CN105913092B - Figure canonical hyperspectral image band selection method based on sub-space learning - Google Patents
Figure canonical hyperspectral image band selection method based on sub-space learning Download PDFInfo
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Abstract
The step of the invention proposes a kind of figure canonical hyperspectral image band selection method based on sub-space learning, specific implementation are as follows: (1) input hyperspectral image data matrix；(2) normalization data matrix；(3) figure canonical wave band similarity matrix is calculated；(4) figure canonical wave band similarity diagonal matrix is calculated；(5) restructuring matrix is constructed；(6) restructuring matrix is initialized；(7) the number of iterations is set；(8) subspace waveband selection matrix is calculated；(9) judge whether current iteration number is greater than maximum number of iterations, if so, thening follow the steps (10), otherwise, current iteration number is added 1, is executed step (8)；(10) subspace waveband selection matrix is exported；(11) constructor spatial data matrix.The present invention provides study mechanisms to improve the accuracy of waveband selection using spectral space geometry information.
Description
Technical field
The invention belongs to technical field of image processing, further relate to Hyperspectral imaging (Hyperspectral
Imagery) figure canonical hyperspectral image band selection method of one of the sorting technique field based on sub-space learning.This hair
The bright feature excessive for image redundancy wave band in Hyperspectral imaging processing, a kind of method of waveband selection of proposition are selected
Comprising the wave band to contain much information, redundancy is eliminated, reduces the dimension of image, can be used for the dimension of high spectrum image about
Letter, the wave band that simultaneous selection comes out also are conducive to image classification, improve the nicety of grading of high spectrum image.
Background technique
With the continuous development of domestic and international high spectrum resolution remote sensing technique, many method quilts for being directed to high spectrum image waveband selection
Put forward.
Paper " the Band selection for hyperspectral images that V.Kumar et al. is delivered at it
One kind is proposed in based on self-tuning spectral clustering " (EUSIPCO, 2013:1-50) to be based on
The EO-1 hyperion band selection method of self-adjusting spectral clustering.This method is first clustered all wave bands for K class with the method for spectral clustering；
Then the covariance matrix of all kinds of medium wave bands is obtained with the method for principal component analysis, and calculates characteristic value and the spy of covariance matrix
Vector is levied, these feature vectors as the feature vector base of respective class；A suitable characteristic value is finally obtained by training
Selection ratio, and it is all kinds of it is middle choose the ratios under characteristic values corresponding to feature vector as class feature vector base,
All kinds of feature vector bases is merged into a transformation matrix, the data matrix of higher-dimension can be transformed to by transformation matrix
Low-dimensional matrix realizes the purpose of dimensionality reduction.Similar wave band is divided into one kind by this method, and piecemeal processing eliminates superfluous well
It is remaining.But the shortcoming that this method still has is, this method calculates spectral clustering and transformation matrix substep, still
It is interactional between this two step, therefore this method lacks study mechanism, is unable to better choice and provides representational wave
Section.Also, this method reaches dimensionality reduction purpose using a transformation matrix to carry out low-dimensional mapping to initial data, without encumbrance
According to original physical significance, lack interpretation.
Patent " hyperspectral image band selection method based on low-rank representation " (patent of Xian Electronics Science and Technology University's application
Application number: CN201510411250.9, publication number: CN105046276A) propose a kind of high-spectrum of low-rank representation cluster
As band selection method.This method carries out low-rank representation to image, and solves low-rank representation using augmented Lagrange multiplier method
Then coefficient clusters low-rank representation coefficient, most representational wave band is selected from each cluster as final
The wave band of selection.The characteristics of low-rank representation is utilized in this method well, represents wave band with the coefficient of low-rank representation, pass through by
Low-rank representation coefficient cluster, has selected representative wave band.Shortcoming existing for this method is the low-rank of this method
Indicate the partial structurtes information that data are not used in the solution of coefficient, the low-rank representation coefficient learnt is not accurate enough, most
The wave band selected eventually is also not representative enough.
Summary of the invention
It is an object of the invention to overcome above-mentioned the deficiencies in the prior art, a kind of figure based on sub-space learning is being proposed just
Then hyperspectral image band selection method.Present invention utilizes the geometry informations of spectral space, and by sub-space learning with
Partial structurtes retain item and optimize simultaneously, have obtained a good study mechanism, and the wave band selected is more representative, improve
The accuracy of waveband selection；Representative wave band is selected from initial data in such a way that wave band is evaluated, and is retained
Data original physical significances.
