CN105320959B - High spectrum image sparse solution mixing method based on end member study - Google Patents
High spectrum image sparse solution mixing method based on end member study Download PDFInfo
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F18/00—Pattern recognition
- G06F18/20—Analysing
- G06F18/23—Clustering techniques
- G06F18/232—Non-hierarchical techniques
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F18/00—Pattern recognition
- G06F18/20—Analysing
- G06F18/23—Clustering techniques
- G06F18/232—Non-hierarchical techniques
- G06F18/2321—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions
- G06F18/23213—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions with fixed number of clusters, e.g. K-means clustering
Abstract
The invention discloses a kind of high spectrum image sparse solution mixing methods based on end member study, mainly solve the prior art during high spectrum image solution of low signal-to-noise ratio is mixed, high spectrum image solution mixes the problem of precision is low, quality reconstruction is poor, time-consuming, low efficiency.Step of the invention is：High-spectral data is inputted, EO-1 hyperion base data is synthesized, end member study solves high-spectral data abundance matrix, calculates the reconstructed error of high-spectral data abundance matrix, and output solves mixed result.Present invention employs new Solution models, introduce the thought of end member study, have the advantages that the mixed precision of solution is high, quality reconstruction is good, high-efficient, while solution procedure is simple, clear principle, can be used for the understanding interpretation of high spectrum image.
Description
Technical field
The invention belongs to technical field of image processing, further relate to image solution and mix one of technical field based on end
The high spectrum image solution mixing method of meta learning.Then the present invention utilizes the end learnt by first carrying out simulation learning to end member
Member carries out the solution of abundance, to accomplish the fast understanding interpretation to high spectrum image.The present invention can be used for setting various numbers
Standby high spectrum image carries out solving mixed processing, can effectively improve the mixed precision of high spectrum image solution.
Background technique
High-spectrum seems to be made of up to a hundred very narrow wave bands, it not only has the information of spectral domain, further comprises
Spatial information abundant.But the deficiency of sensor spatial resolution, so that for high spectrum image, pixel therein
Point is difficult to be pure pixel, but the point of mixed pixel made of being merged as many kinds of substance, effective to utilize in order to better
Hyperspectral image data must just decompose mixed pixel point therein, the substance being broken down into the presence of image
Collect the product of (being commonly called as end member) and corresponding proportion set (being commonly called as abundance).
Paper " the Hyperspectral that Y.Qian, S.Jia, J.Zhou and A.Robles-Kelly are delivered at it
unmixing via L0.5sparsity-constrained nonnegative matrix factorization”(IEEE
Transactions on Geoscience and Remote Sensing, vol.49, no 11, pp.4282-4297,
No.2011 a kind of non-negative matrix factorization method based on L0.5 norm sparse constraint) is proposed in.This method passes through to abundance
Matrix carries out the sparse constraint of L0.5 norm, using alternative iteration method, carries out Non-negative Matrix Factorization to high-spectral data matrix, from
And obtain end member matrix and abundance matrix.Deficiency existing for this method is, during the high spectrum image solution of low signal-to-noise ratio is mixed,
When solving end member matrix and abundance matrix simultaneously using alternative iteration method, high spectrum image solution mixes result, and time-consuming, low efficiency.
" a kind of high spectrum image sparse solution based on accidental projection is mixed for the patented technology that Beijing Space aviation university is possessed
Method " (number of patent application：201110207433.0 Authorization Notice No.：CN102314685A it) proposes a kind of based on random throwing
The high spectrum image sparse solution mixing method of shadow.This method has four big steps：One, by reading data into software MATLAB；Two, it counts
Calculation machine carries out accidental projection to hyperspectral image data and EO-1 hyperion library data；Three, the mixed objective function of building sparse solution, uses
Division Bregman algorithm optimization objective function seeks extreme value, until reaching convergence stop condition.Four, suitable threshold process is set
Abundance matrix obtains final abundance figure and end member.Present invention utilizes high-spectral data libraries to select end member, overcome previous
End member calculated by algorithm and the pure substance spectra in standard high-spectral data library can not tight corresponding disadvantages；It realizes to height
The qualitative analysis of spectrum picture.The deficiency that this method still has is that the different spectrum phenomenon of jljl will lead to practical end member and standard is high
End member has a certain difference in spectra database, directly using end member in high-spectral data library, can make high spectrum image solution
Mixed result precision is low, and quality reconstruction is poor.
The content of invention
It is an object of the invention to be directed to the deficiency of above-mentioned prior art, a kind of high-spectrum based on end member study is proposed
As sparse solution mixing method, precision is mixed to improve the solution of high spectrum image, overcomes the problems, such as that high spectrum image solution mixes low efficiency, reduces
The mixed time-consuming of high spectrum image solution.
