CN113094645A - Hyperspectral data unmixing method based on morphological component constraint optimization - Google Patents

Hyperspectral data unmixing method based on morphological component constraint optimization Download PDF

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CN113094645A
CN113094645A CN202110267926.7A CN202110267926A CN113094645A CN 113094645 A CN113094645 A CN 113094645A CN 202110267926 A CN202110267926 A CN 202110267926A CN 113094645 A CN113094645 A CN 113094645A
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汪顺清
肖亮
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Nanjing University of Science and Technology
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Abstract

The invention discloses a morphological component constraint optimization hyperspectral data unmixing method, which mainly utilizes a batch of hyperspectral data and a pure substance spectrum library to construct a spectrum sample expansion matrix; by estimating the band noise standard deviation and the sparsity structure noise decomposition, use l1Norm to constrain the sparse noise,/2,0The norm constrains the global row sparsity of abundance coefficients of different pure substances; and establishing a morphological component constraint optimized hyperspectral data unmixing model, and alternately iterating to realize linear unmixing of the mixed spectrum. The invention comprehensively considers Gaussian random noise and sparsityThe structural noise influences the linear unmixing precision, the mixed noise is robust, the waveform morphological structure difference between the same batch of spectral data can be effectively overcome, the rapid and high-precision unmixing is realized through optimization iteration, and the root mean square error of the unmixing is less than 0.0025; the method has wide application prospect for rock mineral identification, hyperspectral remote sensing ground object fine identification and the like.

Description

Hyperspectral data unmixing method based on morphological component constraint optimization
Technical Field
The invention belongs to the technical field of hyperspectral remote sensing image processing, and particularly relates to a hyperspectral data unmixing method based on morphological component constraint optimization.
Background
The remote sensing technology is a technology for acquiring electromagnetic signals reflected by ground objects from a long-distance space (aerospace) or an outer space (aviation) through an optical sensor, acquiring required target information and analyzing and processing data. Since the 80 s in the 20 th century, with the gradual improvement of spectral resolution of optical sensors, hyperspectral remote sensing has gradually become a research hotspot in the field. The hyperspectral remote sensing refers to an optical remote sensing technology which utilizes a sensor to obtain electromagnetic wave signals reflected by the surface of a substance and has spectral resolution of 10nm from visible light to near-infrared wave bands. Due to the limitation of the spatial resolution of the sensor and the complex diversity of the earth surface, one pixel often comprises various ground objects, the pixel is called a mixed pixel, and the development and application of the hyperspectral remote sensing are restricted by the mixed pixel widely existing in the hyperspectral data, so that how to decompose the mixed pixel becomes an important research topic in the field of the hyperspectral remote sensing. The hyperspectral unmixing or mixed pixel decomposition is a method for decomposing a mixed pixel into a pure substance (called an end member) and a corresponding component proportion (called an abundance coefficient), and is widely applied to the fields of ground surface classification, precise agriculture, mineral exploration and the like at present.
At present, hyperspectral unmixing models can be mainly divided into linear mixing models and nonlinear mixing models. The nonlinear mixed model considers the multiple scattering effect between the end members, the linear mixed model ignores the influence of the multiple scattering effect, and the mixed pixel spectrum is considered to be linear mixing of the end member spectrum, so the structure is simple, the physical meaning is clear, and the application is the most extensive.
