CN107578421A - A kind of statistical model approximating method of EO-1 hyperion abnormality detection subspace projection figure - Google Patents
A kind of statistical model approximating method of EO-1 hyperion abnormality detection subspace projection figure Download PDFInfo
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Abstract
The invention discloses a kind of statistical model approximating method of EO-1 hyperion abnormality detection subspace projection figure, comprise the steps：The first step：Estimate the non-central evolution distributed model of perspective view；Second step:Estimate non-middle evolution distributed model free degree parameter；3rd step：Estimate non-middle evolution distributed model non-centrality parameter；4th step:The statistical distribution of diagram data is projected using non-central evolution fitting of distribution, realizes the CFAR detection of the statistical distribution based on this non-central evolution fitting of distribution projection diagram data.Present invention improves the effect being fitted to EO-1 hyperion abnormality detection perspective view statistical model, the influence detected due to statistical model error to follow-up CFAR is reduced.
Description
Technical field
The present invention relates to space flight, aviation and close shot high spectrum image target or abnormality detection technical field, more specifically
Say, be related to a kind of constant false alarm rate (CFAR) detection technique field of hyperspectral image abnormal detection linear subspaces perspective view.
Background technology
High light spectrum image-forming can select hundreds of continuous spectral coverages pair in 400~2500nm visible ray and near-infrared wave zone
Scene is observed, and spectral resolution can be better than 10nm.High spectrum image has " collection of illustrative plates " characteristic, its three-dimensional data cube
Body (two-dimensional geometry space+one-dimensional spectrum) contains the space geometry information and complete spectrum information of object in observation scene.It is logical
The nuance of resolution target and the reflective spectral property of background is crossed, high spectrum image can accurately be distinguished from complex background
Target.
Hyperspectral image abnormal detection is a kind of practical stronger object detection method, and it does not need priori spectral information
Support can detects suspected target in image, reduces shadow of the image pre-processing methods such as reflectivity inverting to Detection results
Ring.Currently used abnormality detection operational form is typically a linear projection, by linear projection by higher-dimension high-spectral data
Project in a lower-dimensional subspace and (be called perspective view), CFAR (CFAR) detection side is then utilized in this sub-spaces
Method realizes target and background separation.
, it is necessary to effectively be estimated its statistical model after perspective view is generated, CFAR methods could be utilized to determine suitable
Threshold value come segmentation object and background.In actual applications, abnormality detection perspective view statistical model may be selected normal distribution or
Logarithm normal distribution etc., but due to the complexity of hyperspectral image data statistical model itself, simply with normal distribution or
Larger error be present to be fitted perspective view in logarithm normal distribution.
The content of the invention
To solve the above problems, the invention provides a kind of statistical model of EO-1 hyperion abnormality detection subspace projection figure plan
Conjunction method, present invention improves the effect being fitted to EO-1 hyperion abnormality detection perspective view statistical model, reduce due to statistical model
The influence that error detects to follow-up CFAR.
To reach above-mentioned technique effect, the technical scheme is that：
A kind of statistical model approximating method of EO-1 hyperion abnormality detection subspace projection figure, comprises the steps：
The first step：Estimate the non-central evolution distributed model of perspective view；
Second step:Estimate non-middle evolution distributed model free degree parameter；
3rd step：Estimate non-middle evolution distributed model non-centrality parameter；
4th step:Using the statistical distribution of non-central evolution fitting of distribution projection diagram data, realize and non-central opened based on this
The CFAR detection of the statistical distribution of square fitting of distribution projection diagram data.
It is further to improve, the first step, comprise the following steps：
A. the operational form of the Outlier Detection Algorithm based on orthogonal subspaces is as follows：
D (x) represents pixel x projection result, and wherein pixel x is that l ties up pixel spectra vector, and l represents wave band number,For the average spectral vector of high-spectral data, N represents image picture elements number, and subscript i represents i-th of picture in data
Member, x represent pixel spectrum；It is Orthogonal subspace projection matrix, I represents unit matrix；U represents to represent
The matrix of background spectrum characteristic, U+It is U pseudoinverse, U+=UT(UUT)-1, wherein T representing matrixs transposition；If U matrixes are by representing
Image background distribution end member vector form, then formed the Outlier Detection Algorithm based on subspace, if U matrixes be by data compared with
Big characteristic vector is formed, then forms low probability Outlier Detection Algorithm；
B. the projection matrix in operator is considered first
Therefore projection matrixIt is a symmetric idempotent matrix, thus formula (1) is rewritten as：
IfThen formula (3) becomes：
D (y)=yyT (4)
D (y) represents projection diagram data, and wherein y is l dimension m-vectors；Therefore original high spectrum image pixel spectral vector
It is considered as the random vector for obeying Diversity normal distribution；After subspace projection, background data is suppressed, original EO-1 hyperion
Image statisticses distribution levels off to the multivariate normal distributions of l dimension zero-mean, then has：
Y~Nl(0, ∑) (5)
Wherein, Σ is random vector y Cross-covariance；It is l's to project diagram data D (y) and then obey one degree of freedom
Evolution is distributed：
D (y)~X2(l) (6)
It is to be distributed sums by multiple center evolutions compared with low degree-of-freedom to project diagram data D (y), thus its be distributed as one it is non-
Center evolution distribution：
D (y)~X2(n, δ) (7)
Wherein：N is the free degree of non-middle evolution distribution, and in general n ＜ l, δ are its non-centrality parameter.