The present invention realizes that the thinking of above-mentioned purpose is: hyperspectral image data matrix being done normalized, using Gauss
Kernel function is as weight metric, and the similarity matrix for calculating normalized hyperspectral image data matrix and similarity are to angular moment
Battle array；Utilize the more new formula of the diagonal matrix of normalized hyperspectral image data matrix, normalized hyperspectral image data
The more new formula of the coefficient matrix of matrix, normalized hyperspectral image data matrix waveband selection matrix more new formula,
It is updated by iteration, obtains the waveband selection matrix of the normalized hyperspectral image data matrix after the completion of the number of iterations；It adopts
It is calculated normalized with wave band evaluation of estimate method using the waveband selection matrix of normalized hyperspectral image data matrix
The wave band evaluation of estimate vector of hyperspectral image data matrix, by the wave band evaluation of estimate of normalized hyperspectral image data matrix to
Element in amount sorts from large to small, and selects the maximum wave band of wave band evaluation of estimate, constitutes new hyperspectral image data matrix.
The present invention realizes that specific step is as follows:
(1) hyperspectral image data matrix is inputted；
(2) hyperspectral image data matrix is normalized:
Element all in hyperspectral image data matrix is normalized, normalized high spectrum image is obtained
Data matrix, using every a line of normalized hyperspectral image data matrix as a wave band；
(3) figure canonical wave band similarity is calculated:
Using weight metric algorithm, the figure canonical wave band phase of normalized all wave bands of hyperspectral image data matrix is calculated
Like degree；
(4) figure canonical wave band similarity diagonal matrix is calculated:
The figure canonical wave band similarity of normalized all wave bands of hyperspectral image data matrix is diagonally handled, is obtained
To the figure canonical wave band similarity diagonal matrix of normalized all wave bands of hyperspectral image data matrix；
(5) restructuring matrix is constructed:
Using all 1's matrix method, diagonal matrix, the normalized EO-1 hyperion of normalized hyperspectral image data matrix are constructed
Three, subspace waveband selection matrix reconstruct of the coefficient matrix of image data matrix, normalized hyperspectral image data matrix
Matrix；
(6) restructuring matrix is initialized:
It is to the diagonal matrix of normalized hyperspectral image data matrix, normalized hyperspectral image data matrix
Matrix number, normalized hyperspectral image data matrix three restructuring matrixes of subspace waveband selection matrix initialized；
(7) the number of iterations is set:
0 is set by the number of iterations, sets 30 for maximum number of iterations；
(8) subspace waveband selection matrix is calculated:
(8a) obtains current iteration time using the more new formula of the diagonal matrix of normalized hyperspectral image data matrix
The diagonal matrix of the normalized hyperspectral image data matrix of several lower updates；
(8b) obtains current iteration time using the more new formula of the coefficient matrix of normalized hyperspectral image data matrix
The coefficient matrix of the normalized hyperspectral image data matrix of several lower updates；
(8c) is obtained using the more new formula of the subspace waveband selection matrix of normalized hyperspectral image data matrix
The subspace waveband selection matrix of the normalized hyperspectral image data matrix updated under current iteration number；
(9) judge whether current iteration number is greater than maximum number of iterations, if so, thening follow the steps (10), otherwise, will work as
Preceding the number of iterations adds 1, executes step (8)；
(10) subspace waveband selection matrix；
(11) high spectrum image subspace data matrix is constructed:
(11a) uses wave band evaluation of estimate formula, is selected using the subspace wave band of normalized hyperspectral image data matrix
Matrix is selected, the wave band evaluation of estimate vector of normalized hyperspectral image data matrix is calculated；
(11b) arranges the element in the wave band evaluation of estimate vector of normalized hyperspectral image data matrix from big to small
The maximum wave band of wave band evaluation of estimate selected in sequence is configured to high spectrum image subspace data matrix by sequence.
It is calculated using wave band evaluation of estimate method using the waveband selection matrix of normalized hyperspectral image data matrix
The wave band evaluation of estimate vector of normalized hyperspectral image data matrix out, by the wave of normalized hyperspectral image data matrix
Element in section evaluation of estimate vector sorts from large to small, and selects the maximum wave band of wave band evaluation of estimate, constitutes new high-spectrum
As data matrix.
