CN107274387B - The end member extraction method of target in hyperspectral remotely sensed image based on Evolutionary multiobjective optimization - Google Patents
The end member extraction method of target in hyperspectral remotely sensed image based on Evolutionary multiobjective optimization Download PDFInfo
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Abstract
A kind of end member extraction method of the target in hyperspectral remotely sensed image based on Evolutionary multiobjective optimization, belong to Hyperspectral imagery processing field, by using end member number as an objective function of multiple-objection optimization, different number of Endmember extraction result is obtained using single operation algorithm, accelerate the execution speed of algorithm, improves precision；Regard target in hyperspectral remotely sensed image Endmember extraction as a multi-objective problem, optimize two objective functions simultaneously using discrete particle group optimizing method, single run it is available with different end member numbers to get to optimizing end member；Overcome need multiple single operation algorithm in the prior art and obtain there is different number of end member result.Using the leader selection strategy inversely grown, all end members are needed not search for, computation complexity is reduced.
Description
Technical field
The invention belongs to Hyperspectral imagery processing field, the line spectrum solution for being related to high spectrum image mixes method, specifically
The end member extraction method of target in hyperspectral remotely sensed image based on Evolutionary multiobjective optimization.
Background technique
The 1980s remote sensing technology one of maximum achievement be exactly high-spectrum remote-sensing rise.High-spectrum remote-sensing device has
Ability, which captures hundreds of continuous spectrum bands, can be used to improve the class for identifying different atural objects.High spectrum image is due to its spectrum abundant
Information has been more and more widely used, such as in mineral exploration, environmental monitoring and military monitoring etc..Mixed pixel decomposes
Problem is to limit a major issue of target in hyperspectral remotely sensed image development, and this problem can mix technology by spectrum solution and solve.One
As, the pixel of target in hyperspectral remotely sensed image is mixed pixel rather than pure pixel.Mixing picture is presented on more than a type of substance
In element.Therefore, the spectrum of several covered grounds is referred to as the measure spectrum that end member is blended in single pixel.
Endmember extraction is a mixed important step of spectrum solution.Since high light spectrum image-forming sensor improves high spatial and light
Spectral resolution, Endmember extraction become more and more important in high spectrum image analysis.One end member is an ideal pure feature class.
Many end member extraction methods are based on linear spectral mixture model and to assume that pure pixel exists in high spectrum image, including pixel
Purity index (PPI), internal largest body area method (N-FINDR), fixed point constituent analysis (VCA), Convex Cone Analysis (CCA), monomorphous
Growth algorithm (SGA) etc..
These algorithms have low computation complexity and accurate extraction result.However, they have some disadvantages.One is to mention
Take precision that will reduce, if true data are unsatisfactory for pure structure.The other is lacking the information and end member of feedback mechanism
Number relies on broadband number.Therefore initial end member is randomly generated in these algorithms, when it is not that an effective initialization will spend very long
Between find desired result.In order to solve these problems, some new methods based on evolution are proposed, column such as discrete particle cluster is excellent
Change, ant group optimization (ACO) and adaptive differential evolve (ADDE).This method is converted to an optimization for Endmember extraction problem
It problem and establishes a feasible solution space and removes evaluation goal function.
However, there are some disadvantages for the implementation of these algorithms.It goes to determine production without guidance in many Endmember extraction algorithms
Raw how many end member.Virtual dimension (VD) signal subspace estimation (SSE) is the side of most widely used two kinds of end member numbers estimation
Method has been applied successfully to many Endmember extraction algorithms.It may be evident, however, that Endmember extraction be it is ill posed, there are no make us
Satisfied solution this problem.In other words, fixed end member number this be inappropriate.In many documents, for different numbers
Purpose Endmember extraction result.However, these most of algorithms by execute a series of individual operations obtain it is different as a result, this
It is very time-consuming.
Summary of the invention
Aiming at the problems existing in the prior art, the present invention provides a kind of high-spectrum remote-sensing based on Evolutionary multiobjective optimization
The end member extraction method of image, speed is fast, and precision is high, can be obtained by single operation non-dominant with different end member numbers
Solution.