It is further to improve, in the second step, using principal component analytical method, figure is estimated using the number of characteristic value
As background end member number, wherein, characteristic value sum used accounts for more than the 99% of All Eigenvalues sum.
It is further to improve, in the 3rd step,
3rd step：Non- middle evolution distributed model non-centrality parameter estimation
For non-centrality parameter δ, according to the concept of 1 rank moment of the orign, projection diagram data D (y) desired value and two parameters
Between following relation be present：
E (D (y))=M1=n+ δ (8)
Wherein E (D (y)) represents the mathematic expectaion of projection diagram data, M1It is the 1 rank moment of the orign for projecting diagram data；Thus count
Calculate non-centrality parameter：
δ=M1-n (9)。
Further to improve, the 4th step is n using the free degree, and the non-central evolution distribution that non-centrality parameter is δ is intended
The statistical distribution of projection diagram data is closed, realizes the CFAR detection based on this distribution.
Brief description of the drawings
Fig. 1 is the flow chart of the perspective view statistical model fitting based on the distribution of non-central evolution；
The original airborne hyperspectral image cubes of Fig. 2；
Perspective view after abnormality detection processing of the Fig. 3 based on subspace projection；
The matched curve of the histogram of Fig. 4 perspective views and different statistical models.
Embodiment
Illustrated below by way of embodiment and with reference to accompanying drawing to technical scheme.
Embodiment 1
A kind of statistical model approximating method of EO-1 hyperion abnormality detection subspace projection figure as shown in Figure 1, input difference
It is hyper-spectral image data cube and abnormality detection perspective view.Estimating for free degree parameter in non-central evolution distribution is carried out first
Calculate, the Cross-covariance of original high-spectral data is calculated, it is then determined that a ratio value (such as 99.5%) determines larger spy
Value indicative number, it is defined as the free degree n of statistical model with this numerical value；Then non-centrality parameter δ is calculated using formula (9)；Connect down
To utilize two parameters of estimation, the probability density function of non-central evolution distribution is generated, and in terms of being come by this probability density function
Calculate CFAR detection threshold values.
Specifically include following step：
The first step：The presumption of the non-central evolution distributed model of perspective view
In the present invention, the non-central evolution of the projection diagram data obedience of the abnormality detection based on subspace projection is derived and has been distributed this
One theoretical foundation, while illustrate the theoretical foundation of model parameter estimation.
In general, the operational form of the Outlier Detection Algorithm based on orthogonal subspaces are as follows：
Wherein x is that l ties up pixel spectra vector, and l represents wave band number,For the average spectrum of high-spectral data
Vector,It is Orthogonal subspace projection matrix, U+It is mono- pseudoinverse of U, U+=UT(UUT)-1, U matrix forms composition
The key of the operator, it is also different according to algorithms of different, its composition.If the matrix from representative image background distributions end member to
Amount is formed, then forms the Outlier Detection Algorithm based on subspace, is formed if the matrix is the larger characteristic vector for having data,
Form low probability abnormality detection (LPAD) algorithm.
It is all a quadratic form form to notice these operational forms.Obviously, such as the number for being present in subspace after projecting
According to if meeting multivariate normal distributions, then final projection diagram data will meet the statistical property of evolution distribution.
Consider the projection matrix in operator first
Perceptible projections matrixIt is a symmetric idempotent matrix, thus formula (1) is rewritable is：
If haveThen formula (3) becomes：
D (y)=yyT (4)
Wherein y is also l dimension m-vectors.Original high spectrum image pixel spectral vector is considered as to obey Diversity normal state
The random vector of distribution.After subspace projection, background data is suppressed, and its statistical distribution levels off to l dimension zero-mean
Multivariate normal distributions.
Y~Nl(0, ∑) (5)
Wherein, Σ is random vector y Cross-covariance.Thus, in general, diagram data D (y) is projected then should
The evolution that one degree of freedom is l is obeyed to be distributed.
D (y)~χ2(l) (6)
But because high spectrum image wave band is shown in the presence of stronger correlation, then without independent between random vector y
Property, it is believed that projection diagram data D (y) can be considered by multiple center evolution distribution sums compared with low degree-of-freedom, therefore it is distributed
The non-central evolution that should level off to is distributed：
D (y)~X2(n, δ) (7)
Wherein：N is the free degree of non-middle evolution distribution, and in general n ＜ l, δ are its non-centrality parameter.