Compared with the prior art, the present invention has the following advantages:
First, since the present invention is using the update of the waveband selection matrix using normalized hyperspectral image data matrix
Formula, the method for obtaining the waveband selection matrix of the normalized hyperspectral image data matrix updated under current iteration number,
It overcomes the prior art and lacks study mechanism, the problem of better choice provides representational wave band is unable to, so that of the invention
Can be by a good study mechanism, the wave band selected is more representative, improves the accuracy of waveband selection.
Second, due to taking full advantage of the several of spectral space present invention uses the method for calculating wave band similarity matrix
What structural information, overcomes the problem of prior art does not use the partial structurtes information of data, so that the present invention improves
The accuracy of waveband selection.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is the experimental result comparison diagram of the present invention with the prior art；
Fig. 3 is the analogous diagram of the present invention with the prior art.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
Referring to attached drawing 1, the specific steps of the present invention are as follows.
Step 1, hyperspectral image data matrix is inputted.
In embodiments of the present invention, the hyperspectral image data matrix of input is by Indian Pines high spectrum image
It obtains.
Step 2, hyperspectral image data matrix is normalized.
Element all in hyperspectral image data matrix is normalized, normalized high spectrum image is obtained
Data matrix, using every a line of normalized hyperspectral image data matrix as a wave band.
Hyperspectral image data matrix is normalized specific step is as follows:
Step 1: an element is arbitrarily chosen from hyperspectral image data matrix；
The difference of step 2: calculating selected element and the element is expert at middle least member；
Step 3: it calculates selected element and is expert at the difference of middle greatest member and least member；
Step 4: the difference that the difference obtained with step 2 is obtained divided by step 3 obtains the normalization knot of selected element
Fruit；
Step 5: judging whether element all in hyperspectral image data matrix has selected, if so, output is normalized
Otherwise hyperspectral image data matrix executes step 1.
In embodiments of the present invention, using the mapmaxmin function in Matlab R2011b software to high spectrum image number
It is normalized according to matrix.
Step 3, figure canonical wave band similarity matrix is calculated.
Using weight metric algorithm, the figure canonical wave band phase of normalized all wave bands of hyperspectral image data matrix is calculated
Like degree matrix.
Weight metric algorithm is as follows:
Step 1: according to the following formula, the Euclidean distance between normalized all wave bands of hyperspectral image data matrix is calculated:
Wherein, E indicates the Euclidean distance between normalized all wave bands of hyperspectral image data matrix,Expression is opened
Square operation, X indicate that normalized hyperspectral image data matrix, * indicate the operation of Hadamard matrix multiple, and A indicates n × d
All 1's matrix, n indicates that the pixel sum of normalized hyperspectral image data matrix, d indicate normalized high spectrum image
The wave band sum of data matrix, B indicate that all 1's matrix of d × n, T indicate transposition operation；
Step 2: according to the following formula, the figure canonical wave band for calculating normalized all wave bands of hyperspectral image data matrix is similar
Spend matrix；
S=exp (- E/ σ2)
Wherein, S indicates the figure canonical wave band similarity matrix of normalized all wave bands of hyperspectral image data matrix,
Exp () indicates that index operation, E indicate the Euclidean distance between normalized all wave bands of hyperspectral image data matrix, σ table
Show Gauss scale parameter, the value of σ is 10.
Step 4, wave band similarity diagonal matrix is calculated.
Diagonal angle is carried out to the figure canonical wave band similarity matrix of normalized all wave bands of hyperspectral image data matrix
Reason, obtains the figure canonical wave band similarity diagonal matrix of normalized all wave bands of hyperspectral image data matrix.
Diagonal processing refers to be acquired according to the following formula:
Wherein, D indicates the figure canonical wave band similarity diagonal matrix of normalized hyperspectral image data matrix, diag
() indicates construction diagonal matrix operation, and ∑ indicates overlap-add operation, [S]jIndicate normalized hyperspectral image data matrix institute
There is the jth of the figure canonical wave band similarity matrix of wave band to arrange, j ∈ { 1,2 ..., d }, d indicate normalized high spectrum image number
According to the wave band sum of matrix.
