Bayesian Nonnegative Matrix Factoization with Volume Constraints for Unmixing af Hyperspectral Images 
Morten Arngren, Mikkel N. Schmidt, Jan Larsen

Abstract  In hyperspectral image analysis the objective is to unmix
a set of acquired pixels into pure spectral signatures (endmembers)
and corresponding fractional abundances. The
NonnegativeMatrix 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. 
Keywords  Bayesian, volume constraint, Gibbs sampling, NMF, Hyperspectral images 
Type  Conference paper [With referee] 
Conference  2009 IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2009) 
Editors  T. Adali, J. Chanussot, C. Jutten, J. Larsen 
Year  2009 Month September 
Publisher  IEEE Press 
ISBN / ISSN  ISBN 9781424449477 
Note  DOI 10.1109/MLSP.2009.5306262 
Electronic version(s)  [pdf] 
BibTeX data  [bibtex] 
IMM Group(s)  Intelligent Signal Processing 