CN107274387A - 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 multiple-objection optimization an object function, different number of Endmember extraction result is obtained using single operation algorithm, accelerate the execution speed of algorithm, improve precision；Regard target in hyperspectral remotely sensed image Endmember extraction as a multi-objective problem, two object functions are optimized simultaneously using discrete particle group optimizing method, single operation can obtain with different end member numbers, that is, obtaining optimizing end member；Overcome need multiple single operation algorithm in the prior art and obtain with different number of end member result.Employ the leader selection strategies inversely grown, it is not necessary to search for all end members, reduce computation complexity.
Description
Technical field
The invention belongs to Hyperspectral imagery processing field, the line spectrum solution for being related to high spectrum image mixes method, is specifically
The end member extraction method of target in hyperspectral remotely sensed image based on Evolutionary multiobjective optimization.
Background technology
One of maximum achievement of 1980s remote sensing technology is exactly the rise of high-spectrum remote-sensing.High-spectrum remote-sensing device has
Ability captures hundreds of continuous spectrum bands can recognize the class of different atural objects for raising.High spectrum image is due to its abundant spectrum
Information is increasingly widely applied, such as in mineral exploration, in terms of environmental monitoring and military monitoring.Mixed pixel is decomposed
Problem is a major issue for limiting 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 material
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.Because high light spectrum image-forming sensor improves high spatial and light
Spectral resolution, Endmember extraction becomes more and more important in high spectrum image analysis.One end member is a preferable pure feature class.
Many end member extraction methods are based on linear spectral mixture model and assume that pure pixel is present 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 shortcomings.One is to carry
Precision is taken to reduce, if real data are unsatisfactory for pure structure.Another is a lack of the information and end member of feedback mechanism
Number relies on broadband number.Therefore these algorithms randomly generate initial end member, when it is not that an effective initialization will take for very long
Between find desired result.In order to solve these problems, it is proposed that some new methods based on evolution, row such as discrete particle cluster is excellent
Change, ant group optimization (ACO) and adaptive differential evolve (ADDE).This method is converted to an optimization by Endmember extraction problem
Problem goes to evaluate object function with a feasible solution space is set up.
However, there are some shortcomings in the implementation of these algorithms.There is no guidance to go to determine to produce 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 the Endmember extraction algorithm of many.It may be evident, however, that Endmember extraction is ill posed, do not make us also
This problem of satisfied solution.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 obtain different results by performing a series of single operations, this
It is very time-consuming.
The content of the invention
For problems of 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, and the non-dominant with different end member numbers can be just obtained by single operation
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 the group's optimization of evolution multiple target, comprises the following steps：
Step 1, it is determined that needing high-spectrum remote sensing I to be processed to be used as original image；
Step 2, spectral resolution is carried out to high-spectrum remote sensing I using linear spectral mixture model, for Endmember extraction；
OrderRepresent the high-spectrum remote sensing of n pixel of L wavestrip, riIt is the spectrum row arrow for representing ith pixel
Amount, then linear spectral mixture model LSMM is defined as,
In above formula, m is end member number,End member set is represented,It is abundance of j-th of end member in ith pixel,
εiThe error term of i-th of wave band is represented, end member abundance needs to meet two constraintss：
Step 3, obtained estimating end member abundance with staff cultivation least square, obtained by linear spectral mixture model and mix figure again
PictureAnd then obtain original image and mix the root-mean-square error (RMSE) of image again as an object function；And
It regard the end member number ∑ (x) of original image as another object function；
Step 4, root mean square is smaller, represents original image and mixes image again closer to if end member number is reduced, root mean square is missed
Difference will become big, thus combine the object function of two obtained contradiction, 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, the multi-objective optimization question to foundation passes through target letter of the Discrete Particle Swarm Optimization Algorithm to two contradiction
Number is optimized simultaneously, using elitist selection strategy, obtains final Endmember extraction result.