Step 5, restructuring matrix is constructed.
Using all 1's matrix method, diagonal matrix, the normalized EO-1 hyperion of normalized hyperspectral image data matrix are constructed
Three, subspace waveband selection matrix reconstruct of the coefficient matrix of image data matrix, normalized hyperspectral image data matrix
Matrix.
Specific step is as follows for all 1's matrix method:
Step 1: construction size is the diagonal matrix for the normalized hyperspectral image data matrix that d × d element is all 1, d
Indicate the wave band sum of normalized hyperspectral image data matrix；
Step 2: construction size is the coefficient matrix for the normalized hyperspectral image data matrix that l × d element is all 1, l
Indicate that the wave band number of selected normalization hyperspectral image data matrix, the value range of l are { 1,2 ..., d }, d is indicated
The wave band sum of normalized hyperspectral image data matrix；
Step 3: construction size is the subspace wave band for the normalized hyperspectral image data matrix that d × l element is all 1
Selection matrix, l indicate the wave band number of selected normalization hyperspectral image data matrix, the value range of l for 1,
2 ..., d }, d indicates the wave band sum of normalized hyperspectral image data matrix.
Step 6, restructuring matrix is initialized.
It is to the diagonal matrix of normalized hyperspectral image data matrix, normalized hyperspectral image data matrix
Matrix number, normalized hyperspectral image data matrix three restructuring matrixes of subspace waveband selection matrix initialized.
To reconstruct matrix initialisation, specific step is as follows:
Step 1: using unit matrix initial method, and the diagonal matrix of normalized hyperspectral image data matrix is initial
The unit matrix of d × d is turned to, d indicates the wave band sum of normalized hyperspectral image data matrix；
Step 2: random initializtion method is used, the coefficient matrix of normalized hyperspectral image data matrix is initialized as
The random matrix of l × d, l indicate that the wave band number of selected normalization hyperspectral image data matrix, the value range of l are
{ 1,2 ..., d }, d indicate the wave band sum of normalized hyperspectral image data matrix；
Step 3: random initializtion method is used, by the subspace waveband selection square of normalized hyperspectral image data matrix
Battle array is initialized as the random matrix of d × l, and l indicates the wave band number of selected normalization hyperspectral image data matrix, l's
Value range is { 1,2 ..., d }, and d indicates the wave band sum of normalized hyperspectral image data matrix.
In embodiments of the present invention, using the eye function in Matlab R2011b software to normalized high spectrum image
The diagonal matrix of data matrix is initialized, using the rand function in Matlab R2011b software to normalized bloom
The subspace waveband selection matrix of the coefficient matrix and normalized hyperspectral image data matrix of composing image data matrix carries out
Initialization.
Step 7, the number of iterations is set.
0 is set by the number of iterations, sets 30 for maximum number of iterations.
Step 8, subspace waveband selection matrix is calculated.
Firstly, the more new formula of the diagonal matrix using normalized hyperspectral image data matrix, obtains current iteration
The diagonal matrix of the normalized hyperspectral image data matrix updated under number.
The more new formula of the diagonal matrix of normalized hyperspectral image data matrix is as follows:
Wherein, U(t+1)Indicate pair of the normalized hyperspectral image data matrix updated when current iteration number is t+1
Angular moment battle array, diag () indicate construction diagonal matrix operation, and ∑ indicates overlap-add operation, [W(t)]jIndicate that last the number of iterations is
The jth of the subspace waveband selection matrix of the normalized hyperspectral image data matrix obtained when t arranges, j ∈ 1,2 ...,
L }, l indicates that the wave band number of selected normalization hyperspectral image data matrix, the value range of l are { 1,2 ..., d }, d
Indicate the wave band sum of normalized hyperspectral image data matrix.
Secondly, the more new formula of the coefficient matrix using normalized hyperspectral image data matrix, obtains current iteration
The coefficient matrix of the normalized hyperspectral image data matrix updated under number.
