CN109829946A - MAP-TV high spectrum sub-pixel localization method based on quick mixed iteration - Google Patents
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Abstract
This application discloses a kind of MAP-TV high spectrum sub-pixel localization method based on quick mixed iteration, method include obtaining Hyperspectral imaging；Decomposition of Mixed Pixels is carried out to the Hyperspectral imaging, obtains the abundance of different end-member compositions；Seek maximum a posteriori probability regularization model MAP-TV；X is calculated using the algorithm that FISTA algorithm and division Bregman algorithm combinec；Determine that policy calculation goes out final sub-pixed mapping positioning result using the classification of winner-take-all.The present invention calculates the positioning result of sub-pixed mapping using the algorithm that FISTA algorithm and division Bregman algorithm combine, and positioning accuracy is high, and arithmetic speed is fast, the time needed for improving sub-pixed mapping positioning significantly.Complex model by splitting nonlinearity is the subproblem of several closed solutions for being easy to calculate, and is effectively reduced nonlinear operation, saves a large amount of time and operand, it is only necessary to which a few step iteration just can obtain locally optimal solution.
Description
Technical field
The present invention relates to high spectrum sub-pixel field of locating technology more particularly to a kind of MAP- based on quick mixed iteration
TV high spectrum sub-pixel localization method.
Background technique
Sub-pixed mapping positioning (Subpixel Mapping) technology is proposed by Atkinson earliest, it is intended to be based on spatial dependence
Assuming that generating the classification image of higher resolution from low resolution abundance image.Specific practice is by cutting mixed pixel
At smaller unit, according to the Abundances of end member each in pixel, according to spatial coherence criterion etc. is maximized, by specific atural object
Classification is assigned to accordingly in these lesser sub-pixed mappings, to realize the positioning to atural object.
Sub-pixed mapping location algorithm is to solve maximum a posteriori probability regularization model using gradient descent method in the prior art
Objective function under MAP-TV frame.But gradient descent method is used to solve the inefficiency for minimizing MAP-TV, and need
A large amount of time and operand.
Summary of the invention
The invention discloses a kind of MAP-TV high spectrum sub-pixel localization method based on quick mixed iteration, including step
It is rapid:
Obtain Hyperspectral imaging；
Decomposition of Mixed Pixels is carried out to the Hyperspectral imaging, obtains the abundance of different end-member compositions；
Maximum a posteriori probability regularization model MAP-TV is sought, comprising steps of
Define observation model；
Corresponding x when obtaining MAP estimation by the observation modelcCalculation formula；
According to Bayesian formula to the xcCalculation formula is handled, the x that obtains that treatedcCalculation formula；
To treated the xcCalculation formula carries out TV regularization, obtains maximum a posteriori probability regularization model MAP-
TV；
X is calculated using the algorithm that FISTA algorithm and division Bregman algorithm combinec, comprising steps of
The maximum a posteriori probability regularization model MAP-TV is subjected to the second Taylor series, after obtaining the second Taylor series
Model formation；
The intermediate result of iteration is obtained using model formation after the second Taylor series and the FISTA algorithm
Calculation formula are as follows:
Wherein, η is hyper parameter, xcFor the sub-pixed mapping positioning result of atural object end member classification c, κ is parameter,For gradient operator,The x obtained for kth time iterationc,The x obtained for+1/2 iteration of kthc, D is down-sampling matrix, ycFor atural object end
The abundance image of first classification c, DTFor the transposition of down-sampling matrix；
It is solved by the division Bregman algorithm
It willWithIt does linear operation and obtains the starting point of next iteration
Iteration terminates to obtain xc；
Determine that policy calculation goes out final sub-pixed mapping positioning result using the classification of winner-take-all.
Preferably, the observation model are as follows:
yc=Dxc+nc,
Wherein, ycFor the abundance image of atural object end member classification c, xcFor the sub-pixed mapping positioning result of atural object end member classification c, D is
Down-sampling matrix, ncFor the noise of classification c.