The present invention is to be achieved through the following technical solutions:
The end member extraction method of target in hyperspectral remotely sensed image based on evolution multiple target group optimization, includes the following steps:
Step 1, determine high-spectrum remote sensing I to be treated as original image；
Step 2, spectral resolution is carried out to high-spectrum remote sensing I using linear spectral mixture model, is used for Endmember extraction；
It enablesIndicate the high-spectrum remote sensing of n pixel of L wavestrip, riIt is the spectrum column arrow for indicating ith pixel
Amount, then linear spectral mixture model LSMM is defined as,
In above formula, m is end member number,Indicate end member set,It is abundance of j-th of end member in ith pixel,
εiIndicate that the error term of i-th of wave band, end member abundance need to meet two constraint conditions:
Step 3, estimation end member abundance is obtained with staff cultivation least square, is obtained by linear spectral mixture model and mixes figure again
PictureAnd then it obtains original image and mixes the root-mean-square error (RMSE) of image again as an objective function；And
And it regard the end member number ∑ (x) of original image as another objective function；
Step 4, root mean square is smaller, indicates original image and mixed image is closer again, if end member number is reduced, root mean square is missed
Difference will become larger, the contradictory objective function of two thus combined, and the Endmember extraction problem of high-spectrum remote sensing is modeled
For the multi-objective optimization question MOPs as described in following formula；
Step 5, Discrete Particle Swarm Optimization Algorithm is passed through to two contradictory target letters to the multi-objective optimization question of foundation
It counts while optimizing, using elitist selection strategy, obtain final Endmember extraction result.
Preferably, in step 3, using the mixed estimation end member abundance of staff cultivation least square FCLS linear solution；Its specific steps
It is as follows:
Step 3a, uses original imageWith end member collectionGo estimation abundance
Step 3b passes through estimation abundance and end member ejObtain estimation pixelAgain mix image such as following formula；
Step 3c calculates original image and its root-mean-square error RMSE for mixing image again, as an objective function；
Preferably, when establishing multi-objective optimization question in step 4, it is assumed that all pixels are end members in high-spectrum remote sensing
And ignore error ε, then again mix image be entirely capable of being indicated with original image, i.e., original image and again mix image RMSE be 0；Work as shifting
When except an end member, original image and its root-mean-square error RMSE for mixing image again will not be in holding 0；RMSE is with end member
Several reductions and become larger, use RMSE to be able to maintain end member as much as possible as objective function.
Preferably, the step 5 specifically comprises the following steps,
Step 5a, using Discrete Particle Swarm Optimization Algorithm to the multi-objective optimization question of foundation the basis in solution space
The fitness function value search particle for adapting to particle optimizes position；
Solution space is expressed as follows,
Wherein, m indicates end member number, it is assumed that end member number is it is known that then xn,m={ x1,x2,…,xnIndicate discrete particle position
It sets, i.e., the one of feas ible space solves；
Step 5b initializes the position of discrete particle in solution space, then updates the state of discrete particle, that is, updates
Self optimal location of particle and in history all particles global optimum position；
Multi-objective optimization question is resolved into several subproblems according to the variation number of end member by step 5c, using step 5a and
Step 5b carries out discrete particle cluster optimization to each subproblem, obtains the optimal location of each particle, obtains each subproblem
Globally optimal solution；
Step 5d obtains multi-objective optimization question by elitist selection algorithm according to the globally optimal solution of each subproblem
Globally optimal solution；The end member in high spectrum image is determined according to multi-objective optimization question globally optimal solution, that is, particle optimal location
Position.
Preferably, in step 5a, particle is constantly moved in solution space, and calculates the fitness function of each particle
Value；The position and speed that each particle is updated according to the fitness value of particle establishes new position by speed；
For Endmember extraction problem, decision vector xn,m={ x1,x2,…,xnIndicate high-spectrum remote sensing in xiTable
The state for showing ith pixel, for each pixel it there are two types of state, that is, xi∈{0,1}；If a pixel is chosen as end member
Then its state is 1, and other is 0；Therefore the number that state is 1 is equal to end member number, i.e.,
Preferably, in step 5b, x is usedk(t) and vk(t) k-th of particle is respectively indicated in the particle position and speed of t moment
Degree；Use xk,best(t) and xgbest(t) indicate that k-th of particle self optimizes position and all particles before t moment in moment t
Global optimization position；
The directed movement calculating formula of particle is as follows:
vk(t+1)=T ((xk,best(t)-xk(t))+(xgbest(t)-xk(t))) (7)
Wherein, T (x) is a random selection function, and when the positive value of x is selected, the value of T (x) is 1, when the negative value quilt of x
The value of T (x) is -1 when selecting, and when the other values of x are selected, the value of T (x) is 0；
The random movement of particle is described as follows:
vk(t+1)=R (xk(t)) (8)
Wherein, R (x) is also a random function, be the value of R (x) is -1 when x be 1, the value of R (x) when x is other values
It is 1；
Selection particle is gone to be oriented mobile or random movement, the speed of more new particle by a random selection probability
Degree；
After the speed of particle updates, particle goes to establish new position using new speed, obtains the position of more new particle
It sets such as following formula:
xk(t+1)=xk(t)+vk(t) (9)；
Stop algorithm up to algorithmic statement or after reaching maximum number of iterations, update obtains self optimal location of particle.