The more new formula of the coefficient matrix of normalized hyperspectral image data matrix is as follows:
Wherein, H(t+1)Indicate that the normalized hyperspectral image data matrix updated when current iteration number is t+1 is
Matrix number, H(t)Indicate the coefficient matrix of the normalized hyperspectral image data matrix obtained when last the number of iterations is t, *
Indicate the operation of Hadamard matrix multiple, α indicates balance parameters, and the value range of α is { 10-3,10-4,10-5,10-6,10-7, W(t)Indicate the subspace waveband selection square of the normalized hyperspectral image data matrix obtained when last the number of iterations is t
Battle array, T indicate transposition operation, and X indicates that normalized hyperspectral image data matrix, S indicate normalized hyperspectral image data
The figure canonical wave band similarity matrix of all wave bands of matrix, D indicate the figure canonical wave of normalized hyperspectral image data matrix
Section similarity diagonal matrix.
Finally, the more new formula of the subspace waveband selection matrix using normalized hyperspectral image data matrix, obtains
The subspace waveband selection matrix of the normalized hyperspectral image data matrix updated under to current iteration number.
The more new formula of the subspace waveband selection matrix of normalized hyperspectral image data matrix is as follows:
Wherein, W(t+1)Indicate the son of the normalized hyperspectral image data matrix updated when current iteration number is t+1
Space wave band selection matrix, * indicate the operation of Hadamard matrix multiple, and α indicates balance parameters, and the value range of α is { 10-3,
10-4,10-5,10-6,10-7, X indicates that normalized hyperspectral image data matrix, T indicate transposition operation, H(t)Indicate last
The coefficient matrix for the normalized hyperspectral image data matrix that the number of iterations obtains when being t, λ indicate Orthogonal Parameter, the value of λ
It is 10+8, β expression Sparse parameter, the value range of β is { 10+3,10+4,10+5,10+6,10+7, U(t)Indicate last iteration time
The diagonal matrix for the normalized hyperspectral image data matrix that number obtains when being t.
Step 9, judge whether current iteration number is greater than maximum number of iterations, if so, thening follow the steps 9, otherwise, will work as
Preceding the number of iterations adds 1, executes step 7.
Step 10, subspace waveband selection matrix.
Step 11, high spectrum image subspace data matrix is constructed.
Using wave band evaluation of estimate formula, the subspace waveband selection square of normalized hyperspectral image data matrix is utilized
Battle array, calculates the wave band evaluation of estimate vector of normalized hyperspectral image data matrix.
Wave band evaluation of estimate formula is as follows:
Wherein, a indicates that the wave band evaluation of estimate vector of normalized hyperspectral image data matrix, ∑ indicate overlap-add operation, W
Indicate that the subspace waveband selection matrix of normalized hyperspectral image data matrix, * indicate the operation of Hadamard matrix multiple,
[W*W]jJth column after indicating the subspace waveband selection matrix square of normalized hyperspectral image data matrix, j ∈ 1,
2 ..., l }, l indicates the wave band number of selected normalization hyperspectral image data matrix, the value range of l for 1,
2 ..., d }, d indicates the wave band sum of normalized hyperspectral image data matrix,Indicate extraction of square root operation.
Element in the wave band evaluation of estimate vector of normalized hyperspectral image data matrix is sorted from large to small, will be arranged
The maximum wave band of wave band evaluation of estimate selected in sequence is configured to high spectrum image subspace data matrix.
Below with reference to emulation experiment, the present invention will be further described.
1. emulation experiment condition:
The hardware test platform that emulation experiment of the invention uses is: processor is for Inter Core i5, dominant frequency
2.30GHz, memory 4GB；Software platform are as follows: 7 Ultimate of Windows, 64 bit manipulation system, MatlabR2011b carry out emulation survey
Examination.
2. emulation experiment content:
To using the Indian Pines high spectrum image obtained by airborne visual light imaging spectrometer AVIRIS
Carry out waveband selection and sorting algorithm emulation.
The Indian Pines high spectrum image that emulation experiment of the invention uses, it includes 16 class main vegetations and 220
A wave band.It in experiment, is studied mainly for 16 class main vegetations, and to remove water absorption bands, therefore in experiment only
10366 pixels and 200 wave bands are used to get to 200 × 10366 high spectrum image image data matrix.
Waveband selection carried out to image data matrix with the present invention, and by KNN of the result after selection in the tool box KNN
Classifier is classified, and waveband selection effect is verified with classification accuracy, and 7% pixel conduct is randomly selected in this experiment
Training sample, remaining is set as 6 as test sample, neighbour's parameter K of KNN classifier, is averaged for independent operating 10 times
As classification results.