According to whether a spectral library needs to be provided in the unmixing process, the existing hyperspectral data unmixing algorithm can be divided into a blind source unmixing algorithm and a semi-blind source unmixing algorithm. The blind source unmixing algorithm needs to extract end members from the current hyperspectral data, and then perform abundance inversion to obtain abundance coefficients. And the semi-blind source unmixing algorithm uses a spectrum library consisting of a large number of pure end member spectrums as an end member dictionary, then selects a proper end member from the end member dictionary, and calculates a corresponding abundance coefficient. Because the number of end members in the spectral library is far greater than that of end members contained in the hyperspectral data, the abundance coefficient shows sparsity,thus, such algorithms typically add sparsity constraints to the abundance coefficients, e.g., Iordache M et al, considering that mixed pixels in the local neighborhood are generally composed of the same terrain, apply l to the abundance coefficients2,1Norm constraint, and finally solving the model by using a Lagrange method and an alternative direction multiplier method [ Iordache M D, Bioucas-Dias J M, plant A. Collaborative space regression for hyperspectral unmixing [ J].IEEE Transactions on Geoscience and Remote Sensing,2013,52(1):341-354.](ii) a Use of l by Rui Wang et al1On the basis of norm constraint abundance coefficients, double weighting is provided in spectral and spatial dimensions, and sparsity [ Wang R, Li H C, Liao W, et al]//2016 IEEE International Geoscience and Remote Sensing Symposium(IGARSS).IEEE,2016:6986-6989.]. However, due to the influence of factors such as mechanical failure of the sensor, the hyperspectral data is inevitably polluted by various noises such as gaussian noise, impulse noise, stripe noise and the like in the acquisition and transmission processes, the methods default that the intensities of the gaussian noise of different wave bands of the hyperspectral data are the same, and the existence of sparse noise such as impulse noise and the like is also ignored, which is not always in accordance with the actual situation, and l1The norm does not express the structural sparsity of the abundance coefficient well, so that the unmixing algorithm cannot achieve higher precision.
Disclosure of Invention
The invention aims to provide a hyperspectral data unmixing method for morphological component constraint optimization with noise robustness and strong sparsity aiming at the hyperspectral unmixing problems of mineral exploration, accurate agriculture, environmental monitoring and disaster assessment.
The technical solution for realizing the purpose of the invention is as follows: a hyperspectral data unmixing method based on morphological component constraint optimization comprises the following steps:
step 1, inputting hyperspectral data and an end member spectrum library;
step 2, constructing a spectrum sample expansion matrix;
step 3, establishing a shape and composition constraint optimized hyperspectralA data unmixing model; based on the assumption that the Gaussian noise of different wave bands of the hyperspectral data has different intensities and other sparse noise, the method uses l by estimating the standard deviation of the wave band noise and the noise decomposition of a sparse structure1Norm-constrained sparse noise,/2,0The norm constrains the global row sparsity of different pure substance abundance coefficients, and a morphological component constraint optimization hyperspectral data unmixing model is established;
step 4, calculating the noise standard deviation of each wave band of the hyperspectral data: firstly, calculating a noise correlation matrix, then calculating a regression vector band by band, estimating noise, and finally calculating the standard deviation of the noise;
and 5, alternately and iteratively solving: converting the model into an equivalent augmented Lagrange form, performing alternate iteration on each variable according to an alternate direction multiplier method to solve an optimization problem, and respectively using a soft threshold limiting operator and a hard threshold operator to solve the subproblem;
and 6, outputting the abundance coefficient.
Compared with the prior art, the invention has the following remarkable advantages: (1) comprehensively considering the influence of Gaussian random noise and sparse structure noise on linear unmixing precision, and using l1Norm-constrained sparse noise,/2,0The norm constrains the global row sparsity of different pure substance abundance coefficients, and a morphological component constraint optimization hyperspectral data unmixing model is established; (2) solving for l by line-hard threshold method2,0The norm problem further describes the sparsity of the abundance coefficient to obtain a more accurate solution; (3) simulation experiment results show that the method has good robustness on mixed noise, can effectively overcome waveform morphological structure difference between the same batch of spectral data, realizes quick and high-precision unmixing through optimization iteration, and has wide application prospect on rock mineral identification, hyperspectral remote sensing ground object fine identification and the like, wherein the root mean square error of the unmixing is less than 0.0025.
Drawings
FIG. 1 is a flow chart of a morphological component constraint optimization hyperspectral data unmixing method of the invention.
Fig. 2(a) is a true abundance map generated to simulate hyperspectral data.
Fig. 2(b) is an abundance map obtained by simulating hyperspectral data using the SUnSAL algorithm.
Fig. 2(c) is an abundance map obtained by simulating hyperspectral data using the CLSUnSAL algorithm.
Fig. 2(d) is an abundance map obtained by simulating hyperspectral data using the csun l0 algorithm.
FIG. 2(e) is an abundance map obtained by simulating hyperspectral data by using the hyperspectral data unmixing method of morphological component constraint optimization of the invention.
