31 January 1995 Models of spectral unmixing: simplex versus least squares method of resolution
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Abstract
Spectral unmixing is referred to in textbooks as a straightforward technique the application of which encounters apparently no problem. Operational applications are however scarce in the literature. The method usually used is based on the least square method of minimizing the error in search of the best fit solution. This method, however, poses problems when applied to real data when the number of end-members increases and/or the composition of end-members is similar. An alternative method based on linear algebra has several advantages: (1) no inversion of matrix is required, no meaningless values are thus generated; (2) not only a condition of the closed system can be introduced, but the end-members remain independent (i.e., the last one is not the complement to 1 of the sum of the other, as in the least square method); (3) a condition of positive value of the weights can be imposed. The latter condition yields a supplementary equation to the system, one more end-member may be taken into account, thus improving both the qualitative and the quantitative aspects of the mixture problem. Examples based on Landsat TM imagery are shown in the fields of vegetation monitoring (subtraction of the vegetal component in the landscape) and spectral geology in arid terrains (end-members being defined through a principal components analysis of the image).
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Johan Lavreau, Johan Lavreau, } "Models of spectral unmixing: simplex versus least squares method of resolution", Proc. SPIE 2314, Multispectral and Microwave Sensing of Forestry, Hydrology, and Natural Resources, (31 January 1995); doi: 10.1117/12.200779; https://doi.org/10.1117/12.200779
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