It is preferred that, in step 3, using the mixed estimation end member abundance of staff cultivation least square FCLS linear solutions；Its specific steps
It is as follows：
Step 3a, uses original imageWith end member collectionGo to estimate abundance
Step 3b, by estimating abundance and end member ejObtain estimating pixelMix image such as following formula again；
Step 3c, calculates original image and its root-mean-square error RMSE for mixing image again, is used as an object function；
It is preferred that, when setting up 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 represented with original image, i.e., original image and again mix image RMSE be 0；Work as shifting
During 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 reduction and become big, can keep end member as much as possible as object function with RMSE.
It is preferred that, described step 5 specifically includes 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 represents end member number, it is assumed that end member number is, it is known that then xn,m={ x1,x2,…,xnRepresent discrete particle position
Put, you can a solution in row space；
The position of discrete particle, then updates the state of discrete particle, that is, updates in step 5b, initialization solution space
Self optimal location of particle and in history all particles global optimum position；
Step 5c, some subproblems are resolved into according to the change number of end member by multi-objective optimization question, 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, according to the globally optimal solution of each subproblem, multi-objective optimization question is obtained by elitist selection algorithm
Globally optimal solution；The end member in high spectrum image is determined according to the optimal location that multi-objective optimization question globally optimal solution is particle
Position.
It is preferred that, in step 5a, particle is constantly moved in solution space, and calculates the fitness function of each particle
Value；Position and the speed of each particle are updated according to the fitness value of particle, new position is set up by speed；
For Endmember extraction problem, decision-making vector xn,m={ x1,x2,…,xnRepresent high-spectrum remote sensing in xiTable
Show the state of ith pixel, it has two states i.e. x for each pixeli∈{0,1}；If a pixel is chosen as end member
Then its state is 1, and other is 0；Therefore state is equal to end member number for 1 number, i.e.,
It is preferred that, in step 5b, use xkAnd v (t)k(t) particle position and speed of k-th of particle in t are represented respectively
Degree；Use xk,bestAnd x (t)gbest(t) represent that k-th of particle self optimizes position and all particles before t 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, when x T (x) value when being chosen is 1, when x negative value quilt
T (x) value is -1 during selection, and when x other values are chosen, T (x) value 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, and it 1 is that R (x) value is -1 to be as x, R (x) value when x is other values
For 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 set up new position using new speed, obtains the position of more new particle
Put such as following formula：
xk(t+1)=xk(t)+vk(t) (9)；
Until algorithmic statement or reaching and stopping algorithm after maximum iteration, self optimal location for obtaining particle is updated.
It is preferred that, in step 5c,
5c1, the change number of input 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, fixed population is set in order to promote diversity to distribute to each subproblem；
5c4, each subproblem produces globally optimal solution by external storage sharing information.
It is preferred that, in step 5d, based on the elitist selection inversely grown, global optimum is used as elite；Final solution is retouched
State for：
Y={ Ya,…,Ym,…,Yb,m∈[a,b]} (10)
Wherein, YmRepresent there be m end member in the particle, end member number is limited in [a, b]；WithRepresent that ith pixel turns into
The amount of end member chance, is obtained；
Wherein, ciBigger, the chance that ith pixel turns into end member is bigger；Use firstValue sort in descending order these pictures
Element, then, the subproblem for having m end member select m pixel as elite；The speed of more new particle and position, are used afterwards
Represent the elite of m-th of subproblem；
New speed more new formula is：
Go to set up the position of subsequent time by new speed for each subproblem, the overall situation is determined most by elitist selection
Excellent solution is that the optimal location of particle determines the end member position in high spectrum image.
Compared with prior art, the present invention has following beneficial technique effect：
The present invention is by the way that end member number, as an object function of multiple-objection optimization, is obtained not using single operation algorithm
With the Endmember extraction result of number, accelerate the execution speed of algorithm, improve precision；Target in hyperspectral remotely sensed image Endmember extraction is regarded as
It is a multi-objective problem, two object functions is optimized simultaneously using discrete particle group optimizing method, single operation can be obtained
With different end member numbers, that is, obtain optimizing end member；Overcome need multiple single operation algorithm in the prior art and obtain
With different number of end member result.Employ the leader selection strategies inversely grown, it is not necessary to search for all end members, subtract
Small computation complexity.