Second step：Non- middle evolution distributed model free degree parameter estimation
When realizing the fitting of statistical model, it is necessary to calculate two parameters of non-central evolution distribution：The free degree and non-
Center Parameter.Theoretical indeed according to multivariate data analysis, projection diagram data D (y) free degree is equal to projection matrix's
Order, and in Outlier Detection Algorithm, projection matrixTo be made up of image background end member, so, the distribution of non-central evolution from
It should be equal to the number of view data background end member by spending n.In actual applications, the most frequently used estimation high spectrum image background end
The method of first number is exactly principal component analysis (PCA), can estimate image background end member using the number of larger characteristic value
Number.
3rd step：Non- middle evolution distributed model non-centrality parameter estimation
For another parameter of non-central evolution distribution：Non-centrality parameter δ, according to the concept of 1 rank moment of the orign, perspective view
Following relation be present between data D (y) desired value and two parameters：
E (D (y))=M1=n+ δ (8)
Wherein E (D (y)) represents the mathematic expectaion of projection diagram data, M1It is the 1 rank moment of the orign for projecting diagram data.Thus I
Non-centrality parameter can be gone out by freedom calculation：
δ=M1-n (9)
So far we can be n using one degree of freedom, and the non-central evolution that non-centrality parameter is δ is distributed to be fitted projection
The statistical distribution of diagram data, realize the CFAR detections based on this distribution.As shown in figure 4, being experimental results, given in figure
The histogram of perspective view after abnormality detection, and the probability density curve of three kinds of different evolution distributions.It is it can be seen that non-central
(free degree 6, non-middle parameter are 15.3) ideal to the fitting effect of histogram for evolution distribution.Using actual measurement Beijing suburb
Airborne hyperspectral remotely-sensed data is tested to the inventive method, test result indicates that the present invention estimates statistical model to throwing
The fitting degree of shadow figure statistical property is optimal.
The specific guiding embodiment of the present invention is above are only, but the design concept of the present invention is not limited thereto,
All changes for carrying out unsubstantiality to the present invention using this design, all should belong to the behavior for invading protection scope of the present invention.
Claims (5)
1. a kind of statistical model approximating method of EO-1 hyperion abnormality detection subspace projection figure, it is characterised in that including following steps
Suddenly：
The first step：Estimate the non-central evolution distributed model of perspective view；
Second step:Estimate non-middle evolution distributed model free degree parameter；
3rd step：Estimate non-middle evolution distributed model non-centrality parameter；
4th step:Using the statistical distribution of non-central evolution fitting of distribution projection diagram data, realize based on this non-central evolution point
The CFAR detection of the statistical distribution of cloth fitting projection diagram data.
2. the statistical model approximating method of EO-1 hyperion abnormality detection subspace projection figure as claimed in claim 1, its feature exist
In the first step, comprising the following steps：
A. the operational form of the Outlier Detection Algorithm based on orthogonal subspaces is as follows：
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Big characteristic vector is formed, then forms low probability Outlier Detection Algorithm；
B. the projection matrix in operator is considered first
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IfThen formula (3) becomes：
D (y)=yyT
D (y) represents projection diagram data, and wherein y is l dimension m-vectors；Therefore original high spectrum image pixel spectral vector is considered as
Obey the random vector of Diversity normal distribution；After subspace projection, background data is suppressed, original high spectrum image
Statistical distribution levels off to the multivariate normal distributions of l dimension zero-mean, then has：
Y~Nl(0, ∑) (5)
Wherein, ∑ is random vector y Cross-covariance；Project diagram data D (y) and then obey the evolution that one degree of freedom is l
Distribution：
D (y)~χ2(l) (6)
It is to be distributed sums by multiple center evolutions compared with low degree-of-freedom to project diagram data D (y), thus its be distributed as one it is non-central
Evolution is distributed：
D(y)-χ2(n, δ) (7)
Wherein：N is the free degree of non-middle evolution distribution, and in general n ＜ l, δ are its non-centrality parameter.
3. the statistical model approximating method of EO-1 hyperion abnormality detection subspace projection figure as claimed in claim 1, its feature exist
In, in the second step, using principal component analytical method, image background end member number is estimated using the number of characteristic value, its
In, characteristic value sum used accounts for more than the 99% of All Eigenvalues sum.
4. the statistical model approximating method of EO-1 hyperion abnormality detection subspace projection figure as claimed in claim 1, its feature exist
In, in the 3rd step,
3rd step：Non- middle evolution distributed model non-centrality parameter estimation
For non-centrality parameter δ, according to the concept of 1 rank moment of the orign, between projection diagram data D (y) desired value and two parameters
In the presence of following relation：
E (D (y))=M1=n+ δ (8)
Wherein E (D (y)) represents the mathematic expectaion of projection diagram data, M1It is the 1 rank moment of the orign for projecting diagram data；Thus calculate non-
Center Parameter：
δ=M1-n (9)。
5. the statistical model approximating method of EO-1 hyperion abnormality detection subspace projection figure as claimed in claim 4, its feature exist
In the 4th step is n using the free degree, and non-centrality parameter is that δ non-central evolution fitting of distribution projects the statistics of diagram data
Distribution, realize the CFAR detection based on this distribution.
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