CN110135448B - Hyperspectral image virtual dimension estimation method based on ridge ratio shrinkage - Google Patents

Hyperspectral image virtual dimension estimation method based on ridge ratio shrinkage Download PDF

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CN110135448B
CN110135448B CN201811595570.4A CN201811595570A CN110135448B CN 110135448 B CN110135448 B CN 110135448B CN 201811595570 A CN201811595570 A CN 201811595570A CN 110135448 B CN110135448 B CN 110135448B
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朱学虎
康越
刘军民
罗兰
王一成
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Abstract

The invention discloses a method for estimating a virtual dimension of a hyperspectral image based on ridge ratio shrinkage, which comprises the following steps of: extracting a sample matrix of a hyperspectral image to be processed; calculating a covariance matrix and a correlation matrix of the obtained sample matrix, calculating characteristic values of the covariance matrix and the correlation matrix, and sequencing the characteristic values; constructing a ratio sequence according to the characteristic value sequence; and comparing the sequence value in the ratio sequence with a preset constraint value to obtain the virtual dimension of the hyperspectral image to be processed. The estimation method of the invention abandons the idea of hypothesis test, and directly adopts the algorithm for constructing the ratio series for estimation, thereby improving the accuracy of the virtual dimension estimation of the hyperspectral image.

Description

Hyperspectral image virtual dimension estimation method based on ridge ratio shrinkage
Technical Field
The invention belongs to the technical field of virtual dimension estimation of hyperspectral images, and particularly relates to a virtual dimension estimation method of a hyperspectral image based on ridge ratio shrinkage.
Background
Spectral images with spectral resolution in the order of 10nm are called hyperspectral images. By means of high spectrum sensors carried on different space platforms, namely an imaging spectrometer, a target area is imaged simultaneously in tens of to hundreds of continuous and subdivided spectral bands in ultraviolet, visible light, near infrared and mid-infrared areas of an electromagnetic spectrum; the earth surface image information is obtained, and simultaneously the spectrum information is also obtained, so that the combination of the spectrum and the image is really realized. Compared with multispectral remote sensing images, the hyperspectral images not only greatly improve the information abundance, but also provide possibility for more reasonable and effective analysis and processing of the type of spectral data in the aspect of processing technology. The influence and the development potential of the hyperspectral image technology are incomparable with the development stages of the prior art. It not only draws attention from the remote sensing world, but also draws great interest in other fields (such as medicine, agriculture, etc.). In practical application, direct analysis of data faces dimensionality disasters, and the problem of dimensionality reduction of a hyperspectral image is an important link.
The hyperspectral image is composed of a series of pixel points, and each pixel point can be expressed as an L-dimensional vector, wherein L represents the number of channels. In the actual processing of the image, the information of all the pixel points of the image is highly correlated and can be expanded by a group of low-dimensional signal end members. Defining an image Virtual Dimension (VD) as a dimension of a minimum signal end metabase expanded into hyperspectral image data, wherein the value is usually far smaller than L, and thus great possibility is provided for dimension reduction processing of the user; by processing the hyperspectral image in a lossless dimension reduction way, the calculation time and the storage space can be greatly reduced.
In order to define the features of hyperspectral images, the concept of virtual dimensions is now commonly used. The conventional method is to adopt an HFC method, the HFC method is simple and effective based on characteristic value analysis and a Neyman-Pearson detection theory, but the assumed inspection thought cannot ensure the estimated consistency, and the first type of error needs to be selected in an attempt, so that the accuracy of the hyperspectral image virtual dimension estimation is poor.
In summary, a new hyperspectral image virtual dimension estimation algorithm is needed.
Disclosure of Invention
The invention aims to provide a method for estimating a virtual dimension of a hyperspectral image based on ridge ratio shrinkage, so as to solve the existing technical problems. The method abandons the idea of hypothesis test, and directly adopts an algorithm for constructing a ratio array to carry out estimation, so that the accuracy of the virtual dimension estimation of the hyperspectral image can be improved.