FIG. 3(a) is raw single bar of simulated hyperspectral data.
Fig. 3(b) is a single piece of hyperspectral data contaminated by sparse noise such as gaussian noise and impulse noise.
Fig. 3(c) is the reconstruction result of a single piece of hyperspectral data by different unmixing algorithms.
Figure 4 is a distribution plot of the three minerals on the Cuprite dataset and the corresponding abundance plots obtained using different unmixing algorithms.
Detailed Description
The invention discloses a hyperspectral data unmixing method based on morphological component constraint optimization, which is characterized in that an unmixing model is established by estimating the standard deviation of waveband noise and the noise decomposition of a sparse structure, adding sparsity constraints to sparse components and abundance coefficients, and alternately iterating to realize linear unmixing of a mixed spectrum, as shown in figure 1, the method comprises the following specific steps:
step 1, inputting hyperspectral data and an end member spectrum library. Inputting a batch of hyperspectral data to be unmixed
Figure BDA0002972995420000031
yi∈RBAnd end-member spectral library E epsilon RB×MB is the number of bands, P is the number of pixels, and M is the number of end-members.
And 2, constructing a spectrum sample expansion matrix. Arranging input hyperspectral data according to pixel-by-pixel spectral vectors to form a spectrum-pixel matrix Y ═ Y1,y2,...,yN]∈RB×P。
And 3, establishing a morphological component constraint optimized hyperspectral data unmixing model. Based on the assumption that the intensity of Gaussian noise of different wave bands of the hyperspectral data is different and other sparse noise exists, a hyperspectral data unmixing model is established:
Y＝EA+S+N
wherein A ∈ RM×PThe element in each column represents the proportion of the corresponding end member spectrum in a single mixed pixel; s is belonged to RB×PThe sparse component represents mixed noise such as pulse noise, stripe noise and the like which only pollute a few wave bands of the hyperspectral data; n is an element of RB×PIs gaussian noise. Introducing sparse constraint to obtain an optimized solving function of the model:
Figure BDA0002972995420000041
s.t.A≥0
where λ and α are regularization parameters, λ>0，α>0; w is a diagonal matrix and W is a diagonal matrix,
Figure BDA0002972995420000042
Figure BDA0002972995420000043
the element on the opposite angle is the reciprocal of the standard deviation of Gaussian noise of each wave band; II-FAn F norm representing a matrix;
Figure BDA0002972995420000044
l representing a matrix2,0A norm;
Figure BDA0002972995420000045
l representing a matrix1And (4) norm. The above formula is converted into:
Figure BDA0002972995420000046
wherein, V1,V2,V3As an auxiliary variable, D1,D2,D3Is Lagrange multiplier, mu>0 is punishmentThe penalty factor is a function of the number of bits,
Figure BDA0002972995420000047
Xi,jelements representing the ith row and jth column of the matrix X when X isi,jIn the case of a non-negative value,
Figure BDA0002972995420000048
equal to 0, otherwise equal to positive infinity;
and 4, calculating the noise standard deviation of each wave band of the hyperspectral data to obtain a diagonal matrix W. The method comprises the following steps:
step 4.1, calculating regression vector
Figure BDA0002972995420000049
Figure BDA00029729954200000410
Wherein the content of the first and second substances,
Figure BDA00029729954200000411
representation matrix
Figure BDA00029729954200000412
Z ═ Y in the ith row ofT，
Figure BDA00029729954200000413
A correlation matrix is represented that represents the correlation matrix,
Figure BDA00029729954200000414
Figure BDA00029729954200000415
representing slave matrices
Figure BDA00029729954200000416
In deletion of
Figure BDA00029729954200000417
And row and column
Figure BDA00029729954200000418
The matrix obtained after the columns is formed,
Figure BDA00029729954200000419
representation matrix
Figure BDA00029729954200000420
The number of the ith row of (a),
Figure BDA00029729954200000421
i＝1,…,L；
step 4.2, calculating noise vector
Figure BDA00029729954200000422
Figure BDA0002972995420000051
Wherein the content of the first and second substances,
Figure BDA0002972995420000052
representing estimated noise
Figure BDA0002972995420000053
Row i of (1), ziThe ith row of the matrix Z is represented,
Figure BDA0002972995420000054
indicating deletion of the first from the matrix Z
Figure BDA00029729954200000515
A matrix obtained after the column;
step 4.3, calculating the reciprocal W of the standard deviation of the Gaussian noise of each wave bandiiObtaining a matrix W:
Figure BDA0002972995420000056
wherein beta represents
Figure BDA0002972995420000057
P represents the number of spectral samples.