3. analysis of simulation result:
Fig. 2 is the experimental result comparison diagram of the present invention with the prior art, and Fig. 2 shows KNN classifier to the present invention, self-regulated
The selection result of whole spectral clustering band selection method and the full choosing method of wave band carries out obtained nicety of grading comparison of classifying.Figure
Abscissa in 2 indicates waveband selection number l, ordinate presentation class precision OA.The curve generation indicated with triangle in Fig. 2
It is that the table present invention emulates as a result, with diamond shape indicate curve represent self-adjusting spectral clustering band selection method emulation as a result, with
The result of the method emulation of the curve table oscillography Duan Quanxuan of circle mark.As seen from Figure 2, the present invention is in most wave bands
Classification results under selection number are all better than self-adjusting spectral clustering band selection method, and when selecting wave band number is 50,
Nicety of grading is higher than the method selected entirely of wave band, this indicates that the present invention not only realizes the dimensionality reduction to data, but also also improves point
Class precision, has fully demonstrated advantages of the present invention.
Fig. 3 is analogous diagram of the invention, and Fig. 3 (a) is the true value figure of original I ndian Pines high spectrum image, Fig. 3 (b)
It is KNN classification results figure when self-adjusting spectral clustering band selection method selects 50 wave bands, Fig. 3 (c) is present invention selection 50
KNN classification results figure when a wave band, Fig. 3 (d) are KNN classification results figures when wave band selects entirely.As seen from Figure 3, this hair
Bright obtained classification results figure closer to the true value figure of original I ndianPines high spectrum image, divide completely by basic class
Out, wrong point of point is relatively fewer, it was demonstrated that the present invention can obtain better waveband selection results.
Claims (10)
1. a kind of figure canonical hyperspectral image band selection method based on sub-space learning, includes the following steps:
(1) hyperspectral image data matrix is inputted；
(2) hyperspectral image data matrix is normalized:
Element all in hyperspectral image data matrix is normalized, normalized hyperspectral image data is obtained
Matrix, using every a line of normalized hyperspectral image data matrix as a wave band；
(3) figure canonical wave band similarity matrix is calculated:
Using weight metric algorithm, the figure canonical wave band for calculating normalized all wave bands of hyperspectral image data matrix is similar
Degree, obtains the figure canonical wave band similarity matrix of normalized all wave bands of hyperspectral image data matrix；
(4) figure canonical wave band similarity diagonal matrix is calculated:
The figure canonical wave band similarity matrix of normalized all wave bands of hyperspectral image data matrix is diagonally handled, is obtained
To the figure canonical wave band similarity diagonal matrix of normalized all wave bands of hyperspectral image data matrix；
(5) restructuring matrix is constructed:
Using all 1's matrix method, diagonal matrix, the normalized high spectrum image of normalized hyperspectral image data matrix are constructed
Three reconstruct squares of subspace waveband selection matrix of the coefficient matrix of data matrix, normalized hyperspectral image data matrix
Battle array；
(6) restructuring matrix is initialized:
To the coefficient square of the diagonal matrix of normalized hyperspectral image data matrix, normalized hyperspectral image data matrix
Battle array, normalized hyperspectral image data matrix three restructuring matrixes of subspace waveband selection matrix initialized；
(7) the number of iterations is set:
0 is set by the number of iterations, sets 30 for maximum number of iterations；
(8) subspace waveband selection matrix is calculated:
(8a) is obtained under current iteration number using the more new formula of the diagonal matrix of normalized hyperspectral image data matrix
The diagonal matrix of the normalized hyperspectral image data matrix updated；
(8b) is obtained under current iteration number using the more new formula of the coefficient matrix of normalized hyperspectral image data matrix
The coefficient matrix of the normalized hyperspectral image data matrix updated；
(8c) is obtained current using the more new formula of the subspace waveband selection matrix of normalized hyperspectral image data matrix
The subspace waveband selection matrix of the normalized hyperspectral image data matrix updated under the number of iterations；
(9) judge whether current iteration number is greater than maximum number of iterations, if so, thening follow the steps (10), otherwise, will currently change
Generation number adds 1, executes step (8)；
(10) subspace waveband selection matrix；
(11) high spectrum image subspace data matrix is constructed:
(11a) uses wave band evaluation of estimate formula, utilizes the subspace waveband selection square of normalized hyperspectral image data matrix
Battle array, calculates the wave band evaluation of estimate vector of normalized hyperspectral image data matrix；
(11b) sorts from large to small the element in the wave band evaluation of estimate vector of normalized hyperspectral image data matrix, will
The maximum wave band of wave band evaluation of estimate selected in sequence is configured to high spectrum image subspace data matrix.