In order to achieve the purpose, the invention adopts the following technical scheme:
a virtual dimension estimation method of a hyperspectral image based on ridge ratio shrinkage comprises the following steps:
step 1, extracting a sample matrix of a hyperspectral image to be processed
Figure BDA0001921270280000021
Step 2, obtaining a sample matrix according to the step 1
Figure BDA0001921270280000022
Calculating to obtain a sample covariance matrix
Figure BDA0001921270280000023
And a sample correlation matrix
Figure BDA0001921270280000024
Step 3, respectively calculating and obtaining the covariance matrix of the sample obtained in the step 2
Figure BDA0001921270280000025
And a sample correlation matrix
Figure BDA0001921270280000026
The eigenvalues of (a) are ranked;
step 4, sorting according to the characteristic values obtained in the step 3, and constructing a ratio series;
and 5, comparing the sequence value in the ratio sequence with a preset constraint value to obtain the virtual dimension of the hyperspectral image to be processed.
Further, in step 1, a sample matrix
Figure BDA0001921270280000027
Expressed as:
Figure BDA0001921270280000028
wherein, the matrix
Figure BDA0001921270280000029
Is an L x n matrix, L is the number of bands, n is the number of pixel points,
Figure BDA00019212702800000210
each column vector of (a) represents an end-member,
Figure BDA00019212702800000211
each column vector of the matrix represents the abundance of the corresponding pixel point under the end member,
Figure BDA00019212702800000212
is white noise.
Further, in step 2, the covariance matrix of the sample
Figure BDA00019212702800000213
And a sample correlation matrix
Figure BDA00019212702800000214
The specific expressions of (a) are respectively:
Figure BDA00019212702800000215
Figure BDA0001921270280000031
wherein the content of the first and second substances,
Figure BDA0001921270280000032
representing the corresponding pixel points;
Figure BDA0001921270280000033
representing the sample mean vector.
Further, step 3 specifically includes calculating and obtaining a sample covariance matrix
Figure BDA0001921270280000034
Is positive ordering of the eigenvalues of
Figure BDA0001921270280000035
Sample correlation matrix
Figure BDA0001921270280000036
Is positive ordering of the eigenvalues of
Figure BDA0001921270280000037
Further, in step 4, the ratio series
Figure BDA0001921270280000038
The expression of (a) is:
Figure BDA0001921270280000039
in the formula (I), the compound is shown in the specification,
Figure BDA00019212702800000310
Figure BDA00019212702800000311
furthermore, k is more than or equal to 0.2 and less than or equal to 0.5.
Further, in step 5, the expression of the estimated amount of the virtual dimension is:
Figure BDA00019212702800000312
constructing a ratio sequence
Figure BDA00019212702800000313
Is provided with
Figure BDA00019212702800000314
The constraint of τ is: 0<τ<1; selecting the index j from small to large, and selecting the corresponding sequence value
Figure BDA00019212702800000315
Comparing with tau, and determining the last index value smaller than tau as the virtual dimension; or the index j is selected from large to small, and the index corresponding to the first ratio sequence item smaller than tau is the solved virtual dimension.
Furthermore, the value range of tau is more than or equal to 0.4 and less than or equal to 0.6.
Further, τ is 0.5.
Further, a noise reduction processing step is arranged between the step 1 and the step 2, and the noise reduction processing method is to carry out noise reduction processing on the obtained signal
Figure BDA00019212702800000316
Carrying out pretreatment; the pretreatment comprises the following steps: de-averaging and whitening.
Compared with the prior art, the invention has the following beneficial effects:
the method of the invention inherits the simple effectiveness of the HFC algorithm; in the face of huge data of a hyperspectral image, the method can greatly reduce the processing time and the storage space under the condition of not losing information, has greater significance to practical application, and simultaneously lays a foundation for wide popularization; the method has no bias of an HFC algorithm, abandons the idea of hypothesis test, directly adopts the method of constructing a ratio series, is quick, simple and convenient, and can greatly improve the accuracy.
Furthermore, the parameters are determined according to theoretical proof and actual inspection, a new parameter selection problem does not need to be considered when the method is used, and the method has strong operability and reproducibility; the selection of the ridge function is data-driven, and has great universality and reasonableness.
Drawings
FIG. 1 is a schematic block diagram of a flow chart of a virtual dimension estimation method of a hyperspectral image based on ridge ratio shrinkage according to the invention.
