RECOVERY OF CONSTITUENT SPECTRA IN 3D CHEMICAL SHIFT IMAGING USING NON-NEGATIVE MATRIX FACTORIZATION

In this paper we describe a non-negative matrix factorization (NMF) for recovering constituent spectra in 3D chemical shift imaging (CSI). The method is based on the NMF algorithm of Lee and Seung [1], extending it to include a constraint on the minimum amplitude of the recovered spectra. This constrained NMF (cNMF) algorithm can be viewed as a maximum likelihood approach for finding basis vectors in a bounded subspace. In this case the optimal basis vectors are the ones that envelope the observed data with a minimum deviation from the boundaries. Results for P human brain data are compared to Bayesian Spectral Decomposition (BSD) [2] which considers a full Bayesian treatment of the source recovery problem and requires computationally expensive Monte Carlo methods. The cNMF algorithm is shown to recover the same constituent spectra as BSD, however in about less computational time.