CN110428369A - CHNMF remote sensing images solution based on comentropy mixes algorithm - Google Patents
CHNMF remote sensing images solution based on comentropy mixes algorithm Download PDFInfo
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- 239000011159 matrix material Substances 0.000 claims abstract description 53
- 238000001228 spectrum Methods 0.000 claims abstract description 25
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- LIKBJVNGSGBSGK-UHFFFAOYSA-N iron(3+);oxygen(2-) Chemical compound [O-2].[O-2].[O-2].[Fe+3].[Fe+3] LIKBJVNGSGBSGK-UHFFFAOYSA-N 0.000 description 5
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- 235000003140 Panax quinquefolius Nutrition 0.000 description 1
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
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- 239000011045 chalcedony Substances 0.000 description 1
- 238000010835 comparative analysis Methods 0.000 description 1
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- BERDEBHAJNAUOM-UHFFFAOYSA-N copper(I) oxide Inorganic materials [Cu]O[Cu] BERDEBHAJNAUOM-UHFFFAOYSA-N 0.000 description 1
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Abstract
The present invention provides the CHNMF remote sensing images solutions based on comentropy to mix algorithm, comprising: current remote sensing images S1, are established with the mixed algorithm of the remote sensing images solution based on NMF；S2, algorithm is mixed according to the remote sensing images solution based on NMF to the mixed algorithm of CNMF remote sensing images solution of the current remote sensing images foundation based on smoothness constraint, to obtain the L that the CNMF remote sensing images solution based on smoothness constraint mixes algorithm2Norm；S3, the comentropy for obtaining current remote sensing images；S4, algorithm is mixed for the remote sensing images solution based on NMF, with the L obtained in S22Norm constrains endmember spectra matrix M as Regularization function, and the comentropy obtained in S3 is used to constrain abundance matrix S as Regularization function, mixes algorithm to establish the CHNMF remote sensing images solution based on comentropy.The present invention has compared to traditional algorithm preferably solves mixed effect.
Description
Technical field
The present invention relates to the CHNMF remote sensing images solutions based on comentropy to mix algorithm.
Background technique
Remote sensing technology is one and has intersected the multi-disciplinary new technology such as detection and infomation detection.With imaging spectrometer
Research and development constantly make new breakthroughs, and image analysis techniques are more and more deep, and remote sensing technology research and development have started a piece of upsurge, obtain vast
The favor of scientific research personnel occupies one seat in every field.
The prototype of remote sensing technology is imaging spectrometer Development Scheme, and the program is tested by California Institute of Technology's jet-propulsion
It is proposed is formulated for the first time in room (Jet Propulsion Lab, JPL).First generation high-resolution aerial imagery spectrometer in the world ---
AIS-1 is born in nineteen eighty-three in the U.S..It is also succeeded in developing in the U.S. after second generation hyperspectral imager --- AVIRIS 4 years.From
Last century the eighties so far, at home and abroad paid attention to by the development of imaging spectrometer, and development shows thriving
Trend.At abroad, the states such as Canada, Finland, U.S. have developed the series spectrometers such as CASI, AISI, Hymap, in spectrometer
Field maintains the leading position.At home, thermal infrared spectrum, multiband spectrum are had developed at present, and multispectral scanner etc. is excellent
Good equipment, reduce with world-class gap, realize the great-leap-forward development of China's spectrometer.
Interference and library of spectra due to remotely-sensed data vulnerable to environment is limited, and causing to obtain end member automatically becomes very tired
It is difficult.Therefore, the mode of blind decomposition is generally selected to decompose, obtain to remote sensing images that is, under conditions of other information is to know
Its endmember spectra and Abundances.
Three classes are generally comprised based on non-supervisory mixed pixel decomposition method: independent component analysis method, Non-negative Matrix Factorization
Method and analysis of complexity method.Non-negative Matrix Factorization method is mainly introduced herein.
NMF is appeared in earliest on an article of Paatero and Tapper in 1994.Lee and Seung exists within 1999
In one text of " Nature ", propose Non-negative Matrix Factorization (NMF) algorithm, this algorithm be all elements of original matrix all
In the case where being non-negative, non-negative linear decomposition is carried out to it.