Brief description of the drawings
Fig. 1 is that leader figures are selected from external storage described in present example.
Fig. 2 is selection leader schemes from external storage in the iterative process described in present example.
Fig. 3 is the AVIRIS figures of the 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 process figure of discrete particle cluster optimization described in present example.
Embodiment
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 is based on the end member extraction method of Evolutionary multiobjective optimization (MOEE), accurately can be extracted from high spectrum image
End member.It is main solve prior art complexity it is high and need to be run multiple times algorithm and obtain with different numbers
End member result the problem of.The step of realizing of the invention is：(1) object function is determined；(2) construct initial solution population, using with
Machine method is initialized to 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 satisfaction presets number of iterations, then performs (6), otherwise go to step (3)；(6) optimum solution is selected according to elitist selection.The present invention
Optimize two object functions simultaneously, realize the Endmember extraction to EO-1 hyperion sense image.
The technical scheme is that：Regard 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 average of spectral modeling drawing are used as target letter
Number, the two object functions are optimized using the evolution multi-target method based on decomposition simultaneously, and introduce the elite choosing inversely grown
Strategy is selected, globally optimal solution is finally given, implementation step includes as follows：
Step 1, input high-spectrum remote sensing I, I is the high spectrum image of a width 350*400*50, the scope 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 represent the spectral signature of each end member and its occupied area percentage in pixel
The linear function of ratio, orderRepresent the remote sensing images of n pixel of L wavestrip, riIt is the spectrum row arrow for representing ith pixel
Amount.Then LSMM is defined as,
M is end member number in above formula,End member set is represented,It is abundance of j-th of end member in ith pixel, εi
Represent in the error term (such as noise and model error) of i-th of wave band, 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 constraintss：
Step 3, it is mixed using staff cultivation least square (FCLS) linear solution：
Step 3a, uses original imageWith end member collectionGo to estimate abundance
Step 3b, by estimating abundance and end member ejObtain estimating pixelAgain mix image it is as follows,
Step 3c, and then the root-mean-square error (RMSE) for obtaining original image and its again mixed image is calculated, it is used as one
Object function；
Also, it regard end member number ∑ (x) as another object 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 represented 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, end member as much as possible is kept as object function with RMSE.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 object function of the two contradictions simultaneously with Discrete Particle Swarm Optimization Algorithm, obtain 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 is optimized, using elitist selection strategy, obtains final Endmember extraction result.
Step 5a, particle swarm optimization algorithm searches for the optimal location of particle in solution space.Particle is in feasible sky
Between constantly move, and calculate fitness function value.Each particle has two attribute, and " position " and " speed " " should be remembered
The optimum position and global optimum position of " self " of history " in history.Improvement based on particle cluster algorithm, D-PSO makes grain
Son can be searched in discrete solution space.For Endmember extraction problem, decision-making vector xn,m={ x1,x2,…,xnRepresent bloom
The state of ith pixel in spectrum remote-sensing image.For each pixel, it has two states i.e. 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
Step 5b, the state of discrete particle updates；
Use xkAnd v (t)k(t) particle position and speed of k-th of particle in t are represented respectively.Use xk,best(t) and
xgbest(t) represent that k-th of particle self optimizes the global optimization position of position and all particles before t in moment t
Put.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 on the occasion of be selected as its value for 1. when x negative value is chosen it
Value be -1. when x other values be chosen when 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) is also a random function, when x be 1 be its 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 set up new position and pass through following formula：
xk(t+1)=xk(t)+vk(t) (6)
Until algorithmic statement or reaching and stopping algorithm after maximum iteration, self optimal location for obtaining particle is updated.
Because all particles can not possibly be optimal position simultaneously in practice, so we set a maximum iteration, to ensure
Algorithm stops.
Step 5c, multi-objective optimization question resolves into many subproblems；
5c1, the change number of input 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 in the population that each subproblem is fixed, this preferred embodiment, it is contemplated that calculate
The complexity of method we to each subproblem set population be 20.