Preferably, in step 5c,
5c1, the variation number for inputting end member is [a, b], and a and b are positive integer；
5c2, multi-objective optimization question can resolve into b-a+1 subproblem；
5c3, in order to promote diversity to distribute to the fixed population of each subproblem setting；
5c4, each subproblem generate globally optimal solution by external storage sharing information.
Preferably, in step 5d, based on the elitist selection inversely grown, global optimum is as elite；Final solution is retouched
It states are as follows:
Y={ Ya,…,Ym,…,Yb,m∈[a,b]} (10)
Wherein, YmIndicate there be m end member in the particle, end member number is limited in [a, b]；WithIndicate that ith pixel becomes
The amount of end member chance, obtains；
Wherein, ciBigger, the chance that ith pixel becomes end member is bigger；It uses firstValue sort in descending order these pictures
Then element has the subproblem of m end member to select m pixel as elite；The speed of more new particle and position later are used
Indicate the elite of m-th of subproblem；
New speed more new formula are as follows:
The position for removing by new speed to establish subsequent time for each subproblem, by elitist selection determine it is global most
Excellent solution is that the optimal location of particle determines the end member position in high spectrum image.
Compared with prior art, the invention has the following beneficial technical effects:
The present invention using single operation algorithm by being obtained not using end member number as an objective function of multiple-objection optimization
With number Endmember extraction as a result, accelerate algorithm execution speed, improve precision；Target in hyperspectral remotely sensed image Endmember extraction is regarded as
It is a multi-objective problem, optimizes two objective functions simultaneously using discrete particle group optimizing method, single operation is available
With different end member numbers to get to optimizing end member；Overcome need multiple single operation algorithm in the prior art and obtain
With different number of end member result.Using the leader selection strategy inversely grown, all end members are needed not search for, are subtracted
Small computation complexity.
Detailed description of the invention
Fig. 1 is selection leader figure in slave external storage described in present example.
Fig. 2 is to select leader figure in iterative process described in present example from external storage.
Fig. 3 is the AVIRIS figure of true target in hyperspectral remotely sensed image described in present example.
Fig. 4 is Endmember extraction result figure of the present invention to true target in hyperspectral remotely sensed image.
Fig. 5 is the abundance figure of a series of simulating image described in present example, wherein (a) is synthesis, (b)-(f)
For the abundance of 5 end members.
Fig. 6 is Endmember extraction result figure of the present invention to Simu-5 target in hyperspectral remotely sensed image.
Fig. 7 is the implementation flow chart of the optimization of discrete particle cluster described in present example.
Specific embodiment
Below with reference to specific embodiment, the present invention is described in further detail, it is described be explanation of the invention and
It is not to limit.
One kind being based on the end member extraction method of Evolutionary multiobjective optimization (MOEE), can accurately extract from high spectrum image
End member.Mainly solve computation complexity in the prior art it is high and need to be run multiple times algorithm and obtain there are different numbers
End member result the problem of.The realization step of the invention are as follows: (1) determine objective function；(2) construct initial solution population, using with
Machine method initializes the individual in solution population；(3) self optimal location of more new particle and all particles it is global most
Excellent position is in history；(4) its position is updated using the speed of each particle；(5) judge whether to terminate: if iteration time
Number, which meets, presets number of iterations, then executes (6), otherwise go to step (3)；(6) optimum solution is selected according to elitist selection.The present invention
Optimize two objective functions simultaneously, realizes the Endmember extraction to EO-1 hyperion sense image.