NMF algorithm proposes till now, after decades of rapid development, to have arrived at the rank of a comparative maturity from formal
Section, application range have spread over the fields such as image procossing, data mining and speech processes.Many scholars are by NMF in recent years
It is introduced into the mixed problem of non-supervisory remote sensing images solution, and obtains certain achievement.But later it was discovered by researchers that actually answering
In, the non-negative limitation of only Non-negative Matrix Factorization is far from being enough, ideal decomposition value in order to obtain, Pauca and
Piper et al. proposes a kind of Algorithms of Non-Negative Matrix Factorization that band smoothly limits (CNMF)；Zymnis and Kim et al. combine field
Pixel has the characteristics that similar, proposes the Algorithms of Non-Negative Matrix Factorization (APS-NMF) of alternative projection gradient；Miao and Qi et al.
Propose the algorithm (MVC-NMF) of minimum volume constraint and NMF combination；The spy of Wu Bo and Zhao Yindi et al. based on mixed pixel
Property, it proposes using the SPECTRAL DIVERSITY of end member as the Algorithms of Non-Negative Matrix Factorization of restrictive condition；Liu Xuesong and Wang Bin et al. are proposed
The algorithm of abundance separation property and the Non-negative Matrix Factorization of flatness limitation；Faithful and upright and Liu Jinjun et al. is paid to arrive with each vertex of monomorphous
The Weighted distance of data center and minimum limitation propose the Algorithms of Non-Negative Matrix Factorization under weighting end member constraint.These are excellent
Change algorithm and all improve the mixed existing some shortcomings of remote sensing images solution, improves the mixed precision of its solution.
But these above-mentioned optimization algorithms all only consider the spectral information and spatial information of remotely-sensed data, mostly draw
Enter L1、L2Etc. the limitations of norms carry out optimization algorithm, there is no the physical messages for considering remotely-sensed data.
Summary of the invention
The technical problem to be solved in the present invention is that not accounting for the object of remotely-sensed data for above-mentioned current optimization algorithm
The technical issues of managing information provides the CHNMF remote sensing images solution based on comentropy and mixes the above-mentioned technological deficiency of algorithm solution.
CHNMF remote sensing images solution based on comentropy mixes algorithm, comprising:
S1, current remote sensing images are established with the mixed algorithm of the remote sensing images solution based on NMF；
S2, algorithm is mixed according to the remote sensing images solution based on NMF to CNMF of the current remote sensing images foundation based on smoothness constraint
Remote sensing images solution mixes algorithm, to obtain the L that the CNMF remote sensing images solution based on smoothness constraint mixes algorithm2Norm；
S3, the comentropy for obtaining current remote sensing images；
S4, algorithm is mixed for the remote sensing images solution based on NMF, with the L obtained in S22Norm is constrained as Regularization function
Endmember spectra matrix M, uses the comentropy obtained in S3 to constrain abundance matrix S as Regularization function, is based on comentropy to establish
CHNMF remote sensing images solution mix algorithm.
Further, step S2 is specifically included:
According to sparse representation theory, L is used2Norm to the remote sensing images solution based on NMF mix algorithm endmember spectra matrix and
Abundance matrix is constrained, and is obtained the CNMF remote sensing images solution based on smoothness constraint and is mixed algorithm.
Further, step S3 is specifically included:
Assuming that current remote sensing images information source has n kind value: U1...Ui...Un, corresponding probability are as follows: p1...pi...pn, and it is each
The appearance of kind symbol is independent of one another, then the comentropy of current remote sensing images information source are as follows:
Further, step S4 is specifically included:
S41, the objective function that the CHNMF remote sensing images solution based on comentropy mixes algorithm is established:
Wherein, M is endmember spectra matrix, and S is abundance matrix, and first item indicates reconstructed error, and information is used in Section 2 expression
Entropy is sparse to abundance matrix progress, and Section 3, which will be limited smoothly, introduces endmember spectra matrix, and λ and φ are regularization parameters；SijFor
Each element representative corresponds to ratio shared by end member in pixel, and L is remote sensing images wave band number, and R is the remote sensing figure of L wave band
Picture, P are the end member number of remote sensing images to be detected, and N is the pixel number of remote sensing images to be detected；
S42, endmember spectra matrix M and abundance matrix S are solved using multiplying property rule of iteration, according to the property of matrix
Partial derivative is asked to obtain M and S:
It reuses gradient descent method to be iterated, obtains the multiplying property rule of iteration of final M and S:
M←M.*RST./(MSST+ε)
Make score perseverance positive number using small positive number ε, when iterating to certain number, the changing value of f (M, S) is less than default
Value, the CHNMF remote sensing images solution based on comentropy for obtaining final optimization pass mix algorithm.
