Vertex component analysis: a fast algorithm to unmix hyperspectral data
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Citations
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Hyperspectral Remote Sensing Data Analysis and Future Challenges
Sparse Unmixing of Hyperspectral Data
Endmember Extraction From Highly Mixed Data Using Minimum Volume Constrained Nonnegative Matrix Factorization
References
Ground-truthing AVIRIS mineral mapping at Cuprite, Nevada
Mapping of hydrothermal alteration in the Cuprite mining district, Nevada, using aircraft scanner images for the spectral region 0.46 to 2.36µm
Blind separation of sources, Part III: stability analysis
On the complexity of computing determinants
On the relationship between spectral unmixing and subspace projection
Related Papers (5)
Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery
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.