CN110135448A - It is a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction - Google Patents
It is a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction Download PDFInfo
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Abstract
The invention discloses a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, comprising: extracts the sample matrix of high spectrum image to be processed；The covariance matrix and correlation matrix for obtaining sample matrix are calculated, and calculates the characteristic value and sequence of the two；According to characteristic value sequence, ratio ordered series of numbers is constructed；By the sequential value in ratio ordered series of numbers compared with preset binding occurrence, the virtual dimension of high spectrum image to be processed is obtained.Estimation method of the invention abandons this thinking of hypothesis testing, and the algorithm for directlying adopt construction ratio ordered series of numbers is estimated, the accuracy of the virtual dimension estimation of high spectrum image can be improved.
Description
Technical field
It is the invention belongs to high spectrum image virtual dimension estimation technique field, in particular to a kind of higher than contraction based on ridge
The virtual dimension estimation method of spectrum picture.
Background technique
Spectrum picture of the spectral resolution within the scope of the 10nm order of magnitude is known as high spectrum image.By being mounted in different skies
Between bloom spectrum sensor on platform, i.e. imaging spectrometer, in the ultraviolet of electromagnetic spectrum, visible light, near-infrared and middle infrared
Domain is imaged target area with tens of to hundreds of continuous and subdivision spectral band simultaneously；Obtaining earth's surface image information
Meanwhile its spectral information is also obtained, it has been truly realized the combination of spectrum and image.Compared with multi-spectrum remote sensing image, EO-1 hyperion
Image is not only greatly improved in terms of abundant information degree, on processing technique, carries out more to such spectroscopic data
Rationally, effectively analysis processing provides possibility.Influence and development potentiality, are conventional arts possessed by hyper-spectral image technique
Stages it is incomparable.It not only causes the concern of remote sensing circle, while also resulting in other fields (as cured
, agronomy etc.) great interest.In practical applications, directly analysis data will face dimension disaster, the dimensionality reduction of high spectrum image
Problem is a highly important link.
High spectrum image is made of a series of pixels, and each pixel can be expressed as the vector of L dimension, and wherein L is indicated
Channel number.In the actual treatment of image, the information of image all pixels point is highly relevant, can be by one group of signal of low dimensional
End member at.It is to open the dimension of the minimum signal end member base at hyperspectral image data that we, which define image virtual dimension (VD),
This numerical value is generally much less than L, this just provides very big possibility for our dimension-reduction treatment；Pass through lossless dimension-reduction treatment EO-1 hyperion
Image may make that calculating time and storage space is greatly decreased.
In order to define the feature of high spectrum image, this concept of virtual dimension is generally used now.Usual way
It is using HFC method, HFC method is based on Eigenvalues analysis and Nai Man-Pearson came etection theory, and it is simple and effective, but used in it
Hypothesis testing thought do not ensure that the congruence of estimation, and the size of Error type I needs to attempt to choose, and leads to it
The accuracy of the virtual dimension estimation of high spectrum image is poor.
To sum up, a kind of new virtual dimension algorithm for estimating of high spectrum image is needed.
Summary of the invention
The purpose of the present invention is to provide a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, with solution
Certainly above-mentioned technical problem.Method of the invention abandons this thinking of hypothesis testing, directlys adopt construction ratio ordered series of numbers
Algorithm is estimated, the accuracy of the virtual dimension estimation of high spectrum image can be improved.
In order to achieve the above objectives, the invention adopts the following technical scheme:
It is a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, comprising the following steps:
Step 1, the sample matrix of high spectrum image to be processed is extracted
Step 2, the sample matrix obtained according to step 1It calculates and obtains sample covariance matrixAnd sample Correlation Moment
Battle array
Step 3, the sample covariance matrix of the acquisition of obtaining step 2 is calculated separatelyAnd sample correlation matrixFeature
It is worth and sorts；
Step 4, it is sorted according to the characteristic value that step 3 obtains, constructs ratio ordered series of numbers；
Step 5, the sequential value in ratio ordered series of numbers is obtained into the void of high spectrum image to be processed compared with preset binding occurrence
Quasi- dimension.