The technical scheme is that regarding the Endmember extraction problem of target in hyperspectral remotely sensed image as two targets ask
Topic, wherein original image and the inverse of its root-mean-square error for mixing image again and the mean value of spectral modeling drawing are as target letter
Number optimizes the two objective functions using the evolution multi-target method based on decomposition simultaneously, and introduces the elite choosing inversely grown
Strategy is selected, globally optimal solution is finally obtained, implementation step includes the following:
Step 1, high-spectrum remote sensing I is inputted, I is the high spectrum image of a width 350*400*50, the range of end member number
[a,b]。
Step 2, linear spectral mixture model (LSMM) is used for Endmember extraction.Using linear spectral mixture model to EO-1 hyperion
Remote sensing images I carries out spectral resolution；
The reflectivity of the model hypothesis pixel can indicate the spectral signature of each end member and its occupied area percentage in pixel
The linear function of ratio enablesIndicate the remote sensing images of n pixel of L wavestrip, riIt is the spectrum column arrow for indicating ith pixel
Amount.Then LSMM is defined as,
M is end member number in above formula,Indicate end member set,It is abundance of j-th of end member in ith pixel, εi
Indicate the error term (such as noise and model error) of i-th of wave band, in above formula, abundance and non-negative abundance summation are 1, for holding
The abundance ratio of member, in order to allow abundance to have actual physical meaning, ordinary circumstance, end member abundance meets following two constraint condition:
Step 3, mixed using staff cultivation least square (FCLS) linear solution:
Step 3a, uses original imageWith end member collectionGo estimation abundance
Step 3b passes through estimation abundance and end member ejObtain estimation pixelAgain mix image it is as follows,
Step 3c, and then original image and its root-mean-square error (RMSE) for mixing image again is calculated, as one
Objective function；
Also, it regard end member number ∑ (x) as another objective function.
Step 4, it is modeled as multi-objective optimization question (MOPs).
Original image and its root-mean-square error for mixing image again have been obtained in step 3c.Assuming that all pixels are in bloom
Spectrogram as when end member and ignore error ε, then mix image again and be entirely capable of being indicated with original image, i.e. original image and again mixed image
RMSE is 0.When removing an end member, RMSE will not be in holding 0.By analysis, RMSE becomes with the reduction of end member number
Greatly, RMSE is used to keep end member as much as possible as objective function.In addition, it is a solution vector, end member that x, which is Endmember extraction subset,
Number ∑ (x) is the end member number extracted:
Multi-objective optimization question (MOPs) is described as follows:
Optimize the two contradictory objective functions simultaneously with Discrete Particle Swarm Optimization Algorithm, obtains optimizing end member.
Step 5, optimization object function；As shown in fig. 7, the multi-objective optimization question to foundation is optimized by discrete particle cluster
Algorithm optimizes, and using elitist selection strategy, obtains final Endmember extraction result.
Step 5a, particle swarm optimization algorithm search for the optimal location of particle in solution space.Particle is in feasible sky
Between constantly move, and calculate fitness function value.There are two types of attributes for each particle, and " position " and " speed " " should be remembered
The optimum position and global optimum position of " self " of history " in history.Improvement based on particle swarm algorithm, D-PSO make grain
Son can be searched in discrete solution space.For Endmember extraction problem, decision vector xn,m={ x1,x2,…,xnIndicate bloom
The state of ith pixel in spectrum remote-sensing image.For each pixel it there are two types of state, that is, xi∈{0,1}.If a pixel
Being chosen as end member, then its state is 1, and other is 0.Therefore the number of " 1 " is equal to end member number
The state of step 5b, discrete particle update；
Use xk(t) and vk(t) k-th of particle is respectively indicated in the particle position and speed of t moment.Use xk,best(t) and
xgbest(t) indicate that k-th of particle self optimizes the global optimization position of position and all particles before t moment in moment t
It sets.The directed movement calculating formula of particle is as follows:
vk(t+1)=T ((xk,best(t)-xk(t))+(xgbest(t)-xk(t))) (4)
T (x) is a random selection function.When x positive value be selected as it value be 1. when the negative value of x is selected it
Value be -1. when the other values of x are selected its value be 0.In order to promote diversity introduce random movement, it be described as
Under:
vk(t+1)=R (xk(t)) (5)
R (x) be also a random function, when x be 1 be it value be -1, when x is other values, its value is 1.With one
Random selection probability goes selection particle to be oriented mobile or random movement.After the express delivery of particle updates, particle uses new
Speed go to establish new position and pass through following formula:
xk(t+1)=xk(t)+vk(t) (6)
Stop algorithm up to algorithmic statement or after reaching maximum number of iterations, update obtains self optimal location of particle.