Preferably, corresponding x when the MAP estimationcCalculation formula are as follows:
xc=argmax { Pr (xc|yc),
Wherein,
Wherein, Pr (xc|yc) it is that the posterior probability that sub-pixed mapping positions, Pr (y are carried out by abundance imagec|xc) it is low
The likelihood function of classification c in resolution image, Pr (xc) it is xcPrior probability, Pr (yc) it is fixed value.
Preferably, treated the xcCalculation formula are as follows:
xc=argmin { ‖ yc-Dxc‖2+κU(xc),
Wherein, U is regularization term.
Preferably, the maximum a posteriori probability regularization model are as follows:
Wherein,As U (xc)。
Preferably,
Wherein,For xcHorizontal direction gradient,For xcVertical direction gradient, xc[i+1, j] be i-th+
The positioning result of 1 row, jth column image pixel, xc[i, j] is the positioning result of the i-th row, jth column image pixel, xc[i, j+1] is
The positioning result of i-th row ,+1 column image pixel of jth.
Preferably, model formation after the second Taylor series are as follows:
Preferably, the algorithm combined using FISTA algorithm and division Bregman algorithm calculates xc, further are as follows:
Input λ0=0,
When model formation is not up to restrained after the second Taylor series:
It introducesAnd Bregman divergence distance is introduced, above formula becomes:
Operational formula is shunk in definition are as follows:
It solves:
Terminate iteration,
Export xc；
Wherein,The x obtained for+1 iteration of kthc, b is dual variable, bsFor the s times iteration obtain to mutation
Amount, t, x, a are variable, and FFT is Fast Fourier Transform (FFT), FFT-1For inverse fast Fourier transform, div is divergence, and Δ is to draw
General Laplacian operater,The x obtained for the s times iterationc, α is hyper parameter,It is initial pixel location as a result, λ0For initial value,
ts、ts-1、λk+1、λk、γkIt is variable.
Preferably, the Bregman divergence distance are as follows:
Wherein,Bregman divergence distance between point u and point m, J are convex function, and p is at point m
Derivative.
Compared with prior art, the MAP-TV high spectrum sub-pixel positioning side provided by the invention based on quick mixed iteration
Method, reach it is following the utility model has the advantages that
First, the present invention calculates the positioning of sub-pixed mapping using the algorithm that FISTA algorithm and division Bregman algorithm combine
As a result, positioning accuracy is high, arithmetic speed is fast, the time needed for improving sub-pixed mapping positioning significantly.
Second, the present invention is asked by splitting the son that the complex model of nonlinearity is several closed solutions for being easy to calculate
Topic, is effectively reduced nonlinear operation, saves a large amount of time and operand, it is only necessary to which a few step iteration just can obtain part most
Excellent solution.
Below by drawings and examples, technical scheme of the present invention will be described in further detail.
Detailed description of the invention
The drawings described herein are used to provide a further understanding of the present application, constitutes part of this application, this Shen
Illustrative embodiments and their description please are not constituted an undue limitation on the present application for explaining the application.In the accompanying drawings:
Fig. 1 is the stream of the MAP-TV high spectrum sub-pixel localization method based on quick mixed iteration in the embodiment of the present invention 1
Cheng Tu；
Fig. 2 is the win of the MAP-TV high spectrum sub-pixel localization method based on quick mixed iteration in the embodiment of the present invention 2
The classification that person covers all determines policy map.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description.It should be noted that described embodiment only actually is a part of the embodiment of the present invention, rather than whole realities
Example is applied, and is actually merely illustrative, never as to the present invention and its application or any restrictions used.The guarantor of the application
Protect range as defined by the appended claims.
