Recovery of constituent spectra in 3D chemical shift imaging using non-negative matrix factorization

Paul Sajda, S. Du, L. Parra, R. Stoyanova, Truman R. Brown

In this paper we describe a non-negative matrix factoriza- tion (NMF) for recovering constituent spectra in 3D chem- ical 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 ba- sis vectors in a bounded subspace. In this case the opti- mal basis vectors are the ones that envelope the observed data with a minimum deviation from the boundaries. Re- sults 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 re- quires computationally expensive Monte Carlo methods. The cNMF algorithm is shown to recover the same con- stituent spectra as BSD, however in about less com- putational time.

Accepted 1 April 2003
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