5c4, subproblem produces globally optimal solution (leader) by external storage sharing information.
Step 5d, globally optimal solution is obtained by elitist selection.
The end member extraction method of the target in hyperspectral remotely sensed image optimized based on multiple target discrete particle cluster, is selected by leader
Obtain globally optimal solution.
Based on the leader selections inversely grown, global optimum is used as leader.Final solution is described as：
Y={ Ya,…,Ym,…,Yb,m∈[a,b]} (7)
Wherein, YmRepresent there be m end member in the particle, end member number is limited in [a, b].We useRepresent ith pixel
Amount as end member chance, thereforeIt can be calculated with following formula
ciBigger, the chance that ith pixel turns into end member is bigger.As shown in figure 1, using firstValue sort in descending order this
A little pixels, then, the subproblem for having m end member select m pixel as optimal solution.As shown in Fig. 2 the speed of more new particle afterwards
Degree and position, the elite for having the subproblem of m end member are different, are usedRepresent the leader of m-th of subproblem.
New speed more new formula is：
Go to set up the position of subsequent time by new speed for each subproblem, the overall situation is determined most by elitist selection
Excellent solution is that the optimal location of particle determines the end member position in high spectrum image.
The effect of the present invention can be further illustrated by following emulation：
1. simulated conditions
This example is under the systems of Intel (R) Core (TM) i7-4790CPU@3.60GHz Windows 8.1, Matlab
On 2014a operation platforms, of the invention and existing N-FINDR, VCA, the emulation experiment of DPSO methods are completed.
2. emulation experiment content
The present invention chooses true EO-1 hyperion AVIRIS Cuprite images 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 is nineteen ninety-five Nevada ,Usa cuprite area in experiment
From acquisition 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] to set end member number, and randomly selected probability is 0.1, per height
Problem population is 10, and after 300 iteration, obtained Endmember extraction result is shown in Fig. 4.Table 1 show the present invention with
RMSE value comparison sheet of existing N-FINDR, VCA, the DPSO method to AVIRIS figures；
Table 1
Obviously the present invention is than DPSO and N-FINDR, and VCA will get well.Therefore, can by optimizing the two object function this method
With the extraction result for the different end member numbers for obtaining one group.The Endmember extraction result of different end member numbers is obtained by optimized algorithm, is adopted
It is higher with elitist selection strategy efficiency of algorithm, the RMSE value obtained as can be seen from Table 1 for different end member number MOEE algorithms compared with
It is small.
Analogous diagram used generates 80*100 pixels covering 224 with five end member subsets for us from USGS library of spectra in experiment
Wave band EO-1 hyperion analog image.Composograph has 20 rectangle frames to be in the scene center shown in figure at one 4 × 5.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) displays.As shown in figure 5, five features are by United States Geological Survey
Storehouse is selected, alunite AL706 (A), Buddingtonite GDS85 (B), Calcite Co2004 (C) calcite, kaolinite
CM3 (K) and Muscovite GDS107 (M).It is [3,6] to set end member number.
It is 10 that Fig. 5 (a) composite diagram rectangle frame, which is damaged and obtains signal to noise ratio (SNR) by simulated Gaussian white noise,:1,20:
1 and 30:1.Fig. 6 shows that the present invention is 20 in signal to noise ratio:The end member result extracted under conditions of 1.Fig. 6 (a)-(d) difference tables
Show the position of end member when end member number is 3-6.Table 2 shows of the invention and existing N-FINDR, VCA, and DPSO methods are 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 object function this method
Obtain the extraction result of one group of different end member numbers.
The present invention is emulated and true target in hyperspectral remotely sensed image is as experimental subjects, using using Evolutionary Multiobjective Optimization
The object function of original image and its two conflicts of the root-mean-square error (RMSE) for mixing image again and ∑ (x) is carried out while excellent
Change, single operation can obtain the non-domination solution with different end member numbers, that is, obtain optimizing end member.By with some existing sides
Method is compared, and the present invention can obtain good Endmember extraction result while computation complexity is reduced.
