Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1453-1465 |
| Number of pages | 13 |
| Journal | IEEE Transactions on Medical Imaging |
| Volume | 23 |
| Issue number | 12 |
| DOIs | |
| State | Published - Dec 1 2004 |
| Externally published | Yes |
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Keywords
- Blind source separation (BSS)
- Chemical shift imaging (CSI)
- Hierarchical decomposition
- Magnetic resonance (MR)
- Magnetic resonance spectroscopy (MRS)
- Nonnegative matrix factorization (NMF)
ASJC Scopus subject areas
- Biomedical Engineering
- Radiology Nuclear Medicine and imaging
- Radiological and Ultrasound Technology
- Electrical and Electronic Engineering
- Computer Science Applications
- Computational Theory and Mathematics
Cite this
Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain. / Sajda, Paul; Du, Shuyan; Brown, Truman R.; Stoyanova, Radka; Shungu, Dikoma C.; Mao, Xiangling; Parra, Lucas C.
In: IEEE Transactions on Medical Imaging, Vol. 23, No. 12, 01.12.2004, p. 1453-1465.Research output: Contribution to journal › Article
}
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.
PY - 2004/12/1
Y1 - 2004/12/1
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)
UR - http://www.scopus.com/inward/record.url?scp=10044269618&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=10044269618&partnerID=8YFLogxK
U2 - 10.1109/TMI.2004.834626
DO - 10.1109/TMI.2004.834626
M3 - Article
VL - 23
SP - 1453
EP - 1465
JO - IEEE Transactions on Medical Imaging
JF - IEEE Transactions on Medical Imaging
SN - 0278-0062
IS - 12
ER -