And 5, alternately and iteratively solving. The method comprises the following steps:
step 5.1, fixing other variables, updating the abundance coefficient A,
Figure BDA0002972995420000058
step 5.2, fixing other variables, updating the sparse component S,
Figure BDA0002972995420000059
wherein S isτ(. is a soft threshold qualifier, and Sτ(x) Sgn (x) max (| x | - τ,0), where τ is a non-negative parameter, sgn (·) denotes a sign function;
step 5.3, fixing other variables and updating the auxiliary variable V1,V2,V3，
Figure BDA00029729954200000510
Figure BDA00029729954200000511
Figure BDA00029729954200000512
Wherein the content of the first and second substances,
Figure BDA00029729954200000513
represents a line hard threshold operator, an
Figure BDA00029729954200000514
Where τ is a non-negative parameter and B (i,: represents a matrixRow i of B;
step 5.4, fixing other variables and updating the Lagrange multiplier D1,D2,D3，
Figure BDA0002972995420000061
And 6, outputting the abundance coefficient A.
The effect of the invention can be further illustrated by the following simulation experiment:
simulation conditions
The simulation experiment used simulated hyperspectral data and real hyperspectral data (Cuprite dataset). The spectral library is from a geological spectral database released by the United States Geological Survey (USGS) and comprises 224 wave bands and 240 pure material end members. For simulating hyperspectral data, each waveband comprises 3136 pixels, and in order to better simulate the actual situation, all the wavebands are polluted by Gaussian noise with different intensities (the signal-to-noise ratio is between 20dB and 40 dB), 11 wavebands (60-70) are polluted by 30% of impulse noise, and 11 wavebands (120-130) are polluted by stripe noise, namely the input hyperspectral data is Y ═ Y1,y2,...,y3136]∈R224×3136The spectral library is E ∈ R224×240. The real hyperspectral data is derived from an AVIRIS (airborne visible infrared imaging spectrometer) Cuprite data set, 36 water vapor absorption and low signal-to-noise ratio wave bands are removed (the wave bands are 1-2, 105-115, 150-170, 223-224), the remaining 188 wave bands are selected as research objects, correspondingly, the wave bands corresponding to the input spectrum library are also removed, namely the input hyperspectral data is Y ═ Y-1,y2,...,y47750]∈R188×47750The spectral library is E ∈ R188 ×240。
The evaluation index adopted by the simulation experiment is Root Mean Square Error (RMSE), and the smaller the Root Mean Square Error is, the higher the unmixing precision is.
Emulated content
The invention adopts a test algorithm simulating hyperspectral data and real hyperspectral data (Cuprite data set)Unmixing performance. In order to test the performance of the algorithm, the proposed morphological component constraint optimization hyperspectral data unmixing method (SUnMC) is compared with the current internationally popular unmixing algorithm. The comparison method comprises the following steps: sparse unmixing algorithm (SUnSAL) based on variable splitting and augmented Lagrange, collaborative sparse unmixing algorithm (CLSUnSAL) based on variable splitting and augmented Lagrange, and l0Norm cooperative sparse unmixing algorithm (csun l 0).
Analysis of simulation experiment results
Table 1 shows the comparison results of root mean square errors of simulated hyperspectral data under different unmixing algorithms:
TABLE 1 RMSE of different algorithms on simulated hyperspectral data
Figure BDA0002972995420000062
Figure BDA0002972995420000071
As can be seen from table 1, under the condition of simulating hyperspectral data, since the sun mac takes into account the fact that the gaussian noise intensities of different bands are different and sparse noise exists, the root mean square error is significantly lower and the unmixing effect is the best compared with other algorithms.