To achieve the goals above, step of the invention includes as follows：
1. a kind of high spectrum image sparse solution mixing method based on end member study, includes the following steps：
(1) high-spectral data is inputted；
(2) EO-1 hyperion base data is synthesized：
(2a) selects all end members included in high-spectral data from digital spectrum library, obtains alternative end member；
(2b) initializes predeterminable area with alternative end member, obtains alternative area；
(2c) utilizes Di Li Cray method, generates the Abundances of alternative area；
(2d), multiplied by end member corresponding in alternative area, obtains initial base data with the Abundances generated；
(2e) filters out the high frequency signal components in initial base data by low-pass filter；
(2f) chooses the pixel that Abundances are lower than preset threshold 0.8 from initial base data, obtains alternate pixel point；
(2g) initializes alternate pixel point, each end in the alternate pixel point being initialised with end members all in alternative end member
The corresponding Abundances of member are set as the inverse of alternative end member sum, obtain intermediate base data；
Zero mean Gaussian white noise is added into intermediate base data in (2h), obtains the EO-1 hyperion base data of synthesis；
(3) end member learns：
(3a) presets the screening matrix that size is L × P and size is the storage matrix of 1 × P, wherein L indicates alternative end member
The wave band number of middle end member, P indicate end member sum in alternative end member, are depositing for 1 × P by screening matrix and size that size is L × P
Element in storage matrix is initialized as complete zero；
(3b) according to the following formula, constructs slickness bound term：
G=| | A | |F
Wherein, G indicates slickness bound term, and A indicates end member matrix to be learned, | | | |FExpression takes the behaviour of F norm
Make；
(3c) according to the following formula, structural segmentation slickness bound term：
Wherein, R indicates piecewise smooth bound term, and ∑ expression takes sum operation, and l indicates rower, and the value range of l is
{ 1,2 ..., L }, L indicate that the wave band number of end member in alternative end member, p indicate column mark, and the value range of p is { 1,2 ..., P }, P
Indicate that end member sum in alternative end member, i indicate AlpThe label of element, e in the Neighbourhood set of left and right(·)It indicates using natural number the bottom of as
Index operation, AlpIndicate l row pth column element in end member matrix to be learned, BiIndicate AlpI-th yuan in the Neighbourhood set of left and right
Element, the value range of i are { 1,2 }, and γ indicates constraint force parameter, and the value range of γ is [0,1]；
(3d) utilizes K averaging method, the EO-1 hyperion base data of synthesis is carried out cluster operation, the EO-1 hyperion base after being clustered
Data；
(3e) randomly selects a kind of data for not carrying out end member study also, obtains from the EO-1 hyperion base data after cluster
Current subclass EO-1 hyperion base data；
(3f) carries out end member study according to the following formula, to current subclass EO-1 hyperion base data, obtains current subclass EO-1 hyperion base
The end member matrix of data：
Wherein, A(k+1)Indicate that the end member matrix of the current subclass EO-1 hyperion base data of+1 iteration of kth, k are indicated to current
Subclass EO-1 hyperion base data carries out the number of iterations used when end member study, and the value range of k is { 1,2 ..., 100 }, and k's is first
Initial value, which is set as 1, argmin, to be indicated to take the end member when reaching minimum value to the progress end member study of current subclass EO-1 hyperion base data
Matrix manipulation,Expression takes the square operation of F norm, and Z indicates current subclass EO-1 hyperion base data, A(k)Indicate working as kth time
The end member matrix of preceding subclass EO-1 hyperion base data, Y(k)Indicate the abundance square of the current subclass EO-1 hyperion base data of kth time iteration
Battle array, λ1Indicate the parameter of adjusting slickness bound term, λ1Value be set as 0.9, G(k)Indicate the slickness constraint of kth time iteration
, λ2Indicate the parameter of adjusting piecewise smooth bound term, λ2Value be set as 0.1, R(k)Indicate the piecewise smooth of kth time iteration
Property bound term, λ3Indicate balance parameters, λ3Value be set as 1, D and indicate that the abundance matrix of current subclass EO-1 hyperion base data is corresponding
True value；
(3g) utilizes digital spectrum library, screens to the end member matrix of the current subclass EO-1 hyperion base data after study,
Obtain the end member matrix closest to digital spectrum library；
(3h) judges that the whether every class of EO-1 hyperion base data after cluster has all carried out end member study, if so, after obtaining study
End member matrix and currently stored matrix, otherwise, execute step (3e)；
(4) high-spectral data abundance matrix is solved：
(4a) according to the following formula, constructs the canonical Weighted Constraint item of high-spectral data abundance matrix：
Wherein, Q indicates that the canonical Weighted Constraint item of high-spectral data abundance matrix, ∑ indicate sum operation, and i indicates bloom
The number of modal data abundance matrix midrange, the value range of i are { 1,2 ..., N }, and j is indicated in high-spectral data abundance matrix
The number of columns, the value range of j are { 1,2 ..., N }, and N indicates pixel sum in high-spectral data,Indicate amount of orientation
The square operation of 2 norms, yiIndicate the i-th column, y in high-spectral data abundance matrixjIndicate jth in high-spectral data abundance matrix
Column, e(·)It indicates using natural number as the index operation at bottom, ρ indicates constraint force parameter, and the value range of ρ is [0,1]；
(4b) according to the following formula, calculates the degree of rarefication of high-spectral data abundance matrix：
Wherein, α2Indicate the degree of rarefication of high-spectral data abundance matrix,Expression takes radical sign to operate, and L indicates alternative end member
The wave band number of middle end member, ∑ expression take sum operation, and l indicates the number of high-spectral data line number, the value range of l be 1,
2 ..., L }, N indicates pixel sum, x in high-spectral datalIndicate l row in high-spectral data, | | | |1Indicate amount of orientation
The operation of 1 norm, | | | |2Indicate the operation of 2 norm of amount of orientation；
(4c) according to the following formula, calculates high-spectral data abundance matrix：
Wherein, Y(k+1)Indicate the high-spectral data abundance matrix of+1 iteration of kth, k indicates to calculate high-spectral data abundance
The number of iterations when matrix, the value range of k are { 1,2 ..., 100 }, and argmin expression takes when calculating high-spectral data abundance
Matrix reaches abundance matrix operation when minimum value,Expression takes the square operation of F norm, and X indicates high-spectral data, A table
End member matrix after dendrography habit, Y(k)Indicate the high-spectral data abundance matrix of kth time, α1Indicate the canonical of adjusting abundance matrix
The parameter of Weighted Constraint item, α1Value be set as 1, Q(k)Indicate the canonical weighting of the high-spectral data abundance matrix of kth time iteration
Bound term, | | | |2,1Expression takes the sum operation of each 2 norm of column vector in abundance matrix, α2Indicate that high-spectral data is rich
Spend the degree of rarefication of matrix；
(5) according to the following formula, the reconstructed error of high-spectral data abundance matrix is calculated：
Wherein, RMSE indicates that the reconstructed error of high-spectral data abundance matrix, P indicate end member sum, N table in alternative end member
Show that pixel sum in high-spectral data, u indicate to calculate rower used when RMSE, the value range of u is { 1,2 ..., P }, t
Indicate to calculate column mark used when RMSE, the value range of t is { 1,2 ..., N }, and ∑ expression takes sum operation, YutIndicate bloom
Modal data abundance matrix u row t column element,Indicate the u row t column element of high-spectral data abundance matrix true value；
(6) output solves mixed result：
Output solves the reconstructed error of the high-spectral data abundance matrix of mixed result.