Detailed Description
The invention is described in further detail below with reference to the figures and specific examples.
Comparative example
Existing HFC processes include:
step 1, extracting a sample matrix of a hyperspectral image to be processed
Figure BDA0001921270280000041
Specifically, the hyperspectral image to be processed has n pixel points and L wave bands, and each pixel point is composed of a series of end members and white noise. Each pixel point is an L-dimensional column vector and sample matrix
Figure BDA0001921270280000042
The expression of (a) is:
Figure BDA0001921270280000043
step 2, obtaining a sample covariance matrix of the sample matrix
Figure BDA0001921270280000044
And a sample correlation matrix
Figure BDA0001921270280000045
The expressions are respectively:
Figure BDA0001921270280000046
Figure BDA0001921270280000051
Figure BDA0001921270280000052
step 3, calculating and obtaining the covariance matrix of the sample obtained in the step 2
Figure BDA0001921270280000053
And a sample correlation matrix
Figure BDA0001921270280000054
A characteristic value of (d);
Figure BDA0001921270280000055
are respectively
Figure BDA0001921270280000056
And
Figure BDA0001921270280000057
positive ordering of eigenvalues of.
The default source signal is a positive constant, the noise is white,
Figure BDA0001921270280000058
and
Figure BDA0001921270280000059
the characteristic values of (a) have the following properties:
Figure BDA00019212702800000510
Figure BDA00019212702800000511
where VD represents the number of features.
The above comparative example is the basis of the HFC method, and according to the calculation method, roughly speaking, the signal component affects the eigenvalue of the correlation matrix but does not affect the eigenvalue of the covariance matrix, and noise affects both eigenvalues identically. Therefore, if a certain component does not contain a feature, the eigenvalues of the covariance matrix and the correlation matrix are the same. By using this feature, a hypothesis testing problem is derived. The HFC algorithm does not work well in practice. This is mainly because the hypothesis testing concept does not guarantee the consistency of the estimation, and the size of the first error needs to try to select itself, which also increases the difficulty of estimation.
Referring to fig. 1, the method for estimating a virtual dimension of a hyperspectral image based on ridge ratio shrinkage of the present invention discards a hypothesis testing concept for HFC defects, constructs a ratio sequence method to estimate a virtual dimension, and continues to use HFC symbols, and specifically includes the following steps:
step 1, extracting a sample matrix of a hyperspectral image to be processed
Figure BDA00019212702800000512
Sample matrix
Figure BDA00019212702800000513
Expressed as:
Figure BDA00019212702800000514
likewise, the matrix
Figure BDA00019212702800000515
Each column vector of (a) represents an end-member (which can be considered a basis),
Figure BDA00019212702800000516
each column vector of the matrix represents the abundance of the corresponding pixel point under the end member,
Figure BDA00019212702800000517
is white noise.
Step 2, obtaining a sample matrix according to the step 1
Figure BDA00019212702800000518
Calculating to obtain a corresponding covariance matrix
Figure BDA00019212702800000519
And a correlation matrix
Figure BDA00019212702800000520
The specific expressions of the two are respectively as follows:
Figure BDA0001921270280000061
Figure BDA0001921270280000062
wherein the content of the first and second substances,
Figure BDA0001921270280000063
is the sample mean vector.
Step 3, calculating and obtaining the covariance matrix obtained in the step 2
Figure BDA0001921270280000064
And a correlation matrix
Figure BDA0001921270280000065
Positive ordering of eigenvalues of;
Figure BDA0001921270280000066
is positive ordering of the eigenvalues of
Figure BDA0001921270280000067
Figure BDA0001921270280000068
Is positive ordering of the eigenvalues of
Figure BDA0001921270280000069
Step 4, obtaining the covariance matrix according to the step 3
Figure BDA00019212702800000610
And a correlation matrix
Figure BDA00019212702800000611
Positive ordering of characteristic values of (1), constructing a ratio array
Figure BDA00019212702800000612
To solve the situation where 0/0 may occur, a ridge function is added, specifically:
Figure BDA00019212702800000613
in the formula (I), the compound is shown in the specification,
Figure BDA00019212702800000614
Figure BDA00019212702800000615
wherein k is an unknown parameter to be determined, and the preferable value range is that k is more than or equal to 0.2 and less than or equal to 0.5. When k is greater than 0.5, the composition,
this results in a small estimate of the virtual dimension. When k is less than 0.2, the composition,
Figure BDA00019212702800000616
it is not general enough.
