The linear mixture model for hyperspectral images assumes that all the image spectra lie on a high-dimensional
simplex with corners called endmembers. Given the set of endmembers, one typically calculates fractional abundances
for each pixel using constrained least squares. This method likely reconstructs the spectra as combinations
of most, if not all, the endmembers. We instead assume that pixels are combinations of only a few of the endmembers,
yielding sparse abundance vectors. We introduce a new method, similar to Matching Pursuit (MP)
from the signal processing literature, to calculate these sparse abundances. We combine this sparse demixing
algorithm with dictionary learning methods to automatically calculate endmembers for a provided set of spectra.
We apply our method to an AVIRIS image of Cuprite, NV, for which we compare our endmembers with spectral
signatures from the USGS spectral library.
John B. Greer,
"Sparse demixing", Proc. SPIE 7695, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVI, 76951O (13 May 2010); doi: 10.1117/12.850346; https://doi.org/10.1117/12.850346