TY - JOUR
T1 - Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain
AU - Sajda, Paul
AU - Du, Shuyan
AU - Brown, Truman R.
AU - Stoyanova, Radka
AU - Shungu, Dikoma C.
AU - Mao, Xiangling
AU - Parra, Lucas C.
N1 - Funding Information:
Manuscript received December 23, 2003; revised June 28, 2004. This work was supported by a National Science Foundation (NSF) CAREER Award (BES-0133804), by the Department of Defense (DoD) Multidisciplinary University Research Initiative (MURI) program administered by the Office of Naval Research (N00014-01-0625), and by the National Institutes of Health (NIH) under Program Projects Grant P01-CA41078. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was X. Hu. Asterisk indicates corresponding author. *P. Sajda is with the Laboratory of Intelligent Imaging and Neural Computing, Department of Biomedical Engineering, Columbia University, 351 Engineering Terrace Building, Mail Code 8904, 1210 Amsterdam Ave., New York, NY 10027 USA (e-mail: ps629@columbia.edu).
PY - 2004/12
Y1 - 2004/12
N2 - We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using 31P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on 1H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up.
AB - We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using 31P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on 1H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up.
KW - Blind source separation (BSS)
KW - Chemical shift imaging (CSI)
KW - Hierarchical decomposition
KW - Magnetic resonance (MR)
KW - Magnetic resonance spectroscopy (MRS)
KW - Nonnegative matrix factorization (NMF)
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U2 - 10.1109/TMI.2004.834626
DO - 10.1109/TMI.2004.834626
M3 - Article
C2 - 15575404
AN - SCOPUS:10044269618
VL - 23
SP - 1453
EP - 1465
JO - IEEE Transactions on Medical Imaging
JF - IEEE Transactions on Medical Imaging
SN - 0278-0062
IS - 12
ER -