Further, in step 1, sample matrixIt indicates are as follows:
Wherein, matrixIt is L × n matrix, L is wave band number, and n is pixel number,Each column vector indicate one
End member,The each column vector of matrix indicates abundance of the corresponding pixel points under end member,It is white noise.
Further, in step 2, sample covariance matrixAnd sample correlation matrixExpression be respectively as follows:
Wherein,Represent corresponding pixel；Indicate sample mean vector.
Further, step 3 obtains sample covariance matrix specifically, calculatingCharacteristic value be just ordered asSample correlation matrixCharacteristic value be just ordered as
Further, in step 4, ratio ordered series of numbersExpression formula are as follows:
In formula,
Further, the value range of k is 0.2≤k≤0.5.
Further, in step 5, the expression formula of the estimator of virtual dimension are as follows:
Construct ratio columnHaveThe constraint of τ are as follows: 0 < τ < 1；Index j is selected from small to large
It takes, by corresponding sequence valueCompared with τ, the last one index value for being less than τ is exactly required virtual dimension；Alternatively, index j from
Small selection is arrived greatly, and the first corresponding index of sequence of ratio values item less than τ is exactly required virtual dimension.
Further, the value range of τ is 0.4≤τ≤0.6.
Further, the value of τ is 0.5.
Further, noise reduction process step is additionally provided between step 1 and step 2, the method for noise reduction process is pairInto
Row pretreatment；Pretreatment includes: mean value and albefaction.
Compared with prior art, the invention has the following advantages:
Method of the invention inherits the simple and effective property of HFC algorithm；The data huge in face of high spectrum image, the present invention
Method processing time and memory space can be greatly decreased in the case where not losing information, have to practical application biggish
Meaning, meanwhile, also lay a good foundation widely to popularize；There is no the excess kurtosis of HFC algorithm, has abandoned hypothesis testing thought, directly
The way using construction ratio ordered series of numbers is connect, it is quick and easy convenient, and accuracy can be greatly improved.
Further, parameter according to after theoretical proof and practice examining it has been determined that without considering new ginseng when use
Number On The Choice, has extremely strong operability and reproducibility；The selection of ridge function is data-driven, is had greatly general
All over property and reasonability.
Detailed description of the invention
Fig. 1 is a kind of process schematic block based on ridge dimension estimation method more virtual than the high spectrum image of contraction of the invention
Figure.
Specific embodiment
Invention is further described in detail in the following with reference to the drawings and specific embodiments.
Comparative example
Existing HFC method includes:
Step 1, the sample matrix of high spectrum image to be processed is extractedSpecifically, high spectrum image to be processed has n picture
Vegetarian refreshments and L wave band, each pixel are made of a series of end members and white noise.Each pixel is the column vector of L dimension,
Sample matrixExpression formula are as follows:
Step 2, the sample covariance matrix of sample matrix is acquiredAnd sample correlation matrixExpression formula is respectively as follows:
Step 3, the sample covariance matrix that obtaining step 2 obtains is calculatedAnd sample correlation matrixCharacteristic value；It is respectivelyWithCharacteristic value positive sequence.
The constant that default source signal is positive, noise is white noise,WithCharacteristic value have the property that
Wherein, VD represents the quantity of feature.
Above-mentioned comparative example is the basis of HFC method, and roughly according to calculation method, signal component will affect correlation matrix
Characteristic value, but not influence the characteristic value of covariance matrix, and noise two kinds of characteristic values are influenced it is identical.Therefore, such as
The a certain ingredient of fruit does not include feature, and the characteristic value of covariance matrix and correlation matrix is identical.Using this feature, export is false
If check problem.The effect is unsatisfactory in practice for HFC algorithm.This is primarily due to the hypothesis testing thought used in it can not
Guarantee the congruence of estimation, and the size needs of Error type I itself attempt to choose, this is also that estimation increases difficulty.