Since all particles can not be optimal simultaneously position in practice, so a maximum number of iterations is arranged in we, to guarantee
Algorithm stops.
Step 5c, multi-objective optimization question resolve into many subproblems；
5c1, the variation number for inputting end member is [a, b].
5c2, multi-objective optimization question can resolve into b-a+1 subproblem.
5c3, in order to promote diversity to distribute to the fixed population of each subproblem, in this preferred embodiment, it is contemplated that calculate
The complexity of method we to each subproblem setting population be 20.
5c4, subproblem generate globally optimal solution (leader) by external storage sharing information.
Step 5d obtains globally optimal solution by elitist selection.
The end member extraction method of target in hyperspectral remotely sensed image based on the optimization of multiple target discrete particle cluster, is selected by leader
Obtain globally optimal solution.
Based on the leader selection inversely grown, global optimum is as leader.Final solution is described as:
Y={ Ya,…,Ym,…,Yb,m∈[a,b]} (7)
Wherein, YmIndicate there be m end member in the particle, end member number is limited in [a, b].We useIndicate ith pixel
As the amount of end member chance, thereforeIt can be calculated with following formula
ciBigger, the chance that ith pixel becomes end member is bigger.As shown in Figure 1, using firstValue sort in descending order this
Then a little pixels have the subproblem of m end member to select m pixel as optimal solution.As shown in Fig. 2, the speed of more new particle later
Degree and position, have the elite of the subproblem of m end member to be different, and useIndicate the leader of m-th of subproblem.
New speed more new formula are as follows:
The position for removing by new speed to establish subsequent time for each subproblem, by elitist selection determine it is global most
Excellent solution is that the optimal location of particle determines the end member position in high spectrum image.
Effect of the invention can be further illustrated by following emulation:
1. simulated conditions
This example is under 8.1 system of Intel (R) Core (TM) i7-4790CPU@3.60GHz Windows, Matlab
On 2014a operation platform, the present invention and existing N-FINDR, VCA, the emulation experiment of DPSO method are completed.
2. emulation experiment content
The present invention chooses true EO-1 hyperion AVIRIS Cuprite image respectively as shown in Figure 3 and simulation high-light composes Simu-5
Image carries out emulation experiment as shown in Figure 5.High spectrum image used in experiment is nineteen ninety-five Nevada ,Usa cuprite area
It is obtained on imaging spectrometer (AVIRIS) outside airborne visible red.The size of image be (400*350) have 50 wavestrips from
1.9908m (band 172) arrives 2.4790m (band 221).It is [5,20] that end member number, which is arranged, and randomly selected probability is 0.1, every height
Problem population is 10, and after 300 iteration, obtained Endmember extraction is as the result is shown in Fig. 4.Table 1 show the present invention with
Existing N-FINDR, VCA, RMSE value comparison sheet of the DPSO method to AVIRIS figure；
Table 1
Obviously the present invention will be got well than DPSO and N-FINDR, VCA.It therefore, can by optimizing the two objective function this method
To obtain the extraction result of one group of different end member numbers.The Endmember extraction of different end member numbers is obtained as a result, adopting by optimization algorithm
It is higher with elitist selection strategy efficiency of algorithm, the RMSE value that different end member number MOEE algorithms are obtained as can be seen from Table 1 compared with
It is small.
Analogous diagram used in experiment generates 80*100 pixel covering 224 from USGS library of spectra with five end member subsets for us
Wave band EO-1 hyperion analog image.It is in one 4 × 5 scene center shown in figure that composograph, which has 20 rectangle frames,.The first row is
Pure pixel and other three rows are to utilize two to the mixing between four end members not etc..Background is simulation five kinds of material properties of mixing
20% is constituted.The abundance of five end members of Fig. 5 (b)-(f) display.As shown in figure 5, five features are by United States Geological Survey
Library selection, alunite AL706 (A), Buddingtonite GDS85 (B), Calcite Co2004 (C) calcite, kaolinite
CM3 (K) and Muscovite GDS107 (M).It is [3,6] that end member number, which is arranged,.