Compared with prior art, the present invention having the following advantages that：
First, since the present invention utilizes digital spectrum library in end member study, to the current subclass EO-1 hyperion base after study
The end member matrix of data is screened, and the end member matrix closest to digital spectrum library is obtained, and overcoming the different spectrum phenomenon of jljl can lead
It causes practical end member to have a certain difference with end member in standard high-spectral data library, directly utilizes end member in high-spectral data library,
Meeting so that high spectrum image solution mix result precision it is low, the problem of quality reconstruction difference so that the present invention with high spectrum image solution mix
As a result precision is high, the good advantage of quality reconstruction.
Second, since invention introduces the Solution models that end member learns, the prior art is overcome in the height of low signal-to-noise ratio
During spectrum picture solution is mixed, when solving end member matrix and abundance matrix simultaneously using alternative iteration method, high spectrum image solution is mixed
As a result time-consuming, low efficiency, so that there is the present invention high spectrum image solution to mix short, the high-efficient advantage of result time-consuming.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is the waveform diagram for synthesizing 6 kinds of end members used in analogue data；
Fig. 3 is the present invention and NMF technology, L0.5NMF technology, GLNMF technology 25dB noise after adding white Gaussian noise
The comparative result figure of the reconstructed error value of spectral modeling distance value and high-spectral data abundance matrix than under；
Fig. 4 be the present invention with NMF technology, L0.5NMF technology, GLNMF technology after adding white Gaussian noise 15dB,
Spectral modeling distance value and high-spectral data abundance matrix under 20dB, 25dB, 30dB, 35dB, 40dB, 45dB, 100dB signal-to-noise ratio
The comparative result figure of reconstructed error value；
Fig. 5 is the line map that the present invention uses in truthful data emulation；
Fig. 6 is the abundance figure of the present invention obtained 11 kinds of minerals in truthful data emulation.
Specific embodiment
With reference to the accompanying drawing, the present invention is described in further detail.
The step of reference attached drawing 1, the present invention realizes, is described in further detail.
Step 1, high-spectral data is inputted.
Step 2, EO-1 hyperion base data is synthesized：
All end members included in high-spectral data are selected from digital spectrum library, obtain alternative end member.
Predeterminable area is initialized with alternative end member, obtains alternative area.
It is wherein, described that with alternative end member initialization predeterminable area, specific step is as follows：
Step 1 inputs alternative end member.
Step 2, the initial value for setting number of iterations a n, n are set as 1.
Step 3 presets the image-region that a block size is 64 × 64.
Preset image-region is divided equally into 88 × 8 regions, obtains cut zone by step 4.
Step 5 randomly selects d end member from alternative end member, initializes the area not being initialised also in cut zone
Domain, number of iterations n add the value of 1, d to be randomly generated, the end member sum that the maximum value of d is no more than selected.
Step 6, judges whether number of iterations n is greater than 8, if so, obtaining alternative area, otherwise, executes step 5.
Using Di Li Cray method, the Abundances of alternative area are generated.
With the Abundances of generation multiplied by end member corresponding in alternative area, initial base data is obtained.
By low-pass filter, the high frequency signal components in initial base data are filtered out.
The pixel that Abundances are lower than preset threshold 0.8 is chosen from initial base data, obtains alternate pixel point.
Alternate pixel point, each end member pair in the alternate pixel point being initialised are initialized with end members all in alternative end member
The Abundances answered are set as the inverse of alternative end member sum, obtain intermediate base data.
Zero mean Gaussian white noise is added into intermediate base data, obtains the EO-1 hyperion base data of synthesis.
Step 3, end member learns：
(3a) presets the screening matrix that size is L × P and size is the storage matrix of 1 × P, wherein L indicates alternative end member
The wave band number of middle end member, P indicate end member sum in alternative end member, are depositing for 1 × P by screening matrix and size that size is L × P
Element in storage matrix is initialized as complete zero.
(3b) according to the following formula, constructs slickness bound term：
G=| | A | |F
Wherein, G indicates slickness bound term, and A indicates end member matrix to be learned, | | | |FExpression takes the behaviour of F norm
Make.
(3c) according to the following formula, structural segmentation slickness bound term：
Wherein, R indicates piecewise smooth bound term, and ∑ expression takes sum operation, and l indicates rower, and the value range of l is
{ 1,2 ..., L }, L indicate that the wave band number of end member in alternative end member, p indicate column mark, and the value range of p is { 1,2 ..., P }, P
Indicate that end member sum in alternative end member, i indicate AlpThe label of element, e in the Neighbourhood set of left and right(·)It indicates using natural number the bottom of as
Index operation, AlpIndicate l row pth column element in end member matrix to be learned, BiIndicate AlpI-th yuan in the Neighbourhood set of left and right
Element, the value range of i are { 1,2 }, and γ indicates constraint force parameter, and the value range of γ is [0,1]；
(3d) utilizes K averaging method, the EO-1 hyperion base data of synthesis is carried out cluster operation, the EO-1 hyperion base after being clustered
Data.