Referring to Fig. 1, of the invention is a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, it is directed to
The defect of HFC abandons hypothesis testing thinking, and construction sequence of ratio values method estimates virtual dimension, continues to use the symbol of HFC, has
Body the following steps are included:
Step 1, the sample matrix of high spectrum image to be processed is extractedSample matrixIt indicates are as follows:
Similarly, matrixEach column vector indicate an end member (base can be regarded as),The each column of matrix
Vector indicates abundance of the corresponding pixel points under end member,It is white noise.
Step 2, the sample matrix obtained according to step 1It calculates and obtains corresponding covariance matrixAnd correlation matrixThe expression of the two is respectively as follows:
Wherein,For sample mean vector.
Step 3, the covariance matrix that obtaining step 2 obtains is calculatedAnd correlation matrixCharacteristic value positive sequence；
Characteristic value be just ordered as Characteristic value be just ordered as
Step 4, the covariance matrix obtained according to step 3And correlation matrixCharacteristic value positive sequence, construct ratio
It is worth ordered series of numbersIn order to solve the case where being likely to occur 0/0 addition ridge function, specifically:
In formula,
Wherein, k is a unknown parameter to be determined, and preferred value range is 0.2≤k≤0.5.When k is greater than 0.5
When,
The estimated value that will lead to virtual dimension is less than normal.When k is less than 0.2,
Not enough there is generality.
Step 5, the ratio ordered series of numbers obtained according to step 4 construction compares calculating and obtains virtual dimension number.
The expression formula of the estimator of virtual dimension are as follows:
The constraint of τ are as follows: 0 < τ < 1.
When n tends to infinite, it has therefore proved thatVD represents true value of the virtual dimension under total meaning.It is the estimated value of VD.
Since general virtual dimension is much smaller than L/4, calculates for convenience, calculating can be progressed since [L/4].It is first
The corresponding j value of a item less than τ is exactly desired virtual dimension number p.
According to the thought of plug-in, the value range of our preferred τ is 0.4≤τ≤0.6；Further preferred τ takes
Value is 0.5.
It should be noted that the selection about parameter k, find by a series of simulations and after actual experiment, it is of the invention
Method is to the selection of k and insensitive, and effect is best when our final selected k are 1/4.
The principle of the present invention analysis
When sufficiently large in view of n,WithWith the rate of radical sign n/mono- close to (λiAnd γiGeneration respectively
True value of the corresponding characteristic value of table under total meaning).Construct ridge cnAnd it is required that cnTending to be infinite in n is to be slower than root
The speed of number n/mono- tends to 0.Had according to theorem guaranteeWe can go to pass through searching
The last one minimum point determines VD.
Embodiment 1
First example uses analogue data.By TRR method and NWTRR method proposed by the invention and other methods
It is compared, wherein NWTRR method is that TRR method is reused after noise whitening.Noise whitening method is as follows: rightInto
Row pretreatment.Pretreatment includes going mean value and albefaction.By making its mean value zero to observation data vector progress linear transformation,
Variance is 1, removes the correlation between each observation.
We set the virtual dimension of image as 5 during generating analogue data, and white noise is Legendre white noise,
And signal-to-noise ratio takes 20,40,60 and 80 4 different values to increase the accuracy compared, and the results are shown in Table 1:
The correlation data of 1. embodiment 1 of table
The analysis of table 1 can obtain, and in the case where signal-to-noise ratio is 20, above method performance is substantially good.With mentioning for signal-to-noise ratio
Height, method TRR of the invention and denoising improvement version NWTRR in analogue data compared with other classical ways HySime,
HySURE, ELM, HFC and NWHFC have very significant accuracy.Even if using denoising improvement version NWHFC, accuracy and
NWTRR or even TRR can not be mentioned in the same breath.This embodies the deficiency of HFC method, in contrast be then of the invention
The Optimality of TRR method.With the increase of virtual dimension, this gap only can be increasing.