The composite diagram rectangle frame of Fig. 5 (a) be damaged by simulated Gaussian white noise obtain signal-to-noise ratio (SNR) be 10:1,20:
1 and 30:1.Fig. 6 shows the end member result that the present invention extracts under conditions of signal-to-noise ratio is 20:1.Fig. 6 (a)-(d) difference table
Show the position of end member when end member number is 3-6.Table 2 shows the present invention and existing N-FINDR, and VCA, DPSO method is to Simu-5
The RMSE value comparison sheet of figure；
Table 2
If more pixels are selected as end member.Therefore, it can be obtained by optimizing the two objective function this method
Obtain the extraction result of one group of different end member numbers.
The present invention uses emulation and true target in hyperspectral remotely sensed image as experimental subjects, using using Evolutionary Multiobjective Optimization
Original image and its root-mean-square error (RMSE) for mixing image again and the objective function of ∑ (x) two conflicts are carried out excellent simultaneously
Change, single runs the available non-domination solution with different end member numbers to get optimization end member is arrived.By with existing some sides
Method is compared, and the present invention can obtain good Endmember extraction result while reducing computation complexity.
Claims (8)
1. the end member extraction method of the target in hyperspectral remotely sensed image based on Evolutionary multiobjective optimization, which is characterized in that including walking as follows
It is rapid:
Step 1, determine high-spectrum remote sensing I to be treated as original image；
Step 2, spectral resolution is carried out to high-spectrum remote sensing I using linear spectral mixture model, is used for Endmember extraction；
It enablesIndicate the high-spectrum remote sensing of n pixel of L wavestrip, riIt is the spectrum column vector for indicating ith pixel, then
Linear spectral mixture model LSMM is defined as,
In above formula, m is end member number,Indicate end member set,It is abundance of j-th of end member in ith pixel, εiIt indicates
The error term of i-th of wave band, end member abundance need to meet two constraint conditions:
Step 3, estimation end member abundance is obtained with staff cultivation least square, is obtained by linear spectral mixture model and mixes image againAnd then it obtains original image and mixes the root-mean-square error (RMSE) of image again as an objective function；And
It regard the end member number ∑ (x) of original image as another objective function；
Step 4, root mean square is smaller, indicates original image and mixed image is closer again, if end member number is reduced, root-mean-square error will
Become larger, the Endmember extraction problem of high-spectrum remote sensing is modeled as more by the contradictory objective function of two thus combined
Objective optimisation problems MOPs, is described as follows；
Step 5, same to two contradictory objective functions by Discrete Particle Swarm Optimization Algorithm to the multi-objective optimization question of foundation
When optimize, using elitist selection strategy, obtain final Endmember extraction result.
2. the end member extraction method of the target in hyperspectral remotely sensed image according to claim 1 based on Evolutionary multiobjective optimization,
It is characterized in that, in step 3, using the mixed estimation end member abundance of staff cultivation least square FCLS linear solution；The specific steps of which are as follows:
Step 3a, uses original imageWith end member collectionGo estimation abundance
Step 3b passes through estimation abundance and end member ejObtain estimation pixelAgain mix image such as following formula；
Step 3c calculates original image and its root-mean-square error RMSE for mixing image again, as an objective function；
3. the end member extraction method of the target in hyperspectral remotely sensed image according to claim 1 based on Evolutionary multiobjective optimization,
It is characterized in that, when establishing multi-objective optimization question in step 4, it is assumed that all pixels are end members in high-spectrum remote sensing and ignore
Error ε, then again mix image be entirely capable of being indicated with original image, i.e., original image and again mix image RMSE be 0；When removal one
When end member, original image and its root-mean-square error RMSE for mixing image again will not be in holding 0；RMSE subtracts with end member number
Become larger less, RMSE is used to be able to maintain end member as much as possible as objective function.
4. the end member extraction method of the target in hyperspectral remotely sensed image according to claim 1 based on Evolutionary multiobjective optimization,
It being characterized in that, the step 5 specifically comprises the following steps,
Step 5a, using Discrete Particle Swarm Optimization Algorithm to the multi-objective optimization question of foundation in solution space according to adaptation
The fitness function value search particle of particle optimizes position；
Solution space is expressed as follows,
Wherein, m indicates end member number, it is assumed that end member number is it is known that then xn,m={ x1,x2,···,xnIndicate discrete particle position
It sets, i.e., the one of feas ible space solves；
Step 5b initializes the position of discrete particle in solution space, then updates the state of discrete particle, i.e. more new particle
Self optimal location and in history all particles global optimum position；
Multi-objective optimization question is resolved into several subproblems according to the variation number of end member, utilizes step 5a and step by step 5c
5b carries out discrete particle cluster optimization to each subproblem, obtains the optimal location of each particle, obtains the overall situation of each subproblem
Optimal solution；
Step 5d obtains the multi-objective optimization question overall situation by elitist selection strategy according to the globally optimal solution of each subproblem
Optimal solution；The end member position in high spectrum image is determined according to multi-objective optimization question globally optimal solution, that is, particle optimal location
It sets.