Wherein, specific step is as follows for K averaging method：
Step 1 inputs the EO-1 hyperion base data of synthesis.
Step 2, randomly selects K pixel from the EO-1 hyperion base data of synthesis, the value range of K be 1,2 ...,
30 }, as initial cluster centre.
Step 3 arbitrarily chooses the pixel not clustered from the EO-1 hyperion base data of synthesis, calculates selected picture
The vegetarian refreshments Euclidean distance with current K cluster centre respectively, finds out the corresponding cluster centre of Euclidean distance minimum value, will be selected
The cluster centre corresponding with Euclidean distance minimum value of pixel out is as same class data.
Step 4 judges whether whole pixels all complete cluster in the EO-1 hyperion base data of synthesis, if so, executing the 5th
Otherwise step executes step 3.
Step 5 calculates the mean value of every a kind of pixel after cluster, and using the mean value of one kind pixel every after cluster as more
Cluster centre after new.
Step 6 calculates separately out the residual error that K cluster centre updates front and back according to the following formula：
Cresi=| | fi-hi||2
Wherein, CresiIndicate that the i-th class cluster centre updates the residual error of front and back, the value range of i is { 1,2 ..., K }, K
It is the pixel number randomly selected, | | | |2Indicate the operation of 2 norm of amount of orientation, fiIndicate the updated cluster centre of the i-th class,
hiIndicate the cluster centre before the i-th class updates.
Step 7 judges that calculated K cluster centre updates whether maximum value in the residual error of front and back is less than preset threshold
0.2, if so, the EO-1 hyperion base data of synthesis is considered as the data not clustered, step 8 is executed, otherwise, by the EO-1 hyperion base of synthesis
Data are considered as the data not clustered, execute step 3.
Step 8 arbitrarily chooses the pixel not clustered from the EO-1 hyperion base data of synthesis, calculates selected picture
The vegetarian refreshments Euclidean distance with current K cluster centre respectively, finds out the corresponding cluster centre of Euclidean distance minimum value, will be selected
The cluster centre corresponding with Euclidean distance minimum value of pixel out is as same class data.
Step 9 judges whether whole pixels all complete cluster in the EO-1 hyperion base data of synthesis, if so, being clustered
Otherwise EO-1 hyperion base data afterwards executes step 8.
(3e) randomly selects a kind of data for not carrying out end member study also, obtains from the EO-1 hyperion base data after cluster
Current subclass EO-1 hyperion base data.
(3f) carries out end member study according to the following formula, to current subclass EO-1 hyperion base data, obtains current subclass EO-1 hyperion base
The end member matrix of data：
Wherein, A(k+1)Indicate that the end member matrix of the current subclass EO-1 hyperion base data of+1 iteration of kth, k are indicated to current
Subclass EO-1 hyperion base data carries out the number of iterations used when end member study, and the value range of k is { 1,2 ..., 100 }, and k's is first
Initial value, which is set as 1, argmin, to be indicated to take the end member when reaching minimum value to the progress end member study of current subclass EO-1 hyperion base data
Matrix manipulation,Expression takes the square operation of F norm, and Z indicates current subclass EO-1 hyperion base data, A(k)Indicate working as kth time
The end member matrix of preceding subclass EO-1 hyperion base data, Y(k)Indicate the abundance square of the current subclass EO-1 hyperion base data of kth time iteration
Battle array, λ1Indicate the parameter of adjusting slickness bound term, λ1Value be set as 0.9, G(k)Indicate the slickness constraint of kth time iteration
, λ2Indicate the parameter of adjusting piecewise smooth bound term, λ2Value be set as 0.1, R(k)Indicate the piecewise smooth of kth time iteration
Property bound term, λ3Indicate balance parameters, λ3Value be set as 1, D and indicate that the abundance matrix of current subclass EO-1 hyperion base data is corresponding
True value；
(3g) utilizes digital spectrum library, screens to the end member matrix of the current subclass EO-1 hyperion base data after study,
Obtain the end member matrix closest to digital spectrum library.
Wherein, using digital spectrum library, the current subclass EO-1 hyperion base data end member matrix after study is screened
Specific step is as follows：
Step 1 inputs the end member matrix of current subclass EO-1 hyperion base data, and the screening matrix and size that size is L × P are
The storage matrix of 1 × P, L indicate that the wave band number of end member in alternative end member, P indicate end member sum in alternative end member.
Step 2, the value range that the initial value for setting number of iterations a n, n is 1, n are { 1,2 ..., P }, and P indicates alternative
End member sum in end member.
Step 3, using following formula, the end member matrix for calculating current subclass EO-1 hyperion base data is corresponding with digital spectrum library
Spectral modeling distance between true value：
Wherein, d indicate the end member matrix of current subclass EO-1 hyperion base data and corresponding true value in digital spectrum library it
Between spectral modeling distance, arccos () indicate anticosine operation, T indicate transposition operation, mnIndicate current subclass EO-1 hyperion base
N-th of end member in the end member matrix of data, anIt indicates to correspond to m in digital spectrum librarynTrue value, | | | |2Indicate amount of orientation 2
Norm operation, n indicate current iteration number.
Step 4, judge the end member matrix of current subclass EO-1 hyperion base data and corresponding true value in digital spectrum library it
Between spectral modeling distance whether meet any one in replacement condition, if so, executing step 5, otherwise, execute step 7.