Embodiment 1:
Shown in Figure 1 is the herein described MAP-TV high spectrum sub-pixel localization method based on quick mixed iteration
Specific embodiment, this method comprises:
Step 101 obtains Hyperspectral imaging；
Step 102 carries out Decomposition of Mixed Pixels to the Hyperspectral imaging, obtains the abundance of different end-member compositions；
Step 103 seeks maximum a posteriori probability regularization model MAP-TV, comprising steps of
Define observation model；
Corresponding x when obtaining MAP estimation by the observation modelcCalculation formula (xcImage is positioned for sub-pixed mapping
In different location positioning result, i.e., corresponding pixel location result when having obtained MAP estimation by observation model)；
According to Bayesian formula to the xcCalculation formula is handled, the x that obtains that treatedcCalculation formula；
To treated the xcCalculation formula carries out TV regularization, obtains maximum a posteriori probability regularization model MAP-
TV；
Step 104 calculates x using the algorithm that FISTA algorithm and division Bregman algorithm combinec, comprising steps of
The maximum a posteriori probability regularization model MAP-TV is subjected to the second Taylor series, after obtaining the second Taylor series
Model formation；
The intermediate result of iteration is obtained using model formation after the second Taylor series and the FISTA algorithm
Calculation formula are as follows:
Wherein, η is hyper parameter, xcFor the sub-pixed mapping positioning result of atural object end member classification c, κ is parameter,For gradient operator,The x obtained for kth time iterationc,The x obtained for+1/2 iteration of kthc, D is down-sampling matrix, ycFor atural object end
The abundance image of first classification c, DTFor the transposition of down-sampling matrix；
It is solved by the division Bregman algorithm
It willWithIt does linear operation and obtains the starting point of next iteration
Iteration terminates to obtain xc；
Step 105 determines that policy calculation goes out final sub-pixed mapping positioning result using the classification of winner-take-all.
In above-mentioned steps 103, the observation model are as follows:
yc=Dxc+nc,
Wherein, ycFor the abundance image of atural object end member classification c, xcFor the sub-pixed mapping positioning result of atural object end member classification c, D is
Down-sampling matrix, ncFor the noise of classification c.
Corresponding x when the MAP estimationcCalculation formula are as follows:
xc=argmax { Pr (xc|yc),
Wherein,
Wherein, Pr (xc|yc) it is that the posterior probability that positions of sub-pixed mapping is carried out by abundance image (i.e. according to known rich
Spend the sub-pixed mapping positioning result under image conditions), Pr (yc|xc) be low resolution image in classification c likelihood function, Pr (xc)
For xcPrior probability, Pr (yc) it is fixed value.
Treated the xcCalculation formula are as follows:
xc=argmin { ‖ yc-Dxc‖2+κU(xc),
Wherein, U is regularization term.
The maximum a posteriori probability regularization model are as follows:
Wherein,As U (xc)。
Wherein,
Wherein,For xcHorizontal direction gradient,For xcVertical direction gradient, xc[i+1, j] be i-th+
The positioning result of 1 row, jth column image pixel, xc[i, j] is the positioning result of the i-th row, jth column image pixel, xc[i, j+1] is
The positioning result of i-th row ,+1 column image pixel of jth.
In above-mentioned steps 104, model formation after the second Taylor series are as follows:
The algorithm combined using FISTA algorithm and division Bregman algorithm calculates xc, further are as follows:
Input λ0=0,
When model formation is not up to restrained after the second Taylor series:
It introducesAnd Bregman divergence distance is introduced, above formula becomes:
Operational formula is shunk in definition are as follows:
It solves:
Terminate iteration,
Export xc；
Wherein,The x obtained for+1 iteration of kthc, b is dual variable, bsFor the s times iteration obtain to mutation
Amount, t, x, a are variable, and FFT is Fast Fourier Transform (FFT), FFT-1For inverse fast Fourier transform, div is divergence, and Δ is to draw
General Laplacian operater,The x obtained for the s times iterationc, α is hyper parameter,It is initial pixel location as a result, λ0For initial value,
ts、ts-1、λk+1、λk、γkIt is variable.
The Bregman divergence distance are as follows:
Wherein,Bregman divergence distance between point u and point m, J are convex function, and p is at point m
Derivative.
Embodiment 2:
This application provides another implementations of the MAP-TV high spectrum sub-pixel localization method based on quick mixed iteration
Example, this method comprises:
Hyperspectral imaging is obtained, Decomposition of Mixed Pixels is carried out to the Hyperspectral imaging, obtains the rich of different end-member compositions
Degree；Because sub-pixed mapping positioning purpose be the remote sensing images of low resolution are converted into high-resolution image, for this purpose,
It has to obtain Optimal Distribution of the atural object component in sub-pixed mapping rank, therefore before carrying out sub-pixed mapping positioning to high spectrum image
Mention is to obtain different end-member compositions percentage shared in mixed pixel by the way that spectrum solution is mixed；One in target in hyperspectral remotely sensed image
It include the emission signal of many kinds of substance in pixel, the spectral information characteristics of each pixel are the spectrum letters of multiple single ground object targets
Breath feature combines the mixed spectra signal being formed by stacking, and the pixel with this feature is called mixed pixel, single in the pixel
The spectrum of ground object target is called end member, and the percentage of contained end member is called abundance.
