Vertex component analysis: a fast algorithm to unmix hyperspectral data
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...• The vertex component analysis (VCA) algorithm [123] iteratively projects data onto a direction orthogonal to the subspace spanned by the endmembers already determined....
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...The endmembers identified by VCA and N-FINDR area also represented....
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...Representative algorithms of class a) are pixel purity index (PPI) [43], vertex component analysis (VCA) [44], simplex growing algorithm (SGA) [45] successive volume maximization (SVMAX) [46], and the recursive algorithm for separable NMF (RSSNMF) [47]; Representative algorithms of class b) are N-FINDR [48], iterative error analysis (IEA), [49], sequential maximum angle convex cone (SMACC), and alternating volume maximization (AVMAX) [46]. c. non-puRe pixel BAseD AlgoRithMs Fig....
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...9 show the identified endmember signatures with the VCA algorithm [44]....
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...Soil 1 Soil 2 Soil 3 Data N-FINDR VCA Grass Grass Shade Trees Trees (a) (b) (c) (d) (e) (f) Soil 1 Soil 2 Soil 3 Grass Shade Trees Soil 1 june 2013 ieee Geoscience and remote sensinG maGazine 17 The bilinear model is valid when the scene can be partitioned in successive layers with similar scattering properties....
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...Representative algorithms of class a) are pixel purity index (PPI) [43], vertex component analysis (VCA) [44], simplex growing algorithm (SGA) [45] successive volume maximization (SVMAX) [46], and the recursive algorithm for separable NMF (RSSNMF) [47]; Representative algorithms of class b) are N-FINDR [48], iterative error analysis (IEA), [49], sequential maximum angle convex cone (SMACC), and alternating volume maximization (AVMAX) [46]....
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...First, this site has been extensively used for remote-sensing experiments since the 1980s, and many research works have been published with high-accuracy ground truth available [11], [35], [36]; second, the Cuprite area is a relatively undisturbed hydrothermal system with many well-exposed minerals....
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...It is apparent that under the pure-pixel assumption [9]–[11], the best simplex is uniquely determined by the pure pixels, which are the vertices of the simplex....
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...To speed up the process, some algorithms [9]–[11] assume the presence of pure pixels, i....
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...Vertex component analysis (VCA) [11] is one of the most advanced convex-geometry-based endmember detection methods with the pure-pixel assumption....
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...in [35] is even higher, since the temperature of the simulated annealing algorithm therein used shall follow a law [ 37 ] to assure convergence (in probability) to the desired solution....
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Related Papers (5)
Frequently Asked Questions (11)
Q2. What are the three well-known projection techniques?
Principal component analysis (PCA) [45], maximum-noise fraction (MNF) [46], and singular value decomposition (SVD) [47] are three well-known projection techniques widely used in remote sensing.
Q3. What is the algorithm for a simplex?
VCA is more robust to topographic modulation, since it seeks for the extreme projections of the simplex, whereas N-FINDR seeks for the maximum volume, which is more sensitive to fluctuations on .
Q4. What is the probability of being null?
Since is the projection of a zero-mean Gaussian independent random vector onto the orthogonal space spanned by the columns of , then the probability of being null is zero.
Q5. How do the authors estimate the number of endmembers in the processed area?
In order to estimate the number of endmembers present in the processed area, the authors resort to the virtual dimensionality (VD), recently proposed in [61].
Q6. What is the signal energy of the first eight eigenvalues?
The authors can see that the signal energy contained in the first eight eigenvalues is higher than 99.93% of the total signal energy, meaning that the other six endmembers only occurs in a small percentage of the subimage.
Q7. What is the reason for generating a random vector?
Notice that the underling reason for generating a random vector is only to get a non null projection onto the orthogonal space generated by the columns of .
Q8. What are the different types of drichlet distributions?
The Dirichlet density, besidesenforcing positivity and full additivity constraints, displays a wide range of shapes, depending on the parameters .
Q9. What is the spectral signature of the spectral mixture?
Three spectral signatures (A—biotite, B—carnallite, and C—ammonioalunite) were selected from the U.S. Geological Survey (USGS) digital spectral library [48] (see Fig. 2); the abundance fractions follow a Dirichlet distribution; parameter is set to 1; and the noise is zero-mean white Gaussian with covariance matrix , where is the identity matrix and leading to a SNR dB. Fig. 3(a) presents a scatterplot of the simulated spectral mixtures without projection (bands nm and nm).
Q10. What is the colatitude angle between and any vector?
The chosen value of , assures that the colatitude angle between and any vector is between 0 and 45 , then avoiding numerical errors which otherwise would occur for angles near 90 .
Q11. What is the probability of having pure pixels?
In the third experiment, the number of pixels of the scene varies, in order to illustrate the algorithm performance with the size of the covered area: as the number of pixels increases, the likelihood of having pure pixels also increases, improving the performance of the unmixing algorithms; in the fourth experiment, the algorithms are evaluated as function of the number of endmembers present in the scene; finally, in the fifth experiment, the number of floating-point operations (flops) is measured, in order to compare the computational complexity of VCA, N-FINDR, and PPI algorithms.