Embodiment 2:
We answer method TRR of the invention and other methods used in embodiment 1 together in second example
Progress virtual dimension estimation on four real images is used, the results are shown in Table 2:
The correlation data of 2. embodiment 2 of table
Above four real images are common high-spectral data collection.As known from Table 2, method TRR of the invention is at four groups
Performance is good in image, and floating range is small near virtual dimension, is in the main true and has estimated true virtual dimension.And other
Method, such as concentrated in analogue data and show good ELM, there is significant error.The HFC's and NWHFC of denoising improvement version
Show also unsatisfactory in each group image.Therefore, totally apparently, all there is large error in other methods.
To sum up, in the now universal HFC theory of hypothesis testing, it has been found that it is not harmonious, and has inclined estimation, estimation
Accuracy is poor.In actual operation, more it is often found that result there are very important errors.Method of the invention has abandoned vacation
If examining this thinking, the way of construction ratio ordered series of numbers is directlyed adopt.Ratio is constructed using the ordered series of numbers of difference in the present invention.In view of
0/0 situation can be met in practical operation, therefore adds parameter ordered series of numbers cn, obtained new ratio ordered series of numbers can be compared with τ
Available more outstanding result when compared with, τ=0.5.Algorithm of the invention is higher than the accuracy of existing conventional HFC method；This
Invention eliminates hypothesis testing, excess kurtosis is eliminated from source, in actual operation, through experimental results demonstrate inventive algorithms
Accuracy is had more than HFC algorithm.
Claims (10)
1. a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, which comprises the following steps:
Step 1, the sample matrix of high spectrum image to be processed is extracted
Step 2, the sample matrix obtained according to step 1It calculates and obtains sample covariance matrixAnd sample correlation matrix
Step 3, the sample covariance matrix of the acquisition of obtaining step 2 is calculated separatelyAnd sample correlation matrixCharacteristic value simultaneously
Sequence；
Step 4, it is sorted according to the characteristic value that step 3 obtains, constructs ratio ordered series of numbers；
Step 5, by the sequential value in ratio ordered series of numbers compared with preset binding occurrence, the virtual dimension of high spectrum image to be processed is obtained
Number.
2. according to claim 1 a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, feature
It is, in step 1, sample matrixIt indicates are as follows:
Wherein, matrixIt is L × n matrix, L is wave band number, and n is pixel number,Each column vector indicate an end member,The each column vector of matrix indicates abundance of the corresponding pixel points under end member,It is white noise.
3. according to claim 2 a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, feature
It is, in step 2, sample covariance matrixAnd sample correlation matrixExpression be respectively as follows:
Wherein,Represent corresponding pixel；Indicate sample mean vector.
4. according to claim 3 a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, feature
It is, step 3 obtains sample covariance matrix specifically, calculatingCharacteristic value be just ordered asSample
This correlation matrixCharacteristic value be just ordered as
5. according to claim 4 a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, feature
It is, in step 4, ratio ordered series of numbersExpression formula are as follows:
In formula,
6. according to claim 5 a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, feature
It is, the value range of k is 0.2≤k≤0.5.
7. according to claim 5 a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, feature
It is, in step 5, the expression formula of the estimator of virtual dimension are as follows:
Construct ratio columnHaveThe constraint of τ are as follows: 0 < τ < 1；Index j chooses from small to large,
By corresponding sequence valueCompared with τ, the last one index value for being less than τ is exactly required virtual dimension；Alternatively, index j is from big
To small selection, the first corresponding index of sequence of ratio values item less than τ is exactly required virtual dimension.
8. according to claim 7 a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, feature
It is, the value range of τ is 0.4≤τ≤0.6.
9. according to claim 8 a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, feature
It is, the value of τ is 0.5.
10. according to claim 1 a kind of based on ridge dimension estimation method more virtual than the high spectrum image of contraction, feature
It is, noise reduction process step is additionally provided between step 1 and step 2, and the method for noise reduction process is pairIt is pre-processed；Pre- place
Reason includes going mean value and albefaction.
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