The replacement condition is as follows：
Replacement condition 1：The end member matrix of current subclass EO-1 hyperion base data and corresponding true value in digital spectrum library it
Between spectral modeling distance be 0.
Replacement condition 2：The end member matrix of current subclass EO-1 hyperion base data and corresponding true value in digital spectrum library it
Between spectral modeling distance be less than storage matrix in correspond to the value that current iteration numerical digit sets element.
Step 5, will be between the end member matrix of current subclass EO-1 hyperion base data and corresponding true value in digital spectrum library
Spectral modeling distance, be stored in storage matrix on position corresponding with current iteration number.
Step 6 will correspond to the end member of current iteration number, be stored in sieve in the end member matrix of current subclass EO-1 hyperion base data
It selects in matrix on position corresponding with current iteration number.
Step 7, judges whether current iteration number n is equal to end member sum in alternative end member, if so, obtaining closest to digital light
The end member matrix and currently stored matrix in library are composed, otherwise, the value of current iteration number n is added 1, executes step 3.
(3h) judges that the whether every class of EO-1 hyperion base data after cluster has all carried out end member study, if so, after obtaining study
End member matrix and currently stored matrix, otherwise, execute step (3e).
Step 4, according to the following formula, the canonical Weighted Constraint item of high-spectral data abundance matrix is constructed：
Wherein, Q indicates that the canonical Weighted Constraint item of high-spectral data abundance matrix, ∑ indicate sum operation, and i indicates bloom
The number of modal data abundance matrix midrange, the value range of i are { 1,2 ..., N }, and j is indicated in high-spectral data abundance matrix
The number of columns, the value range of j are { 1,2 ..., N }, and N indicates pixel sum in high-spectral data,Indicate amount of orientation
The square operation of 2 norms, yiIndicate the i-th column, y in high-spectral data abundance matrixjIndicate jth in high-spectral data abundance matrix
Column, e(·)It indicates using natural number as the index operation at bottom, ρ indicates constraint force parameter, and the value range of ρ is [0,1]；
According to the following formula, the degree of rarefication of high-spectral data abundance matrix is calculated：
Wherein, α2Indicate the degree of rarefication of high-spectral data abundance matrix,Expression takes radical sign to operate, and L indicates alternative end member
The wave band number of middle end member, ∑ expression take sum operation, and l indicates the number of high-spectral data line number, the value range of l be 1,
2 ..., L }, N indicates pixel sum, x in high-spectral datalIndicate l row in high-spectral data, | | | |1Indicate amount of orientation
The operation of 1 norm, | | | |2Indicate the operation of 2 norm of amount of orientation；
According to the following formula, high-spectral data abundance matrix is calculated：
Wherein, Y(k+1)Indicate the high-spectral data abundance matrix of+1 iteration of kth, k indicates to calculate high-spectral data abundance
The number of iterations when matrix, the value range of k are { 1,2 ..., 100 }, and argmin expression takes when calculating high-spectral data abundance
Matrix reaches abundance matrix operation when minimum value,Expression takes the square operation of F norm, and X indicates high-spectral data, A table
End member matrix after dendrography habit, Y(k)Indicate the high-spectral data abundance matrix of kth time, α1It indicates to adjust the weighting of abundance canonical about
The parameter of beam item, α1Value be set as 1, Q(k)Indicate the canonical Weighted Constraint of the high-spectral data abundance matrix of kth time iteration
, | | | |2,1Expression takes the sum operation of each 2 norm of column vector in abundance matrix, α2Indicate high-spectral data abundance square
The degree of rarefication of battle array.
Step 5, according to the following formula, the reconstructed error of high-spectral data abundance matrix is calculated：
Wherein, RMSE indicates that the reconstructed error of high-spectral data abundance matrix, P indicate end member sum, N table in alternative end member
Show that pixel sum in high-spectral data, u indicate to calculate rower used when RMSE, the value range of u is { 1,2 ..., P }, t
Indicate to calculate column mark used when RMSE, the value range of t is { 1,2 ..., N }, and ∑ expression takes sum operation, YutIndicate bloom
Modal data abundance matrix u row t column element,Indicate the u row t column element of high-spectral data abundance matrix true value；
Step 6, output solves mixed result：
Output solves the reconstructed error of the high-spectral data abundance matrix of mixed result.
Effect of the invention is described further below with reference to emulation experiment.
1. simulated conditions
It is Inter (R) Core (TM) 2Duo T6600 2.20GHZ, carried out in 7 system of memory 2G, WINDOWS in CPU
Emulation.
2. analogue data emulates
The synthetic method of analogue data is identical as EO-1 hyperion base data method is synthesized in step 2, and (Fig. 2 is synthesis simulation number
According to the waveform diagram of 6 kinds of used end members), which contains 64 × 64 pixels, 224 wave bands, wave-length coverage
It is 0.4 to 2.5 microns.The performance that (referred to as LENMF) end member study of the invention is assessed using spectral modeling range formula, by spectrum
Angular distance formula calculating resulting value is lower, illustrates that end member and the pure substance spectra degree of correspondence in standard database are higher.Using
The performance of the acquired abundance of the reconstructed error formula assessment present invention, it is lower by reconstructed error formula calculating resulting value, illustrate bloom
Precision is higher, and it is better that sparse solution mixes effect as sparse solution mixes for spectrogram.
