Geometric unmixing of large hyperspectral images: a barycentric coordinate approach
Résumé
In hyperspectral imaging, spectral unmixing is one of the most challenging and fundamental problems. It consists of breaking down the spectrum of a mixed pixel into a set of pure spectra, called endmembers, and their contributions, called abundances. Many endmember extraction techniques have been proposed in literature, based on either a statistical or a geometrical formulation. However, most, if not all, of these techniques for estimating abundances use a least-squares solution. In this paper, we show that abundances can be estimated using a geometric formulation. To this end, we express abundances with the barycentric coordinates in the simplex defined by endmembers. We propose to write them in terms of a ratio of volumes or a ratio of distances, which are quantities that are often computed to identify endmembers. This property allows us to easily incorporate abundance estimation within conventional endmember extraction techniques, without incurring additional computational complexity. We use this key property with various endmember extraction techniques, such as N-Findr, vertex component analysis, simplex growing algorithm, and iterated constrained endmembers. The relevance of the method is illustrated with experimental results on real hyperspectral images.
Mots clés
hyperspectral
computational complexity
feature extraction
geometry
geophysical image processing
least squares approximations
remote sensing
statistical analysis
geometric unmixing
barycentric coordinate approach
endmember extraction techniques
statistical formulation
geometrical formulation
least-squares solution
N-Findr
vertex component analysis
iterated constrained endmembers
Hyperspectral imaging
Linear systems
Estimation
Algorithm design and analysis
Ice
Vectors
Abundance estimation
Cramer's rule
endmember extraction
hyperspectral image
iterated constrained endmembers algorithm
orthogonal subspace projection
simplex
simplex growing algorithm
unmixing spectral data
| Origine | Fichiers produits par l'(les) auteur(s) |
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