Observation model is defined, model is as follows:
yc=Dxc+nc (1)
Wherein, ncFor the noise of classification c；xcFor the sub-pixed mapping positioning result of atural object end member classification c；ycFor atural object end member class
The abundance image of other c；D is down-sampling matrix, related with the sub-pixed mapping positioning range size of image.
It is on the basis of MAP frame, by drawing based on the high spectrum sub-pixel location observation model under MAP-TV frame
Enter TV regular terms, to provide the regularization model for solving sub-pixed mapping orientation problem, then acquires optimal solution.Assuming that in each atural object
End member classification occur noise be white Gaussian noise, under MAP frame by formula (1) acquire it is corresponding when maximum a posteriori is estimated
xc, specifically:
xc=argmax { Pr (xc|yc)} (2)
According to Bayesian formula:
Wherein, Pr (xc|yc) it is that the posterior probability that sub-pixed mapping positions, Pr (y are carried out by abundance imagec|xc) it is low
The likelihood function of classification c in resolution image, Pr (xc) it is xcPrior probability, Pr (yc) it is fixed value, formula (3) are removed
Denominator simultaneously uses logarithm operation, and formula (2) is converted to:
xc=argmax { logPr (yc|xc)+log Pr(xc)} (4)
Wherein likelihood function can be write as:
xc=argmin { ‖ yc-Dxc‖2+κU(xc)} (5)
Wherein, U is regularization term, and κ is parameter.If using TV as regularization term, formula (5) becomes as follows
MAP-TV model:
Wherein,For gradient operator.In formula (6), which can preferably retain the edge in image
And detailed information, structure are as follows:
Wherein,For xcHorizontal direction gradient,For xcVertical direction gradient, xc[i+1, j] be i-th+
The positioning result of 1 row, jth column image pixel, xc[i, j] is the positioning result of the i-th row, jth column image pixel, xc[i, j+1] is
The positioning result of i-th row ,+1 column image pixel of jth.
Formula (6) is rewritten into following form:
xc=argmin { f (xc)+g(xc)} (10)
Wherein,
By the way that f (x) is carried out the second Taylor series, formula (10) can be written as follow form:
Formula (11) and formula (12) are brought into formula (13), following formula is obtained:
Wherein, η is hyper parameter,The x obtained for kth time iterationc, DTFor the transposition of down-sampling matrix.
It is as follows using the calculating process after FISTA (quick iteration threshold contraction algorithm):
Input: λ0=0,
When not restraining:
Terminate,
Output: xc。
Wherein,The x obtained for+1/2 iteration of kthc,It is initial pixel location as a result, λ0For initial value,
λk+1、λk、γkIt is variable.
In the iterative process each time of algorithm, by by pointThe approximate function at place obtains the point of minimum value
WithPoint does the starting point put as next iteration that linear operation obtains
Using division Bregman algorithm solution formula (17).Firstly, drawing dual variable b to replaceIt is public at this time
Formula (17) becomes:
Above-mentioned restricted problem can become unconstrained problem by using Lagrange multiplier, as follows:
Bregman divergence distance is introduced, form is as follows:
Wherein,Bregman divergence distance between point u and point m, J are convex function, and p is at point m
Derivative.
By introducing Bregman divergence distance, formula (20) becomes:
Formula (22) can split into three minors of equal value.Specific calculating process is as follows:
For solution formula (22), it is as follows that operation is shunk in definition:
Input: λ0=0,
When not restraining:
Terminate iteration,
Output: xc。
Wherein,The x obtained for+1 iteration of kthc, b is dual variable, bsFor the s times iteration obtain to mutation
Amount, t, x, a are variable, and FFT is Fast Fourier Transform (FFT), FFT-1For inverse fast Fourier transform, div is divergence, and Δ is to draw
General Laplacian operater,The x obtained for the s times iterationc, α is hyper parameter, ts、ts-1It is variable.