Fig. 3 is the present invention and NMF technology, L0.5NMF technology, GLNMF technology 25dB noise after adding white Gaussian noise
The fluctuation comparative result figure of the reconstructed error value of spectral modeling distance value and high-spectral data abundance matrix than under.From experimental result
In, it can be seen that：NMF technology the result is that worst, and fluctuation is also the largest, this, which lacks bound term with objective function, is
Related, this point can pass through the experiment show of three kinds of technologies below；The result and GLNMF technology of L0.5NMF technology
Result it is similar, fluctuate also small many；And by acquired results of the present invention, regardless of going back from the point of view of spectral modeling distance value
It is from the point of view of the reconstructed error value of high-spectral data abundance matrix, experimental result is all best, and the fluctuation of result
It is also the smallest.Thus it embodies the present invention and solves the advantage that mixed precision is high, quality reconstruction is good.
Fig. 4 be the present invention with NMF technology, L0.5NMF technology, GLNMF technology after adding white Gaussian noise 15dB,
Spectral modeling distance value and high-spectral data abundance matrix under 20dB, 25dB, 30dB, 35dB, 40dB, 45dB, 100dB signal-to-noise ratio
The linear comparative result figure of reconstructed error value；From experimental result, it can be seen that：It is of the invention compared to other three kinds of technologies
The result is that it is best, there is preferable robustness.When signal-to-noise ratio increases to 25dB from 15dB, four kinds of algorithms, which have, significantly to be changed
Become, but results change of the invention is comparatively a little bit smaller, the result of four kinds of algorithms all tends to flat later, this is because making an uproar
The reason of sound reduction.Thus it embodies solution of the present invention and mixes high-efficient advantage.
3. truthful data emulates
Fig. 5 gives the line map that the present invention uses in truthful data emulation；It is by airborne visual light imaging spectrum
The cuprite that instrument (AVIRIS) was photographed in Nevada ,Usa downstate.The size of image is 250 × 191, wherein containing in 11
Different minerals, they are respectively：Alunite, andradite, water ammonium feldspar, dumortierite, kaolinite 1, kaolinite 2 cover de-
Stone, muscovite, nontronite, pyrope and aspidelite.Cuprite data contain 224 wave bands, and wavelength is micro- from 0.4 micron to 2.5
Meter, in order to preferably utilize the data in experiment, we will remove low signal-to-noise ratio and water vapor absorption wave band, finally be left 188
A wave band.
1 spectral modeling distance value of table
Table 1 gives four kinds of technologies in truthful data emulation, calculate the spectral modeling distance value of resulting 11 minerals with
And their average value.As it can be seen from table 1 the end member that the present invention learns is corresponding with the pure substance spectra in standard database
Degree highest.Fig. 6 is the abundance figure of the present invention obtained 11 kinds of minerals in truthful data emulation.
Claims (4)
1. a kind of high spectrum image sparse solution mixing method based on end member study, includes the following steps：
(1) high-spectral data is inputted；
(2) EO-1 hyperion base data is synthesized：
(2a) selects all end members included in high-spectral data from digital spectrum library, obtains alternative end member；
(2b) initializes predeterminable area with alternative end member, obtains alternative area；
(2c) utilizes Di Li Cray method, generates the Abundances of alternative area；
(2d), multiplied by end member corresponding in alternative area, obtains initial base data with the Abundances generated；
(2e) filters out the high frequency signal components in initial base data by low-pass filter；
(2f) chooses the pixel that Abundances are lower than preset threshold 0.8 from initial base data, obtains alternate pixel point；
(2g) initializes alternate pixel point, each end member pair in the alternate pixel point being initialised with end members all in alternative end member
The Abundances answered are set as the inverse of alternative end member sum, obtain intermediate base data；
Zero mean Gaussian white noise is added into intermediate base data in (2h), obtains the EO-1 hyperion base data of synthesis；
(3) end member learns：
(3a) presets the screening matrix that size is L × P and size is the storage matrix of 1 × P, wherein L indicates alternative end member middle-end
The wave band number of member, P indicate end member sum in alternative end member, the storage square for being 1 × P by screening matrix and size that size is L × P
Element in battle array is initialized as complete zero；
(3b) according to the following formula, constructs slickness bound term：
G=| | A | |F
Wherein, G indicates slickness bound term, and A indicates end member matrix to be learned, | | | |FExpression takes the operation of F norm；
(3c) according to the following formula, structural segmentation slickness bound term：
Wherein, R indicates piecewise smooth bound term, and Σ expression takes sum operation, and l indicates rower, the value range of l be 1,
2 ..., L }, L indicates that the wave band number of end member in alternative end member, p indicate column mark, and the value range of p is { 1,2 ..., P }, and P is indicated
End member sum, i indicate A in alternative end memberlpThe label of element, e in the Neighbourhood set of left and right(·)It indicates using natural number as the index at bottom
Operation, AlpIndicate l row pth column element in end member matrix to be learned, BiIndicate AlpI-th of element, i in the Neighbourhood set of left and right
Value range be { 1,2 }, γ indicates constraint force parameter, and the value range of γ is [0,1]；
(3d) utilizes K averaging method, the EO-1 hyperion base data of synthesis is carried out cluster operation, the EO-1 hyperion radix after being clustered
According to；
(3e) randomly selects a kind of data for not carrying out end member study also from the EO-1 hyperion base data after cluster, obtains current
Subclass EO-1 hyperion base data；