Compared with prior art, the beneficial effects of the present invention are: for the end member spy unevenly distributed of remote sensing images
Property, the physical message of remotely-sensed data is excavated herein, constrains endmember spectra matrix M and abundance matrix S respectively with norm and comentropy,
It proposes the CHNMF remote sensing images solution based on comentropy and mixes algorithm, have the preferably mixed effect of solution compared to traditional NMF and CNMF algorithm
Fruit.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing:
Fig. 1 is that the present invention is based on the CHNMF remote sensing images solutions of comentropy to mix algorithm flow chart；
Fig. 2 is three kinds of end member abundance figures in the embodiment of the present invention one；
Fig. 3 is three kinds of end member abundance figures in the embodiment of the present invention two.
Specific embodiment
For a clearer understanding of the technical characteristics, objects and effects of the present invention, now control attached drawing is described in detail
A specific embodiment of the invention.
CHNMF remote sensing images solution based on comentropy mixes algorithm, as shown in Figure 1, comprising:
S1, current remote sensing images are established with the mixed algorithm of the remote sensing images solution based on NMF；
It establishes the remote sensing images solution based on NMF and mixes algorithm, the optimization problem of the algorithm, which can be regarded as, minimizes following target
Function:
Wherein, M is endmember spectra matrix, and S is abundance matrix, f (M, S)=1/2 | | R-MS | |2, Section 2 and Section 3
It is the regularization function to parameter M, S respectively, for the spies such as smooth, low-rank to be added to endmember spectra matrix or abundance matrix
Property, α and β are regularization parameter.
In above-mentioned Optimized model, can only wherein some parameter is constrained, can also simultaneously to two parameters into
Row constraint, the selection of regularization function directly affect the quality of final result.LpNorm, nuclear norm and trace norm etc. are frequent
The regularization function used, they can realize sparse to varying degrees.
S2, algorithm is mixed according to the remote sensing images solution based on NMF to CNMF of the current remote sensing images foundation based on smoothness constraint
Remote sensing images solution mixes algorithm, and obtains L2Norm；
According to sparse representation theory, L0Norm can describe sparsity well, but L0Regularization function is that a NP is asked
Topic, solution is relatively difficult, is unfavorable for actual application, later Tao and Cande et al. are demonstrated in RIP (restricted
Isometricproperty under the conditions of), L1Norm is L0The optimal convex approximation of norm, and solve simply, therefore scholars use
L1Norm replaces L0Norm is solved.In addition to L1Norm, L2It is also very easy that norm solves, and it can improve well
Fitting problems.When we construct model, not only to guarantee that it can be suitble to training data, it will also so that it will not asking for over-fitting occur
Topic.So L2Norm is well suited for having been widely used for optimization problem.One kind that Pauca and Piper et al. are proposed
With constrained Algorithms of Non-Negative Matrix Factorization (constrained NMF, CNMF), L is exactly used2Norm carries out constraint side to M and S
Face obtains the objective function that the CNMF remote sensing images solution based on smoothness constraint mixes algorithm:
Wherein, M is endmember spectra matrix, and S is abundance matrix, objective function first item representative image reconstructed error, behind
Two smooth limitations represented to endmember spectra matrix and abundance matrix, α and β are regularization parameter, are used for Constraints of Equilibrium and mistake
The strong or weak relation of difference.
The multiplying property rule of iteration of CNMF is as follows:
M←M.*(RST-αM)./(MSST+ε)
S←S.*(MTR-βS)./(MTMS+ε)
Make score perseverance positive number in formula using small positive number ε, when iterating to certain number, the value of f (M, S) tends towards stability,
Obtain final optimization pass based on L2The CNMF remote sensing images solution of norm mixes algorithm.
S3, the comentropy for obtaining current remote sensing images；
Assuming that current remote sensing images information source has n kind value: U1...Ui...Un, corresponding probability are as follows: p1...pi...pn, and it is each
The appearance of kind symbol is independent of one another, then the comentropy of current remote sensing images information source are as follows:
From the foregoing, it will be observed that the confusion degree of the probability distribution of information source has determined the size of comentropy, performance is negative between the two
It is related.Probability distribution is more uneven, and comentropy is smaller.Mixed pixel be in remote sensing images it is very common, in other words, end member
Often uneven distribution.