2. the figure canonical hyperspectral image band selection method according to claim 1 based on sub-space learning, feature
It is, hyperspectral image data matrix is normalized described in step (2) specific step is as follows:
Step 1: an element is arbitrarily chosen from hyperspectral image data matrix；
The difference of step 2: calculating selected element and the element is expert at middle least member；
Step 3: it calculates selected element and is expert at the difference of middle greatest member and least member；
Step 4: the difference that the difference obtained with step 2 is obtained divided by step 3 obtains the normalization result of selected element；
Step 5: judging whether element all in hyperspectral image data matrix has selected, if so, exporting normalized bloom
Image data matrix is composed, otherwise, executes step 1.
3. the figure canonical hyperspectral image band selection method according to claim 1 based on sub-space learning, feature
It is, weight metric algorithm described in step (3) is as follows:
Step 1: according to the following formula, the Euclidean distance between normalized all wave bands of hyperspectral image data matrix is calculated:
Wherein, E indicates the Euclidean distance between normalized all wave bands of hyperspectral image data matrix,Indicate extraction of square root behaviour
Make, X indicates that normalized hyperspectral image data matrix, * indicate the operation of Hadamard matrix multiple, and A indicates complete 1 square of n × d
Battle array, n indicate that the pixel sum of normalized hyperspectral image data matrix, d indicate normalized hyperspectral image data square
The wave band sum of battle array, B indicate that all 1's matrix of d × n, T indicate transposition operation；
Step 2: according to the following formula, the figure canonical wave band similarity of normalized all wave bands of hyperspectral image data matrix is calculated；
S=exp (- E/ σ2)
Wherein, S indicates the figure canonical wave band similarity matrix of normalized all wave bands of hyperspectral image data matrix, exp
() indicates that index operation, E indicate that the Euclidean distance between normalized all wave bands of hyperspectral image data matrix, σ indicate
Gauss scale parameter, the value of σ are 10.
4. the figure canonical hyperspectral image band selection method according to claim 1 based on sub-space learning, feature
It is, diagonal processing refers to described in step (4) acquires according to the following formula:
Wherein, D indicates the figure canonical wave band similarity diagonal matrix of normalized hyperspectral image data matrix, diag () table
Show construction diagonal matrix operation, ∑ indicates overlap-add operation, [S]jIndicate normalized all wave bands of hyperspectral image data matrix
Figure canonical wave band similarity matrix jth column, j ∈ { 1,2 ..., d }, d indicate normalized hyperspectral image data matrix
Wave band sum.
5. the figure canonical hyperspectral image band selection method according to claim 1 based on sub-space learning, feature
It is, specific step is as follows for all 1's matrix method described in step (5):
Step 1: construction size is the diagonal matrix for the normalized hyperspectral image data matrix that d × d element is all 1, and d is indicated
The wave band sum of normalized hyperspectral image data matrix；
Step 2: construction size is the coefficient matrix for the normalized hyperspectral image data matrix that l × d element is all 1, and l is indicated
The wave band number of selected normalization hyperspectral image data matrix, the value range of l are { 1,2 ..., d }, and d indicates normalizing
The wave band sum of the hyperspectral image data matrix of change；
Step 3: construction size is the subspace waveband selection for the normalized hyperspectral image data matrix that d × l element is all 1
Matrix, l indicate the wave band number of selected normalization hyperspectral image data matrix, the value range of l for 1,2 ...,
D }, d indicates the wave band sum of normalized hyperspectral image data matrix.