(3f) carries out end member study according to the following formula, to current subclass EO-1 hyperion base data, obtains current subclass EO-1 hyperion base data
End member matrix：
Wherein, A(k+1)Indicate that the end member matrix of the current subclass EO-1 hyperion base data of+1 iteration of kth, k are indicated to current subclass
EO-1 hyperion base data carries out the number of iterations used when end member study, and the value range of k is { 1,2 ..., 100 }, the initial value of k
Being set as 1, argmin indicates to take the end member matrix when reaching minimum value to the progress end member study of current subclass EO-1 hyperion base data
Operation,Expression takes the square operation of F norm, and Z indicates current subclass EO-1 hyperion base data, A(k)Indicate the current son of kth time
The end member matrix of class EO-1 hyperion base data, Y(k)Indicate the abundance matrix of the current subclass EO-1 hyperion base data of kth time iteration, λ1
Indicate the parameter of adjusting slickness bound term, λ1Value be set as 0.9, G(k)Indicate the slickness bound term of kth time iteration, λ2Table
Show the parameter for adjusting piecewise smooth bound term, λ2Value be set as 0.1, R(k)Indicate the piecewise smooth constraint of kth time iteration
, λ3Indicate balance parameters, λ3Value be set as 1, D and indicate that the abundance matrix of current subclass EO-1 hyperion base data is corresponding true
Value；
(3g) utilizes digital spectrum library, screens, obtains to the end member matrix of the current subclass EO-1 hyperion base data after study
Closest to the end member matrix in digital spectrum library；
(3h) judges that the whether every class of EO-1 hyperion base data after cluster has all carried out end member study, if so, the end after being learnt
Otherwise variable matrix and currently stored matrix execute step (3e)；
(4) high-spectral data abundance matrix is solved：
(4a) according to the following formula, constructs the canonical Weighted Constraint item of high-spectral data abundance matrix：
Wherein, Q indicates that the canonical Weighted Constraint item of high-spectral data abundance matrix, Σ indicate sum operation, and i indicates EO-1 hyperion number
According to the number of abundance matrix midrange, the value range of i is { 1,2 ..., N }, and j indicates high-spectral data abundance matrix midrange
Number, the value range of j is { 1,2 ..., N }, and N indicates pixel sum in high-spectral data,Indicate 2 model of amount of orientation
Several square operations, yiIndicate the i-th column, y in high-spectral data abundance matrixjIndicate jth column, e in high-spectral data abundance matrix(·)It indicates using natural number as the index operation at bottom, ρ indicates constraint force parameter, and the value range of ρ is [0,1]；
(4b) according to the following formula, calculates the degree of rarefication of high-spectral data abundance matrix：
Wherein, α2Indicate the degree of rarefication of high-spectral data abundance matrix,Expression takes radical sign to operate, and L indicates alternative end member middle-end
The wave band number of member, Σ expression take sum operation, and l indicates the number of high-spectral data line number, the value range of l be 1,2 ...,
L }, N indicates pixel sum, x in high-spectral datalIndicate l row in high-spectral data, | | | |1Indicate 1 norm of amount of orientation
Operation, | | | |2Indicate the operation of 2 norm of amount of orientation；
(4c) according to the following formula, calculates high-spectral data abundance matrix：
Wherein, Y(k+1)Indicate the high-spectral data abundance matrix of+1 iteration of kth, k indicates to calculate high-spectral data abundance matrix
When the number of iterations, the value range of k is { 1,2 ..., 100 }, and argmin expression takes when calculating high-spectral data abundance matrix
Reach abundance matrix operation when minimum value,Expression takes the square operation of F norm, and X indicates that high-spectral data, A indicate to learn
End member matrix after habit, Y(k)Indicate the high-spectral data abundance matrix of kth time, α1Indicate that the canonical for adjusting abundance matrix weights
The parameter of bound term, α1Value be set as 1, Q(k)Indicate the canonical Weighted Constraint of the high-spectral data abundance matrix of kth time iteration
, | | | |2,1Expression takes the sum operation of each 2 norm of column vector in abundance matrix, α2Indicate high-spectral data abundance square
The degree of rarefication of battle array；
(5) according to the following formula, the reconstructed error of high-spectral data abundance matrix is calculated：
Wherein, RMSE indicates that the reconstructed error of high-spectral data abundance matrix, P indicate that end member sum in alternative end member, N indicate high
Pixel sum in spectroscopic data, u indicate to calculate rower used when RMSE, and the value range of u is { 1,2 ..., P }, and t is indicated
Column mark used when RMSE is calculated, the value range of t is { 1,2 ..., N }, and Σ expression takes sum operation, YutIndicate EO-1 hyperion number
According to abundance matrix u row t column element,Indicate the u row t column element of high-spectral data abundance matrix true value；
(6) output solves mixed result：
Output solves the reconstructed error of the high-spectral data abundance matrix of mixed result.
2. the high spectrum image sparse solution mixing method according to claim 1 based on end member study, it is characterised in that：Step
(2b) is described, and with alternative end member initialization predeterminable area, specific step is as follows：
Step 1 inputs alternative end member；
Step 2, the initial value for setting number of iterations a n, n are set as 1；
Step 3 presets the image-region that a block size is 64 × 64；
Preset image-region is divided equally into 88 × 8 same areas, obtains cut zone by step 4；
Step 5 randomly selects d end member from alternative end member, initializes the region not being initialised also in cut zone, repeatedly
Algebra n adds the value of 1, d to be randomly generated, the end member sum that the maximum value of d is no more than selected；
Step 6, judges whether number of iterations n is greater than 8, if so, obtaining alternative area, otherwise, executes step 5.