S4, algorithm is mixed for the remote sensing images solution based on NMF, with the L obtained in S22Norm is constrained as Regularization function
Endmember spectra matrix M, uses the comentropy obtained in S3 to constrain abundance matrix S as Regularization function, is based on comentropy to establish
CHNMF remote sensing images solution mix algorithm.
S41, the objective function that the CHNMF remote sensing images solution based on comentropy mixes algorithm is established:
Wherein, M is endmember spectra matrix, and S is abundance matrix, and first item indicates reconstructed error, and information is used in Section 2 expression
Entropy is sparse to abundance matrix progress, and Section 3, which will be limited smoothly, introduces endmember spectra matrix, and λ and φ are regularization parameters；SijFor
Each element representative corresponds to ratio shared by end member in pixel, and L is remote sensing images wave band number, and R is the remote sensing figure of L wave band
Picture, P are the end member number of remote sensing images to be detected, and N is the pixel number of remote sensing images to be detected.
S42, endmember spectra matrix M and abundance matrix S are solved using multiplying property rule of iteration, according to the property of matrix
Partial derivative is asked to obtain M and S:
It reuses gradient descent method to be iterated, obtains the multiplying property rule of iteration of final M and S:
M←M.*RST./(MSST+ε)
Make score perseverance positive number using small positive number ε, when iterating to certain number, the changing value of f (M, S) is less than default
Value, the i.e. value of f (M, S) tend towards stability, and the CHNMF remote sensing images solution based on comentropy for obtaining final optimization pass mixes algorithm.
Illustrate that the present invention is based on the CHNMF remote sensing images solutions of comentropy to mix algorithm and traditional below by embodiment data
NMF algorithm compared with CNMF algorithm it is having the utility model has the advantages that
Embodiment one, in the present embodiment, first verifies the validity of CHNMF algorithm, and with traditional with generated data
NMF algorithm and CNMF algorithm are made comparisons.Initial value is obtained using random method.And the regularization parameter of CHNMF is also ginseng
Examine the empirical value of CNMF.Therefrom still pick carnallite (Carnallite), flint (Chert) and andradite
(Andradite) for these three atural objects as experimental result, which is the average result of 25 experiments.
As shown in Fig. 2, by the mixed three kinds of end member abundance figures come out of these three algorithm solutions of NMF, CNMF and CHNMF and really
End member abundance figure comparison, in table with white rectangle frame enclose come local area become closer to from top to bottom with reference to knot
Fruit, that is to say, that the mixed end member abundance figure come out of CHNMF solution and true end member abundance figure are closest.
Table 1 shows that these four algorithm solutions mix the comparison of the sad value and RMSE value of result.From experimental result, CHNMF
Algorithm is better than CNMF algorithm from spectral modeling distance SAD and root-mean-square error RMSE two indices, certainly also superior to traditional
NMF algorithm.
1 three kinds of NMF of table solve the performance indicator of mixed algorithm
Embodiment two, in the present embodiment, the data of use are the partial datas of the Cuprite of Nevada, USA, are led to
Cross truthful data experiment, the solutions of these three algorithms of further comparative analysis NMF, CNMF and HCNMF mixes situation, wherein abundance figure with
The result of tetracorder operation is reference, for the curve of spectrum of end member, to extract in ENVI4.8 platform to initial data
The curve of spectrum of end member therefrom has chosen bloodstone (hematite), calcedony (chalcedony) and pyroxene as reference result
(pyroxene) these three typical features are as reference result, as shown in figure 3 and table 2, successively give three kinds of algorithm solutions it is mixed after
Three kinds of end members abundance figure and sad value and RMSE value.
From the point of view of abundance figure, for bloodstone, in table secondary series with white box enclose come region, from top to bottom, color
Become closer to black, more approximate reference result；For calcedony, in table third arrange with white box enclose come region, CNMF and
The abundance figure of both algorithms of CHNMF is better than traditional NMF, more approximate reference result, but three is more similar；For pyroxene,
In table the 4th column with white box enclose come region, from top to bottom, color becomes closer to black, more approximate reference result.I.e.