Fig. 2(a) -2 (e) are abundance maps obtained on simulated hyperspectral data using different unmixing algorithms. It can be seen that under the influence of sparse noise such as gaussian noise and impulse noise, abundance maps obtained by SUnSAL, CLSUnSAL and csunol 0 all contain a large amount of noise, and the unmixing precision is not high.
In order to verify the effectiveness of the SUnMC in unmixing a single spectrum, all wave bands on a single pixel in the analog hyperspectral data are taken as input, namely the input single hyperspectral data is y ∈ R224×1The spectral library is E ∈ R224×240. FIG. 3(a) to FIG. 3(c) are the original spectra, respectivelySpectra polluted by sparse noise such as Gaussian noise, impulse noise and the like and reconstruction results of different unmixing algorithms. As can be seen from fig. 3(c), compared with other algorithms, the spectrum reconstructed by the sun c is closer to the original spectrum, which shows that the sun c has good noise immunity and can obtain better results.
Fig. 4 shows abundance maps of three minerals, namely alunite, gefite and chalcedony, obtained by SUnSAL, CLSUnSAL, CSUnL0 and SUnMC algorithms on the Cuprite data set. To facilitate comparative analysis of abundance maps, we used the hyperspectral mineral mapping software, Tetracorder, developed by the United States Geological Survey (USGS) to identify the mineral information contained in the spectra and generate mineral profiles, as shown in the left column of fig. 4. Each pixel point in the graph indicates whether the point belongs to a certain mineral or not, and the content of the certain mineral in the point is not shown, so that the point is only used for qualitative comparative analysis, and is not used as a true abundance graph. The rightmost column in fig. 4 is the unmixing result of the sun mc algorithm, with hotter hues indicating higher mineral content. For alunite minerals, SUnSAL, CLSUnSAL, csun l0 showed little difference from the SUnMC algorithm in the abundance maps, and were very similar to the results obtained by Tetracorder. For two minerals of the hydroammoniate feldspar and the chalcedony, the abundance map obtained by the SUnMC algorithm has more details in visual effect, and the algorithm is proved to be more effective than other algorithms.

Claims (6)

1. A hyperspectral data unmixing method based on morphological component constraint optimization is characterized by comprising the following steps:
step 1, inputting hyperspectral data and an end member spectrum library;
step 2, constructing a spectrum sample expansion matrix;
step 3, establishing a morphological component constraint optimized hyperspectral data unmixing model: based on the assumption that the Gaussian noise of different wave bands of the hyperspectral data has different intensities and other sparse noise, the method uses l by estimating the standard deviation of the wave band noise and the noise decomposition of a sparse structure1Norm-constrained sparse noise,/2,0Norm constraint of global rows of different pure material abundance coefficientsSparsity, establishing a morphological component constraint optimization hyperspectral data unmixing model;
step 4, calculating the noise standard deviation of each wave band of the hyperspectral data: firstly, calculating a noise correlation matrix, then calculating a regression vector band by band, estimating noise, and finally calculating the standard deviation of the noise;
and 5, alternately and iteratively solving: converting the model into an equivalent augmented Lagrange form, and performing alternate iteration on each variable according to an alternate direction multiplier method to solve an optimization problem;
and 6, outputting the abundance coefficient.
2. The morphological component constraint optimization hyperspectral data unmixing method according to claim 1, wherein the input hyperspectral data and the end-member spectrum library in the step 1 are as follows:
inputting a batch of hyperspectral data to be unmixed
Figure FDA0002972995410000011
And end-member spectral library E epsilon RB×MB is the number of wave bands, P is the number of spectral sampling points, and M is the number of end members.
