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Hyper Spectral Image Processing
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Spectral Mixture Analysis of Hyperspectral Data
5. Spectral Unmixing Analysis
The spectral mixture of only two materials can be solved with the data of each band.
According to Eq.(1), the ith spectral band is mixed as:
DNi=(Ri1*F1+Ri2*Ei (4)
Combining Eq.(4) with the constraint expressed in Eq.(2), one can solve F 1 as following,
Let F 1 be the fraction coefficient of the vegetation foreground, then the solutions of F1 in each
band for all the sample data in the data set can be shown graphically in figure 9. Unstable
solutions are obtained when the spectral band has almost the same reflectance, i.e.,
R i1»R i2.
Removing the unstable solutions, the variation of the solutions can be clearly shown in figure 10.
Linearity of spectral mixing can be validated in most of the bands except the absorption bands.
One can remark that while most of the spectral bands provide positive effects, there are some
spectral bands may contaminate the solution.
Figure 9: The solution of F1.
Figure 10: The solution of F1 after removing unstable ones.
For each sample data, the fraction coefficients were also calculated by using CLS. The results
are graphically shown in figure 11. As mentioned above, the spectral bands do not have equal
contributions to the solution of spectral unmixing. In addition, as shown in figure 7, the bands
do not contain equal noise either. A weighted least squares (WLS) computation is, therefore,
proposed to improve the solution. The discrepancy of band reflectance between endmembers
and the noise level of measurements can be the reference to adjust the weights. The final
results are graphically shown in figure 11.
Figure 11: CLS solutions.
Figure 12: WLS solutions.
Conclusding Remarks
A pixel-covered area is commonly recognized as a square. However, the shape of the GIFOV
is actually not a square. This situation causes a problem that the fraction coefficients derived
from spectral unmixing do not correspond with the proportions of the þ endmembers distributed
within a square pixel. A variation of a spatial distribution of objects within a pixel would result
in a large difference.
Due to the differences of the discrepancy of band reflectance between endmembers and the noise
level of measurements, the spectral bands do not have equal contributions to the solution of
spectral unmixing. A weighted least squares (WLS) computation is proved to be effective for
improving the solution of spectral unmixing.
Acknowledgements
This research project was sponsored by the National Science Council of Republic of China
under the grants of NSC88-2211-E006-051.
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