5. the end member extraction method of the target in hyperspectral remotely sensed image according to claim 4 based on Evolutionary multiobjective optimization,
It is characterized in that, in step 5a, particle is constantly moved in solution space, and calculates the fitness function value of each particle；According to
The fitness value of particle updates the position and speed of each particle, and new position is established by speed；
For Endmember extraction problem, decision vector xn,m={ x1,x2,···,xnIndicate high-spectrum remote sensing in xiIt indicates
The state of ith pixel, for each pixel it there are two types of state, that is, xi∈{0,1}；If a pixel is chosen as end member
Its state is 1, and other is 0；Therefore the number that state is 1 is equal to end member number, i.e.,
6. the end member extraction method of the target in hyperspectral remotely sensed image according to claim 4 based on Evolutionary multiobjective optimization,
It is characterized in that, in step 5b, uses xk(t) and vk(t) k-th of particle is respectively indicated in the particle position and speed of t moment；With
xk,best(t) and xgbest(t) indicate that k-th of particle is complete before t moment in self optimization position of moment t and all particles
Office optimizes position；
The directed movement calculating formula of particle is as follows:
vk(t+1)=T ((xk,best(t)-xk(t))+(xgbest(t)-xk(t))) (7)
Wherein, T (x) is a random selection function, and when the positive value of x is selected, the value of T (x) is 1, when the negative value of x is selected
When T (x) value be -1, when the other values of x are selected, the value of T (x) is 0；
The random movement of particle is described as follows:
vk(t+1)=R (xk(t)) (8)
Wherein, R (x) is also a random function, be the value of R (x) is -1 when x be 1, when x is other values, the value of R (x) is 1；
Selection particle is gone to be oriented mobile or random movement, the speed of more new particle by a random selection probability；
After the speed of particle updates, particle goes to establish new position using new speed, obtains the position of more new particle such as
Following formula:
xk(t+1)=xk(t)+vk(t) (9)；
Stop algorithm up to algorithmic statement or after reaching maximum number of iterations, update obtains self optimal location of particle.
7. the end member extraction method of the target in hyperspectral remotely sensed image according to claim 4 based on Evolutionary multiobjective optimization,
It is characterized in that, in step 5c,
5c1, the variation number for inputting end member is [a, b], and a and b are positive integer；
5c2, multi-objective optimization question can resolve into b-a+1 subproblem；
5c3, in order to promote diversity to distribute to the fixed population of each subproblem setting；
5c4, each subproblem generate globally optimal solution by external storage sharing information.
8. the end member extraction method of the target in hyperspectral remotely sensed image according to claim 4 based on Evolutionary multiobjective optimization,
It is characterized in that, in step 5d, based on the elitist selection inversely grown, global optimum is as elite；Final solution is described as:
Y={ Ya,···,Ym,···,Yb,m∈[a,b]} (10)
Wherein, YmIndicate there be m end member in the particle, end member number is limited in [a, b]；WithIndicate that ith pixel becomes end member
The amount of chance, obtains；
Wherein, ciBigger, the chance that ith pixel becomes end member is bigger；It uses firstValue sort in descending order these pixels, so
Afterwards, the subproblem of m end member selects m pixel as elite；The speed of more new particle and position later are usedIndicate the
The elite of m subproblem；
New speed more new formula are as follows:
Wherein, x is usedk(t) indicate k-th of particle in the particle position of t moment；vk(t+1) indicate k-th of particle at the t+1 moment
Particle rapidity；Use xk,best(t) indicate that k-th of particle self optimizes position in moment t；T (x) is a random selection letter
Number, when the positive value of x is selected, its value is 1, and when the negative value of x is selected, its value is -1, when the other values of x are selected
Its value is 0；
The position for removing by new speed to establish subsequent time for each subproblem, determines globally optimal solution by elitist selection
That is the optimal location of particle determines the end member position in high spectrum image.
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