Claims (8)
1. the end member extraction method of the target in hyperspectral remotely sensed image based on the group's optimization of evolution multiple target, it is characterised in that including as follows
Step：
Step 1, it is determined that needing high-spectrum remote sensing I to be processed to be used as original image；
Step 2, spectral resolution is carried out to high-spectrum remote sensing I using linear spectral mixture model, for Endmember extraction；
OrderRepresent the high-spectrum remote sensing of n pixel of L wavestrip, riIt is the spectrum column vector for representing ith pixel, then
Linear spectral mixture model LSMM is defined as,
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In above formula, m is end member number,End member set is represented,It is abundance of j-th of end member in ith pixel, εiRepresent
The error term of i-th of wave band, end member abundance needs to meet two constraintss：
ANC:
ASC:
Step 3, obtained estimating end member abundance with staff cultivation least square, obtained by linear spectral mixture model and mix image againAnd then obtain original image and mix the root-mean-square error (RMSE) of image again as an object function；And will
The end member number ∑ (x) of original image is used as another object function；
Step 4, root mean square is smaller, represents original image and mixes image again closer to if end member number is reduced, root-mean-square error will
Become big, thus combine the object function of two obtained contradiction, by the Endmember extraction problem of high-spectrum remote sensing be modeled as
Multi-objective optimization question MOPs described in following formula；
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<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Step 5, the multi-objective optimization question to foundation is same to the object function of two contradictions by Discrete Particle Swarm Optimization Algorithm
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, its
It is characterised by, in step 3, using the mixed estimation end member abundance of staff cultivation least square FCLS linear solutions；It is comprised the following steps that：
Step 3a, uses original imageWith end member collectionGo to estimate abundance
Step 3b, by estimating abundance and end member ejObtain estimating pixelMix image such as following formula again；
<mrow>
<mover>
<mi>r</mi>
<mo>^</mo>
</mover>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msub>
<mo>&part;</mo>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>e</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Step 3c, calculates original image and its root-mean-square error RMSE for mixing image again, is used as an object function；
<mrow>
<mi>R</mi>
<mi>M</mi>
<mi>S</mi>
<mi>E</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mrow>
<mo>{</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
<mo>}</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mrow>
<mo>{</mo>
<mover>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
<mo>^</mo>
</mover>
<mo>}</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msqrt>
<mrow>
<mfrac>
<mn>1</mn>
<mi>L</mi>
</mfrac>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mover>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
<mo>^</mo>
</mover>
<mo>|</mo>
<msubsup>
<mo>|</mo>
<mn>2</mn>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
3. the end member extraction method of the target in hyperspectral remotely sensed image according to claim 1 based on Evolutionary multiobjective optimization, its
It is characterised by, when setting up multi-objective optimization question in step 4, it is assumed that all pixels are end members in high-spectrum remote sensing and ignored
Error ε, then again mix image be entirely capable of being represented with original image, i.e., original image and again mix image RMSE be 0；When removal one
During 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 big less, end member as much as possible can be kept as object function with RMSE.
4. according to the Endmember extraction side of the target in hyperspectral remotely sensed image optimized based on multiple target discrete particle cluster described in claim 1
Method, it is characterised in that described step 5 specifically includes 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,
<mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>m</mi>
</mrow>
</msub>
<mo>=</mo>
<mo>{</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>x</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>|</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>&Element;</mo>
<mo>{</mo>
<mn>0</mn>
<mo>,</mo>
<mn>1</mn>
<mo>}</mo>
<mo>,</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mi>m</mi>
<mo>}</mo>
<mo>,</mo>
</mrow>
Wherein, m represents end member number, it is assumed that end member number is, it is known that then xn,m={ x1,x2,…,xnRepresent discrete particle position,
I.e. one of feas ible space solves；
The position of discrete particle, then updates the state of discrete particle, i.e. more new particle in step 5b, initialization solution space
Self optimal location and in history all particles global optimum position；
Step 5c, resolves into some subproblems by multi-objective optimization question according to the change number of end member, utilizes step 5a and step
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, according to the globally optimal solution of each subproblem, obtains multi-objective optimization question global by elitist selection algorithm
Optimal solution；The end member position in high spectrum image is determined according to the optimal location that multi-objective optimization question globally optimal solution is particle
Put.
