,ni) Representation residual in the l-th categoryThe specific process is as follows:
(C31) input the sub-dictionary of each category
Figure FDA0002750158190000045
And test specimen Yi,j∈Rp×qModel parameter λ, tolerance error;
(C32) initializing intermediate variables
Figure FDA0002750158190000046
μ；
(C33) Calculating
Figure FDA0002750158190000047
Wherein
Figure FDA0002750158190000048
Vec (-) denotes the operator that converts the matrix into a vector;
(C34) calculating
Figure FDA0002750158190000049
Wherein
Figure FDA00027501581900000410
SVD denotes SVD decomposition;
(C35) calculating
Figure FDA00027501581900000411
(C36) Judging whether the iteration is stopped or not, if the following two conditions are met simultaneously, stopping the iteration,
Figure FDA00027501581900000412
Figure FDA0002750158190000051
(C37) the output represents the residual error
Figure FDA0002750158190000052
(C4) Representing residual errors by means of outputs
Figure FDA0002750158190000053
Obtaining Y according to the minimum residual error criterioni,jAnd obtaining classification results of all the wave bands according to the subordination categories.
4. The hyperspectral image classification method based on the subspace kernel norm regularization regression model according to claim 3 is characterized in that: step (D), fusing the classification results of all wave bands, solving the classification of each pixel point by using a voting mode, and outputting the classification result of the hyperspectral image, comprising the following steps,
(D1) counting the times of different categories of the jth pixel point in the hyperspectral image in each wave band;
(D2) obtaining the maximum times and the corresponding category thereof, and taking the maximum times and the corresponding category as the final category of the jth pixel point;
(D3) and solving the final category of all the pixel points according to the results of (D1) and (D2), thereby outputting the classification result of the hyperspectral image.
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