Complex model by splitting nonlinearity is the subproblem of several closed solutions for being easy to calculate, effective to reduce
Nonlinear operation, saves a large amount of time and operand, it is only necessary to which a few step iteration just can obtain locally optimal solution.
Overall algorithm is as follows:
Input: λ0, κ, η, α,
When not restraining,
With division Bregman algorithm solution
Terminate iteration,
Output: xc。
Once having obtained the estimation x that all ends are resultc, use the classification of winner-take-all WAT (Winner-take-all)
It is final as a result, as shown in Figure 2 to determine that strategy can calculate.
In Fig. 2, A, B, C represent three classifications, and the number in frame is that the maximum a posteriori of sub-pixed mapping of all categories in the position is general
Rate result.Strategy is determined according to the classification of winner-take-all, and the probability value of each classification on each sub-pixed mapping position is compared
Compared with the corresponding classification of maximum value is the final location category on the sub-pixed mapping position.Such as sub-pixed mapping position in the upper left corner in Fig. 2
On, the probability for belonging to A class is 0.43, and the probability for belonging to B class is 0.15, and the probability for belonging to C class is 0.42, and maximum value is A class
0.43, so the classification that the sub-pixed mapping in the upper left corner finally positions is A.
Comparative experiments:
With the Position-Solving speed that the sub-pixed mapping localization method of the embodiment of the present application 1 obtains, obtained with gradient descent algorithm
Position-Solving speed compare, the results are shown in Table 1.
1 sub-pixed mapping Position-Solving speed of table
It can be seen from Table 1 that the application is compared with division Bregman hybrid algorithm with traditional gradient using FISTA
The likelihood function that descent algorithm solves MAP-TV model effectively reduces nonlinear operation, saves a large amount of time and operation
Amount.According to experimental result it is found that method used in this application only needs 10 step iteration just can obtain locally optimal solution, compared under gradient
300 iteration of algorithm drop, and the number of iterations is greatly reduced, and in the case where possessing same positioning accuracy with gradient decline,
Reduce the time required for sub-pixed mapping positions significantly.
As can be seen from the above embodiments beneficial effect existing for the application is:
First, the present invention calculates the positioning of sub-pixed mapping using the algorithm that FISTA algorithm and division Bregman algorithm combine
As a result, positioning accuracy is high, arithmetic speed is fast, the time needed for improving sub-pixed mapping positioning significantly.
Second, the present invention is asked by splitting the son that the complex model of nonlinearity is several closed solutions for being easy to calculate
Topic, is effectively reduced nonlinear operation, saves a large amount of time and operand, it is only necessary to which a few step iteration just can obtain part most
Excellent solution.
Above by drawings and examples, although having been carried out in detail by example to some specific embodiments of the invention
Describe in detail it is bright, but it should be appreciated by those skilled in the art, example above merely to be illustrated, rather than in order to limit this
The range of invention.Although the present invention is described in detail referring to the foregoing embodiments, come for those skilled in the art
It says, can still modify to technical solution documented by previous embodiment, or part of technical characteristic is carried out
Equivalent replacement.All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in
Within protection scope of the present invention.The scope of the present invention is defined by the appended claims.