3. the high spectrum image sparse solution mixing method according to claim 1 based on end member study, it is characterised in that：Step
Specific step is as follows for K averaging method described in (3d)：
Step 1 inputs the EO-1 hyperion base data of synthesis；
Step 2 randomly selects K pixel from the EO-1 hyperion base data of synthesis, and the value range of K is { 1,2 ..., 30 },
As initial cluster centre；
Step 3 arbitrarily chooses the pixel not clustered from the EO-1 hyperion base data of synthesis, calculates selected pixel
Respectively with the Euclidean distance of current K cluster centre, the corresponding cluster centre of Euclidean distance minimum value is found out, by selected taking-up
Pixel cluster centre corresponding with Euclidean distance minimum value is as same class data；
Step 4 judges whether whole pixels all complete cluster in the EO-1 hyperion base data of synthesis, if so, step 5 is executed, it is no
Then, step 3 is executed；
Step 5, calculates the mean value of every a kind of pixel after cluster, and using the mean value of one kind pixel every after cluster as update after
Cluster centre；
Step 6 calculates separately out the residual error that K cluster centre updates front and back according to the following formula：
Cresi=| | fi-hi||2
Wherein, CresiIndicate that the i-th class cluster centre updates the residual error of front and back, the value range of i is { 1,2 ..., K }, and K is random
The pixel number of selection, | | | |2Indicate the operation of 2 norm of amount of orientation, fiIndicate the updated cluster centre of the i-th class, hiIt indicates
Cluster centre before the update of i-th class；
Step 7 judges that calculated K cluster centre updates whether maximum value in the residual error of front and back is less than preset threshold 0.2, if
It is that the EO-1 hyperion base data of synthesis is considered as the data not clustered, executes step 8, otherwise, the EO-1 hyperion base data of synthesis is regarded
For the data not clustered, step 3 is executed；
Step 8 arbitrarily chooses the pixel not clustered from the EO-1 hyperion base data of synthesis, calculates selected pixel
Respectively with the Euclidean distance of current K cluster centre, the corresponding cluster centre of Euclidean distance minimum value is found out, by selected taking-up
Pixel cluster centre corresponding with Euclidean distance minimum value is as same class data；
Step 9 judges whether whole pixels all complete cluster in the EO-1 hyperion base data of synthesis, if so, after being clustered
Otherwise EO-1 hyperion base data executes step 8.
4. the high spectrum image sparse solution mixing method according to claim 1 based on end member study, it is characterised in that：Step
(3g) is described to utilize digital spectrum library, the specific step screened to the current subclass EO-1 hyperion base data end member matrix after study
It is rapid as follows：
Step 1 inputs the end member matrix of current subclass EO-1 hyperion base data, and the screening matrix and size that size is L × P are 1 × P
Storage matrix, L indicates the wave band number of end member in alternative end member, and P indicates end member sum in alternative end member；
Step 2, the value range that the initial value for setting number of iterations a n, n is 1, n are { 1,2 ..., P }, and P indicates alternative end member
Middle end member sum；
Step 3, using following formula, the end member matrix for calculating current subclass EO-1 hyperion base data is corresponding with digital spectrum library true
Spectral modeling distance between value：
Wherein, d is indicated between the end member matrix of current subclass EO-1 hyperion base data and corresponding true value in digital spectrum library
Spectral modeling distance, arccos () indicate anticosine operation, and T indicates transposition operation, mnIndicate current subclass EO-1 hyperion base data
End member matrix in n-th of end member, anIt indicates to correspond to m in digital spectrum librarynTrue value, | | | |2Indicate 2 norm of amount of orientation
Operation, n indicate current iteration number；
Step 4 judges between the end member matrix of current subclass EO-1 hyperion base data and corresponding true value in digital spectrum library
Whether spectral modeling distance meets any one in replacement condition, if so, executing step 5, otherwise, executes step 7；
The replacement condition is as follows：
Replacement condition 1：Between the end member matrix and corresponding true value in digital spectrum library of current subclass EO-1 hyperion base data
Spectral modeling distance is 0；
Replacement condition 2：Between the end member matrix and corresponding true value in digital spectrum library of current subclass EO-1 hyperion base data
Spectral modeling distance, which is less than in storage matrix, corresponds to the value that current iteration numerical digit sets element；
Step 5, by the light between the end member matrix of current subclass EO-1 hyperion base data and corresponding true value in digital spectrum library
Spectral corner distance is stored in storage matrix on position corresponding with current iteration number；
Step 6 will correspond to the end member of current iteration number, be stored in screening square in the end member matrix of current subclass EO-1 hyperion base data
In battle array on position corresponding with current iteration number；
Step 7, judges whether current iteration number n is equal to end member sum in alternative end member, if so, obtaining closest to digital spectrum library
End member matrix and currently stored matrix otherwise the value of current iteration number n is added 1, executes step 3.
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| CN105976357B (en) * | 2016-04-26 | 2019-05-03 | 中国科学院遥感与数字地球研究所 | A kind of high optical spectrum image end member extraction method and system |
| CN106788714B (en) * | 2016-12-05 | 2019-01-18 | 重庆工商大学 | A kind of sparse solution mixing method based on optical computing |
| CN107368788A (en) * | 2017-06-19 | 2017-11-21 | 太仓埃特奥数据科技有限公司 | A kind of high spectrum image biological information extracting method based on background self study |
| CN108073895B (en) * | 2017-11-22 | 2021-12-14 | 杭州电子科技大学 | Hyperspectral target detection method based on unmixing pretreatment |
| CN108280486B (en) * | 2018-02-02 | 2020-06-23 | 北京航空航天大学 | Hyperspectral image unmixing method based on end member cluster |
| CN109389106B (en) * | 2018-12-20 | 2021-06-08 | 中国地质大学（武汉） | Hyperspectral image unmixing method and system based on 3D convolutional neural network |
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| CN111581879A (en) * | 2020-04-30 | 2020-08-25 | 北京航空航天大学 | Method and system for determining nonlinear abundance of mixed pixels of space artificial target |
| CN112036235A (en) * | 2020-07-17 | 2020-12-04 | 中国科学院空天信息创新研究院 | Hyperspectral image target detection method and system |
| CN112396029B (en) * | 2020-12-03 | 2022-02-18 | 宁波大学 | Clustering segmentation and coupling end member extraction synergistic hyperspectral coastal wetland subpixel change detection method |
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