And 5, constructing the obtained ratio number series according to the step 4, and comparing and calculating to obtain the number of the virtual dimensions.
The expression for the estimator of the virtual dimension is:
Figure BDA00019212702800000617
the constraint of τ is: 0< τ < 1.
When n goes to infinity, it has been demonstrated
Figure BDA0001921270280000071
VD represents the true value of the virtual dimension in the overall sense.
Figure BDA0001921270280000072
Is an estimate of VD.
Since the general virtual dimension is much smaller than L/4, for the convenience of calculation, calculation can be performed from [ L/4] onwards. The value of j corresponding to the first term smaller than τ is the required number p of virtual dimensions.
According to the idea of plug-in, tau is preferably selected to be within a value range of 0.4-0.6; further preferably τ is 0.5.
It should be noted that, regarding the selection of the parameter k, after a series of simulations and practical experiments, it is found that the method of the present invention is not sensitive to the selection of k, and finally, we select k as 1/4 to obtain the best effect.
Principle analysis of the invention
In view of the fact that when n is sufficiently large,
Figure BDA0001921270280000073
and
Figure BDA0001921270280000074
approaching (lambda) at a rate of one-half the root number niAnd gammaiRespectively representing the true values of the corresponding characteristic values in the overall sense). Structural ridge item cnAnd requires cnGoing to infinity at n is going to 0 at a speed that is less than one-n times the root number. According to theorem guarantee that
Figure BDA0001921270280000075
We can determine VD by looking for the last minimum point.
Example 1
The first example uses analog data. Comparing the TRR method and the NWTRR method proposed by the present invention with other methods, wherein the NWTRR method is a method in which the TRR method is used after whitening noise. The noise whitening method is as follows: to pair
Figure BDA0001921270280000076
And (4) carrying out pretreatment. The pre-processing includes de-averaging and whitening. The correlation between each observation is removed by linearly transforming the observation data vector to make the mean value zero and the variance 1.
In generating the simulation data, we set the virtual dimension of the image to be 5, the white noise to be Legendre white noise, and the SNR to take four different values of 20, 40, 60, and 80 to increase the accuracy of the comparison, the results are shown in Table 1:
TABLE 1 comparative data for example 1
Figure BDA0001921270280000081
Table 1 analysis shows that the above method performs substantially well at a signal to noise ratio of 20. With the improvement of the signal to noise ratio, the TRR and the NWTRR of the denoising improved version have very remarkable accuracy in simulation data compared with other classical methods HySime, HySURE, ELM, HFC and NWHFC. Even with the denoised modified version of nwwfc, its accuracy and NWTRR, even TRR, are not comparable. This represents a disadvantage of the HFC process, in contrast to the superiority of the TRR process of the present invention. As the virtual dimension increases, the gap will only grow larger.
Example 2:
in a second example we apply the method TRR of the present invention together with the other methods used in example 1 to four real images for virtual dimension estimation, the results are shown in table 2:
TABLE 2 comparative data for example 2
Figure BDA0001921270280000082
The above four actual images are commonly used hyperspectral datasets. As can be seen from Table 2, the TRR method of the present invention performs well in four groups of images, has a small floating range near the virtual dimension, and estimates the real virtual dimension substantially correctly. While other methods, such as ELM, which perform well in the analog data set, present significant errors. The performance of HFC and denoised modified version of NWHFC is also unsatisfactory in each set of images. Thus, in general, other methods have large errors.
In summary, in the current general theory of HFC hypothesis testing, we find it to be an inappropriate, biased estimate with poor estimation accuracy. In practice, it is more often found that the results have a non-negligible error. The method of the invention abandons the thought of hypothesis test and directly adopts the method of constructing ratio series. The present invention uses the series construction ratio of the differences. Considering that 0/0 is encountered in practical operation, the parameter sequence c is addednThe obtained new ratio sequence can be compared with τ, and excellent results can be obtained when τ is 0.5. The algorithm of the invention has higher accuracy than the existing conventional HFC method; the invention removes hypothesis test and bias from the source, and in actual operation, a large number of experiments prove that the algorithm of the invention has more accuracy than the HFC algorithm.