In general from visual effect, it is all better than CNMF and NMF algorithm to mix effect for the solution of CHNMF algorithm.
As shown in Table 2, from the point of view of sad value, to these three end members of bloodstone, calcedony and pyroxene, the solution of CHNMF mixes effect most
Good, CNMF takes second place, and NMF is worst.From the point of view of RMSE value, for bloodstone and pyroxene both end members, the mixed effect of the solution of CHNMF algorithm
Fruit is best, and CNMF takes second place, and NMF is worst；For calcedony, the mixed effect of the solution of CHNMF algorithm is best, and CNMF takes second place, and NMF is worst.
Each algorithm solution of table 2 mixed sad value and RMSE value
In summary two embodiments, the present invention is based on the CHNMF remote sensing images solution of comentropy mix algorithm obtained it is best
Solution mix effect.
The embodiment of the present invention is described with above attached drawing, but the invention is not limited to above-mentioned specific
Embodiment, the above mentioned embodiment is only schematical, rather than restrictive, those skilled in the art
Under the inspiration of the present invention, without breaking away from the scope protected by the purposes and claims of the present invention, it can also make very much
Form, all of these belong to the protection of the present invention.
Claims (4)
1. the CHNMF remote sensing images solution based on comentropy mixes algorithm characterized by comprising
S1, current remote sensing images are established with the mixed algorithm of the remote sensing images solution based on NMF；
S2, algorithm is mixed according to the remote sensing images solution based on NMF to CNMF remote sensing of the current remote sensing images foundation based on smoothness constraint
Image solution mixes algorithm, to obtain the L that the CNMF remote sensing images solution based on smoothness constraint mixes algorithm2Norm；
S3, the comentropy for obtaining current remote sensing images；
S4, algorithm is mixed for the remote sensing images solution based on NMF, with the L obtained in S22Norm constrains end member as Regularization function
Spectrum matrix M uses the comentropy obtained in S3 to constrain abundance matrix S as Regularization function, to establish based on comentropy
CHNMF remote sensing images solution mixes algorithm.
2. the CHNMF remote sensing images solution according to claim 1 based on comentropy mixes algorithm, which is characterized in that step S2
It specifically includes:
According to sparse representation theory, L is used2Norm mixes the endmember spectra matrix and abundance square of algorithm to the remote sensing images solution based on NMF
Battle array is constrained, and is obtained the CNMF remote sensing images solution based on smoothness constraint and is mixed algorithm.
3. the CHNMF remote sensing images solution according to claim 1 based on comentropy mixes algorithm, which is characterized in that step S3
It specifically includes:
Assuming that current remote sensing images information source has n kind value: U1...Ui...Un, corresponding probability are as follows: p1...pi...pn, and various symbols
Number appearance it is independent of one another, then the comentropy of current remote sensing images information source are as follows:
4. the CHNMF remote sensing images solution according to claim 1 based on comentropy mixes algorithm, which is characterized in that step S4
It specifically includes:
S41, the objective function that the CHNMF remote sensing images solution based on comentropy mixes algorithm is established:
Wherein, M is endmember spectra matrix, and S is abundance matrix, and first item indicates reconstructed error, Section 2 expression comentropy pair
Abundance matrix progress is sparse, and Section 3, which will be limited smoothly, introduces endmember spectra matrix, and λ and φ are regularization parameters；SijIt is each
Element representative corresponds to ratio shared by end member in pixel, and L is remote sensing images wave band number, and R is the remote sensing images of L wave band, P
For the end member number of remote sensing images to be detected, N is the pixel number of remote sensing images to be detected；
S42, endmember spectra matrix M and abundance matrix S are solved using multiplying property rule of iteration, according to the property of matrix to M
Partial derivative is asked to obtain with S:
It reuses gradient descent method to be iterated, obtains the multiplying property rule of iteration of final M and S:
M←M.*RST./(MSST+ε)
Make score perseverance positive number using small positive number ε, when iterating to certain number, the changing value of f (M, S) is less than preset value, obtains
The CHNMF remote sensing images solution based on comentropy to final optimization pass mixes algorithm.
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| CN113836483A (en) * | 2021-08-10 | 2021-12-24 | 中国地质大学（武汉） | Deep non-negative matrix unmixing method based on information entropy sparseness and storage medium |
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