Claims (9)
1. a kind of MAP-TV high spectrum sub-pixel localization method based on quick mixed iteration, which is characterized in that comprising steps of
Obtain Hyperspectral imaging；
Decomposition of Mixed Pixels is carried out to the Hyperspectral imaging, obtains the abundance of different end-member compositions；
Maximum a posteriori probability regularization model MAP-TV is sought, comprising steps of
Define observation model；
Corresponding x when obtaining MAP estimation by the observation modelcCalculation formula；
According to Bayesian formula to the xcCalculation formula is handled, the x that obtains that treatedcCalculation formula；
To treated the xcCalculation formula carries out TV regularization, obtains maximum a posteriori probability regularization model MAP-TV；
X is calculated using the algorithm that FISTA algorithm and division Bregman algorithm combinec, comprising steps of
The maximum a posteriori probability regularization model MAP-TV is subjected to the second Taylor series, obtains model after the second Taylor series
Formula；
The intermediate result of iteration is obtained using model formation after the second Taylor series and the FISTA algorithmMeter
Calculate formula are as follows:
Wherein, η is hyper parameter, xcFor the sub-pixed mapping positioning result of atural object end member classification c, κ is parameter,For gradient operator,
The x obtained for kth time iterationc,The x obtained for+1/2 iteration of kthc, D is down-sampling matrix, ycFor atural object end member
The abundance image of classification c, DTFor the transposition of down-sampling matrix；
It is solved by the division Bregman algorithm
It willWithIt does linear operation and obtains the starting point of next iteration
Iteration terminates to obtain xc；
Determine that policy calculation goes out final sub-pixed mapping positioning result using the classification of winner-take-all.
2. the MAP-TV high spectrum sub-pixel localization method according to claim 1 based on quick mixed iteration, feature
It is, the observation model are as follows:
yc=Dxc+nc,
Wherein, ycFor the abundance image of atural object end member classification c, xcFor the sub-pixed mapping positioning result of atural object end member classification c, D is adopted under being
Sample matrix, ncFor the noise of classification c.
3. the MAP-TV high spectrum sub-pixel localization method according to claim 1 based on quick mixed iteration, feature
Be, when MAP estimation corresponding xcCalculation formula are as follows:
xc=argmax { Pr (xc|yc),
Wherein,
Wherein, Pr (xc|yc) it is that the posterior probability that sub-pixed mapping positions, Pr (y are carried out by abundance imagec|xc) it is low resolution
The likelihood function of classification c in rate image, Pr (xc) it is xcPrior probability, Pr (yc) it is fixed value.
4. the MAP-TV high spectrum sub-pixel localization method according to claim 1 based on quick mixed iteration, feature
It is, treated the xcCalculation formula are as follows:
xc=argmin { ‖ yc-Dxc‖2+κU(xc),
Wherein, U is regularization term.
5. the MAP-TV high spectrum sub-pixel localization method according to claim 1 based on quick mixed iteration, feature
It is, the maximum a posteriori probability regularization model are as follows:
Wherein,As U (xc)。
6. the MAP-TV high spectrum sub-pixel localization method according to claim 5 based on quick mixed iteration, feature
It is, wherein
Wherein,For xcHorizontal direction gradient,For xcVertical direction gradient, xc[i+1, j] be i+1 row,
The positioning result of jth column image pixel, xc[i, j] is the positioning result of the i-th row, jth column image pixel, xc[i, j+1] is i-th
The positioning result of row ,+1 column image pixel of jth.
7. the MAP-TV high spectrum sub-pixel localization method according to claim 1 based on quick mixed iteration, feature
It is, model formation after the second Taylor series are as follows:
8. the MAP-TV high spectrum sub-pixel localization method according to claim 1 based on quick mixed iteration, feature
It is, the algorithm combined using FISTA algorithm and division Bregman algorithm calculates xc, further are as follows:
Input λ0=0,
When model formation is not up to restrained after the second Taylor series:
It introducesAnd Bregman divergence distance is introduced, above formula becomes:
Operational formula is shunk in definition are as follows:
It solves:
Terminate iteration,
Export xc；
Wherein,The x obtained for+1 iteration of kthc, b is dual variable, bsFor the dual variable that the s times iteration obtains, t,
X, a is variable, and FFT is Fast Fourier Transform (FFT), FFT-1For inverse fast Fourier transform, div is divergence, and Δ is Laplce
Operator,The x obtained for the s times iterationc, α is hyper parameter,It is initial pixel location as a result, λ0For initial value, ts、ts-1、
λk+1、λk、γkIt is variable.
9. the MAP-TV high spectrum sub-pixel localization method according to claim 8 based on quick mixed iteration, feature
It is, the Bregman divergence distance are as follows:
Wherein,Bregman divergence distance between point u and point m, J are convex function, and p is the derivative at point m.
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