Bayesian Nonnegative Matrix Factoization with Volume Constraints for Unmixing af Hyperspectral Images

Morten Arngren, Mikkel N. Schmidt, Jan Larsen

AbstractIn hyperspectral image analysis the objective is to unmix
a set of acquired pixels into pure spectral signatures (endmembers)
and corresponding fractional abundances. The
Non-negativeMatrix Factorization (NMF) methods have received
a lot of attention for this unmixing process. Many of
these NMF based unmixing algorithms are based on sparsity
regularization encouraging pure spectral endmembers,
but this is not optimal for certain applications, such as foods,
where abundances are not sparse. The pixels will theoretically
lie on a simplex and hence the endmembers can be estimated
as the vertices of the smallest enclosing simplex. In
this context we present a Bayesian framework employing a
volume constraint for the NMF algorithm, where the posterior
distribution is numerically sampled from using a Gibbs
sampling procedure. We evaluate the method on synthetical
and real hyperspectral data of wheat kernels.
KeywordsBayesian, volume constraint, Gibbs sampling, NMF, Hyperspectral images
TypeConference paper [With referee]
Conference2009 IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2009)
EditorsT. Adali, J. Chanussot, C. Jutten, J. Larsen
Year2009    Month September
PublisherIEEE Press
ISBN / ISSNISBN 9781424449477
NoteDOI 10.1109/MLSP.2009.5306262
Electronic version(s)[pdf]
BibTeX data [bibtex]
IMM Group(s)Intelligent Signal Processing


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