6. the figure canonical hyperspectral image band selection method according to claim 1 based on sub-space learning, feature
It is, to reconstruct matrix initialisation, specific step is as follows described in step (6):
Step 1: unit matrix initial method is used, the diagonal matrix of normalized hyperspectral image data matrix is initialized as
The unit matrix of d × d, d indicate the wave band sum of normalized hyperspectral image data matrix；
Step 2: random initializtion method is used, the coefficient matrix of normalized hyperspectral image data matrix is initialized as l × d
Random matrix, l indicates the wave band number of selected normalization hyperspectral image data matrix, the value range of l for 1,
2 ..., d }, d indicates the wave band sum of normalized hyperspectral image data matrix；
Step 3: using random initializtion method, will be at the beginning of the subspace waveband selection matrix of normalized hyperspectral image data matrix
Beginning turns to the random matrix of d × l, and l indicates the wave band number of selected normalization hyperspectral image data matrix, the value of l
Range is { 1,2 ..., d }, and d indicates the wave band sum of normalized hyperspectral image data matrix.
7. the figure canonical hyperspectral image band selection method according to claim 1 based on sub-space learning, feature
It is, the more new formula of the diagonal matrix of normalized hyperspectral image data matrix described in step (8a) is as follows:
Wherein, U(t+1)Indicate current iteration number be t+1 when update normalized hyperspectral image data matrix to angular moment
Battle array, diag () indicate construction diagonal matrix operation, and ∑ indicates overlap-add operation, [W(t)]jWhen indicating that last the number of iterations is t
The jth of the waveband selection matrix of obtained normalized hyperspectral image data matrix arranges, and j ∈ { 1,2 ..., l }, l indicate institute
The wave band number of the normalization hyperspectral image data matrix of selection, the value range of l are { 1,2 ..., d }, and d indicates normalization
Hyperspectral image data matrix wave band sum.
8. the figure canonical hyperspectral image band selection method according to claim 1 based on sub-space learning, feature
It is, the more new formula of the coefficient matrix of normalized hyperspectral image data matrix described in step (8b) is as follows:
Wherein, H(t+1)Indicate the coefficient square of the normalized hyperspectral image data matrix updated when current iteration number is t+1
Battle array, H(t)Indicate that the coefficient matrix of the normalized hyperspectral image data matrix obtained when last the number of iterations is t, * indicate
The operation of Hadamard matrix multiple, α indicate balance parameters, and the value range of α is { 10-3,10-4,10-5,10-6,10-7, W(t)Table
Show the subspace waveband selection matrix of the normalized hyperspectral image data matrix obtained when last the number of iterations is t, T table
Show that transposition operates, X indicates that normalized hyperspectral image data matrix, S indicate normalized hyperspectral image data matrix institute
There is the figure canonical wave band similarity matrix of wave band, D indicates that the figure canonical wave band of normalized hyperspectral image data matrix is similar
Spend diagonal matrix.
9. the figure canonical hyperspectral image band selection method according to claim 1 based on sub-space learning, feature
It is, the more new formula of the subspace waveband selection matrix of normalized hyperspectral image data matrix described in step (8c)
It is as follows:
Wherein, W(t+1)Indicate the subspace of the normalized hyperspectral image data matrix updated when current iteration number is t+1
Waveband selection matrix, * indicate the operation of Hadamard matrix multiple, and α indicates balance parameters, and the value range of α is { 10-3,10-4,
10-5,10-6,10-7, X indicates that normalized hyperspectral image data matrix, T indicate transposition operation, H(t)Indicate last iteration
The coefficient matrix for the normalized hyperspectral image data matrix that number obtains when being t, λ indicate Orthogonal Parameter, and the value of λ is 10+8, β expression Sparse parameter, the value range of β is { 10+3,10+4,10+5,10+6,10+7, U(t)Indicate that last the number of iterations is t
When the obtained diagonal matrix of normalized hyperspectral image data matrix.
10. the figure canonical hyperspectral image band selection method according to claim 1 based on sub-space learning, feature
It is, wave band evaluation of estimate formula described in step (11a) is as follows:
Wherein, a indicates that the wave band evaluation of estimate vector of normalized hyperspectral image data matrix, ∑ indicate overlap-add operation, and W is indicated
The subspace waveband selection matrix of normalized hyperspectral image data matrix, * indicate the operation of Hadamard matrix multiple, [W*
W]jJth column after indicating the subspace waveband selection matrix square of normalized hyperspectral image data matrix, j ∈ 1,
2 ..., l }, l indicates the wave band number of selected normalization hyperspectral image data matrix, the value range of l for 1,
2 ..., d }, d indicates the wave band sum of normalized hyperspectral image data matrix,Indicate extraction of square root operation.
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