5. according to the Endmember extraction side of the target in hyperspectral remotely sensed image optimized based on multiple target discrete particle cluster described in claim 4
Method, it is characterised in that in step 5a, particle is constantly moved in solution space, and calculates the fitness function value of each particle；
Position and the speed of each particle are updated according to the fitness value of particle, new position is set up by speed；
For Endmember extraction problem, decision-making vector xn,m={ x1,x2,…,xnRepresent high-spectrum remote sensing in xiRepresent i-th
The state of individual pixel, for each pixel, it has two states i.e. xi∈{0,1}；If a pixel is chosen as end member it
State is 1, and other is 0；Therefore state is equal to end member number for 1 number, i.e.,
6. according to the Endmember extraction side of the target in hyperspectral remotely sensed image optimized based on multiple target discrete particle cluster described in claim 4
Method, it is characterised in that in step 5b, use xkAnd v (t)k(t) particle position and speed of k-th of particle in t are represented respectively；
Use xk,bestAnd x (t)gbest(t) represent that k-th of particle self optimizes position and all particles before t 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, when x T (x) value when being chosen is 1, when x negative value is chosen
When T (x) value be -1, when x other values be chosen when T (x) value be 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, and it 1 is that R (x) value is -1 to be as x, and when x is other values, R (x) value 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 set up new position using new speed, obtains the position of more new particle such as
Following formula：
xk(t+1)=xk(t)+vk(t) (9)；
Until algorithmic statement or reaching and stopping algorithm after maximum iteration, self optimal location for obtaining particle is updated.
7. according to the Endmember extraction side of the target in hyperspectral remotely sensed image optimized based on multiple target discrete particle cluster described in claim 4
Method, it is characterised in that in step 5c,
5c1, the change number of input 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, fixed population is set in order to promote diversity to distribute to each subproblem；
5c4, each subproblem produces globally optimal solution by external storage sharing information.
8. according to the Endmember extraction side of the target in hyperspectral remotely sensed image optimized based on multiple target discrete particle cluster described in claim 4
Method, it is characterised in that in step 5d, based on the elitist selection inversely grown, global optimum is used as elite；Final solution is described
For：
Y={ Ya,…,Ym,…,Yb,m∈[a,b]} (10)
Wherein, YmRepresent there be m end member in the particle, end member number is limited in [a, b]；WithRepresent that ith pixel turns into end member
The amount of chance, is obtained；
<mrow>
<mi>C</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mi>a</mi>
</mrow>
<mi>b</mi>
</munderover>
<msub>
<mi>Y</mi>
<mi>m</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein, ciBigger, the chance that ith pixel turns into end member is bigger；Use firstValue sort in descending order these pixels, so
Afterwards, the subproblem for having m end member selects m pixel as elite；The speed of more new particle and position, are used afterwardsRepresent the
The elite of m subproblem；
New speed more new formula is：
<mrow>
<msub>
<mi>v</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>T</mi>
<mrow>
<mo>(</mo>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>b</mi>
<mi>e</mi>
<mi>s</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
<mo>+</mo>
<mo>(</mo>
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<mi>g</mi>
<mi>b</mi>
<mi>e</mi>
<mi>s</mi>
<mi>t</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Go to set up the position of subsequent time by new speed for each subproblem, globally optimal solution is determined by elitist selection
That is the optimal location of particle determines the end member position in high spectrum image.
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| CN113111763A (en) * | 2021-04-08 | 2021-07-13 | 洛阳师范学院 | Method and device for establishing spectral volume index and method for identifying tree species |
| CN113111763B (en) * | 2021-04-08 | 2023-01-24 | 洛阳师范学院 | Method and device for establishing spectral volume index and method for identifying tree species |
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