Claims (6)

1. A virtual dimension estimation method of a hyperspectral image based on ridge ratio shrinkage is characterized by comprising the following steps:
step 1, extracting a sample matrix of a hyperspectral image to be processed
Figure FDA0002884643300000011
Step 2, obtaining a sample matrix according to the step 1
Figure FDA0002884643300000012
Calculating to obtain a sample covariance matrix
Figure FDA0002884643300000013
And a sample correlation matrix
Figure FDA0002884643300000014
Step 3, respectively calculating and obtaining the covariance matrix of the sample obtained in the step 2
Figure FDA0002884643300000015
And a sample correlation matrix
Figure FDA0002884643300000016
The eigenvalues of (a) are ranked;
step 4, sorting according to the characteristic values obtained in the step 3, and constructing a ratio series;
step 5, comparing the sequence value in the ratio sequence with a preset constraint value to obtain a virtual dimension of the hyperspectral image to be processed;
in step 1, a sample matrix
Figure FDA0002884643300000017
Expressed as:
Figure FDA0002884643300000018
wherein, the matrix
Figure FDA0002884643300000019
Is an L x n matrix, L is the number of bands, n is the number of pixel points,
Figure FDA00028846433000000110
each column vector of (a) represents an end-member,
Figure FDA00028846433000000111
each column vector of the matrix represents the abundance of the corresponding pixel point under the end member,
Figure FDA00028846433000000112
is white noise;
in step 2, the sample covariance matrix
Figure FDA00028846433000000113
And a sample correlation matrix
Figure FDA00028846433000000114
The specific expressions of (a) are respectively:
Figure FDA00028846433000000115
Figure FDA00028846433000000116
wherein the content of the first and second substances,
Figure FDA00028846433000000117
representing the corresponding pixel points;
Figure FDA00028846433000000118
representing a sample mean vector;
step 3 specifically includes calculating and obtaining a sample covariance matrix
Figure FDA00028846433000000119
Is positive ordering of the eigenvalues of
Figure FDA00028846433000000120
Sample correlation matrix
Figure FDA00028846433000000121
Is positive ordering of the eigenvalues of
Figure FDA00028846433000000122
In step 4, the ratio series
Figure FDA00028846433000000123
The expression of (a) is:
Figure FDA00028846433000000124
in the formula (I), the compound is shown in the specification,
Figure FDA00028846433000000125
Figure FDA0002884643300000021
2. the method for estimating the virtual dimension of the hyperspectral image based on ridge ratio shrinkage as claimed in claim 1, wherein k is in a range of 0.2-0.5.
3. The method for estimating the virtual dimension of the hyperspectral image based on ridge ratio shrinkage as claimed in claim 1, wherein in step 5, the expression of the estimated amount of the virtual dimension is as follows:
Figure FDA0002884643300000022
constructing a ratio sequence
Figure FDA0002884643300000023
Is provided with
Figure FDA0002884643300000024
The constraint of τ is: tau is more than 0 and less than 1; selecting the index j from small to large, and selecting the corresponding sequence value
Figure FDA0002884643300000025
Comparing with tau, and determining the last index value smaller than tau as the virtual dimension; or the index j is selected from large to small, and the index corresponding to the first ratio sequence item smaller than tau is the solved virtual dimension.
4. The method for estimating the virtual dimension of the hyperspectral image based on ridge ratio shrinkage as claimed in claim 3, wherein τ is in a range of 0.4-0.6.
5. The method for estimating the virtual dimension of the hyperspectral image based on ridge ratio shrinkage as claimed in claim 4, wherein τ is 0.5.
6. The method for estimating the virtual dimension of the hyperspectral image based on ridge ratio shrinkage as claimed in claim 1, wherein a noise reduction processing step is further provided between step 1 and step 2, and the noise reduction processing method is to pair
Figure FDA0002884643300000026
Carrying out pretreatment; the pre-processing includes de-averaging and whitening.
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