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used in future work in order to actually fully assess
the performance of the proposed technique.
Another paper appearing in these proceedings
focuses on a “simulation study of tissue type
differentiation using non-negative matrix
factorization”. In that preliminary research, we
studied the performance of several NMF
implementations on simulated MRSI signals. The
‘(a)hals’ algorithm (Cichocki et al., 2007; Cichocki
et al., 2009; Gillis, 2011) had the best performance
in those simulations and has therefore been used for
all the NMF computations in this paper.
ACKNOWLEDGEMENTS
This research was supported by Research Council
KUL: GOA MaNet, CoE EF/05/006 Optimization in
Engineering (OPTEC), PFV/10/002 (OPTEC), IDO
08/013 Autism, several PhD/postdoc & fellow grants;
Flemish Government: FWO: PhD/postdoc grants,
projects: FWO G.0302.07 (SVM), G.0341.07 (Data
fusion), G.0427.10N (Integrated EEG-fMRI),
G.0108.11 (Compressed Sensing) research
communities (ICCoS, ANMMM); IWT:
TBM070713-Accelero, TBM070706-IOTA3,
TBM080658-MRI (EEG-fMRI), PhD Grants; IBBT
Belgian Federal Science Policy Office: IUAP P6/04
(DYSCO, `Dynamical systems, control and
optimization', 2007-2011); ESA AO-PGPF-
01, PRODEX (CardioControl) C4000103224;
EU: RECAP 209G within INTERREG IVB NWE
programme, EU HIP Trial FP7-HEALTH/ 2007-
2013 (n° 260777) (Neuromath (COST-BM0601):
BIR&D Smart Care. Li thank the China Scholarship
Council.
REFERENCES
Bottomley PA, 1987. Spatial localization in NMR-
spectroscopy in vivo. Ann N Y Acad Sci, 508:333–348.
Brown T, Kincaid B, Ugurbil K, 1982. NMR chemical
shift imaging in three dimensions. PNAS, 79(11):
3523-3526.
Croitor Sava A, Martinez-Bisbal MC, Van Huffel S, Cerda
JM, Sima DM, Celda B, 2011. Ex vivo high resolution
magic angle spinning metabolic profiles describe
intratumoral histopathological tissue properties in
adult human gliomas. Magn Reson Med, 65:320-328.
Cichocki A, Zdunek R, Amari S, 2007. Hierarchical ALS
algorithms for nonnegative matrix and 3D tensor
factorization. Lect Notes Comput Sci, 4666:169-176.
Cichocki A, Phan AH, 2009. Fast local algorithms for
large scale Nonegative Matrix and Tensor
Factorizations. IEICE Trans Fund Electron Comm
Comput Sci, 3:708-721.
Du S, Mao X, Sajda P and Shungu DC, 2008. Automated
tissue segmentation and blind recovery of 1H MRS
imaging spectral patterns of normal and diseased
human brain. NMR in Biomedicine, 21:33-41.
Gillis N, 2011. Nonnegative matrix factorization
complexity, algorithms and applications. PhD Thesis,
Louvan-La-Neuve, Belgium.
Howe FA, Barton SJ, Cudlip SA, Stubbs M, Saunders DE,
Murphy JR, Opstad KS, Doyle VL, McLean MA, Bell
BA, Griffiths JR, 2003. Metabolic profiles of human
brain tumours using quantitative in vivo 1H magnetic
resonance spectroscopy. Magn Res Med, 49:223-232.
Laudadio T, Mastronardi N, Vanhamme L, Van Hecke P,
Van Huffel S, 2002. Improved Lanczos algorithms for
blackbox MRS data quantitation. J Magn Reson, 157:
292-297.
Lawson C.L. and R.J. Hanson, 1974, Solving Least-
Squares Problems, Prentice-Hall, Chapter 23, p. 161,.
Lee DD, Seung HS, 1999. Learning the parts of objects by
non-negative matrix factorization. Nature, 401:788-
791.
Paatero P, Tapper U, 1994. Positive matrix factorization:
A non-negative factor model with optimal utilization
of error. Environmetrics, 5:111-126.
Poullet JB, 2008. Quantification and classification of
magnetic resonance spectroscopic data for brain
tumor diagnosis. PhD Thesis, Leuven, Belgium.
Sajda P, Du S, Brown TR, Parra LC, Stoyanova R, 2003.
Recovery of constituent spectra in 3D chemical shift
imagin using non-negative matrix factorization. In
Proc. 4th Int. Symp. ICA and BSS, 71-76.
Sajda P, Du S, Brown TR, Stoyanova R, Shungu DC, Mao
X, Parra LC, 2004. Nonnegative Matrix Factorization
for Rapid Recovery of Constituent Spectra in
Magnetic Resonance Chemical Shift Imaging of the
Brain. IEEE Trans Med Imaging, 23:1453-1465.
Su Y, Thakur SB., Karimi S, Du S, Sajda P, Huang W,
Parra LC, 2008. Spectrum separation resolves partial-
volume effect of MRSI as demonstrated on brain
tumor scans. NMR Biomed, 21:1030-1042.
TISSUE TYPE DIFFERENTIATION FOR BRAIN GLIOMA USING NON-NEGATIVE MATRIX FACTORIZATION
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