3. The morphological component constraint optimization hyperspectral data unmixing method according to claim 1, wherein the spectrum sample expansion matrix constructed in the step 2 is specifically as follows:
arranging input hyperspectral data according to pixel-by-pixel spectral vectors to form a spectrum-pixel matrix Y ═ Y1,y2,...,yN]∈RB×P。
4. The morphological component constraint optimization hyperspectral data unmixing method according to claim 1, wherein the step 3 of establishing the morphological component constraint optimization hyperspectral data unmixing model specifically comprises the following steps:
based on the assumption that the intensity of Gaussian noise of different wave bands of the hyperspectral data is different and other sparse noise exists, a hyperspectral data unmixing model is established:
Y＝EA+S+N (1)
in the formula (1), A is ∈ RM×PThe element in each column represents the proportion of the corresponding end member spectrum in a single mixed pixel; s is belonged to RB×PFor sparse components, N ∈ RB×PIs Gaussian noise;
introducing sparse constraint to obtain an optimization solution function of the model in the formula (1):
Figure FDA0002972995410000021
in the formula (2), λ and α are regularization parameters, λ>0，α>0; w is a diagonal matrix and W is a diagonal matrix,
Figure FDA0002972995410000022
the element on the opposite angle is the reciprocal of the standard deviation of Gaussian noise of each wave band; II-FAn F norm representing a matrix;
Figure FDA0002972995410000023
l representing a matrix2,0A norm;
Figure FDA0002972995410000024
l representing a matrix1A norm; converting equation (2) into by the augmented Lagrange multiplier method:
Figure FDA0002972995410000025
in the formula (3), V1,V2,V3As an auxiliary variable, D1,D2,D3Is Lagrange multiplier, mu>0 is a penalty factor which is a function of,
Figure FDA0002972995410000026
Xi,jelements representing the ith row and jth column of the matrix X when X isi,jIs non-negativeWhen the value is equal to the preset value,
Figure FDA0002972995410000027
equal to 0, otherwise equal to positive infinity.
5. The morphological component constraint optimization hyperspectral data unmixing method according to claim 1, wherein the step 4 of calculating the noise standard deviation of each wave band of the hyperspectral data to obtain a diagonal matrix comprises the following steps:
calculating a regression vector
Figure FDA0002972995410000028
Figure FDA0002972995410000029
In the formula (4), the reaction mixture is,
Figure FDA00029729954100000210
representation matrix
Figure FDA00029729954100000211
Z ═ Y in the ith row ofT，
Figure FDA00029729954100000212
A correlation matrix is represented that represents the correlation matrix,
Figure FDA00029729954100000213
Figure FDA00029729954100000214
representing slave matrices
Figure FDA00029729954100000215
In deletion of
Figure FDA00029729954100000216
And row and column
Figure FDA00029729954100000217
The matrix obtained after the columns is formed,
Figure FDA00029729954100000218
representation matrix
Figure FDA00029729954100000219
The number of the ith row of (a),
Figure FDA00029729954100000220
computing a noise vector
Figure FDA00029729954100000221
Figure FDA00029729954100000222
In the formula (5), the reaction mixture is,
Figure FDA00029729954100000223
representing estimated noise
Figure FDA00029729954100000224
Row i of (1), ziThe ith row of the matrix Z is represented,
Figure FDA00029729954100000225
indicating deletion of the first from the matrix Z
Figure FDA00029729954100000226
A matrix obtained after the column;
calculating the reciprocal W of the standard deviation of the Gaussian noise of each wave bandiiObtaining a matrix W:
Figure FDA0002972995410000031
in the formula (6), beta represents
Figure FDA0002972995410000032
P represents the number of spectral samples.
6. The morphological component constraint optimization hyperspectral data unmixing method according to claim 1, wherein in step 5, the linear unmixing of the mixed spectrum is realized by alternating iteration, and the method comprises the following steps:
fixing other variables, updating abundance coefficient a:
Figure FDA0002972995410000033
fixing other variables, updating sparse component S:
Figure FDA0002972995410000034
in the formula (8), Sτ(. is a soft threshold qualifier, and Sτ(x) Sgn (x) max (| x | - τ,0), where τ is a non-negative parameter, sgn (·) denotes a sign function;
fixing other variables, updating auxiliary variable V1,V2,V3：
Figure FDA0002972995410000035
Figure FDA0002972995410000036
Figure FDA0002972995410000037
In the formula (10), the compound represented by the formula (10),
Figure FDA0002972995410000038
represents a line hard threshold operator, an
Figure FDA0002972995410000039
Where τ is a non-negative parameter, B (i,: indicates row i of matrix B;
fixing other variables, updating Lagrange multiplier D1,D2,D3：
Figure FDA00029729954100000310
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