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. Author manuscript; available in PMC: 2011 Dec 30.
Published in final edited form as: Linear Algebra Appl. 2010 Dec 30;433(11-12):1719–1721. doi: 10.1016/j.laa.2010.07.011

Table I.

Simulation results for the unconstrained and phase constrained estimation of water and fat based on Eq 8. Results indicate mean values are identical for both methods while standard deviations are up to 41% higher in the unconstrained case.

Water
Fat		 Mean
(unconstrained)		 Mean
(constrained)		 Std. Dev.
(unconstrained)		 Std. Dev.
(constrained)		 Ratio
1.0
0.0		 1.000-0.000i
0.000-0.000i 		1.000-0.000i
-0.000-0.000i 		0.0822
0.0914		 0.0820
0.0649		 1.002
1.408
0.8
0.2		 0.800+0.000i
0.200-0.000i 		0.800+0.000i
0.200-0.000i 		0.0822
0.0914		 0.0801
0.0664		 1.026
1.376
0.6
0.4		 0.600-0.000i
0.400-0.000i 		0.600+0.000i
0.400-0.000i 		0.0822
0.0914		 0.0751
0.0722		 1.094
1.266
0.4
0.6		 0.400-0.000i
0.600-0.000i 		0.400+0.000i
0.600-0.000i 		0.0822
0.0914		 0.0670
0.0814		 1.227
1.123
0.2
0.8		 0.200+0.000i
0.800+0.000i 		0.200+0.000i
0.800+0.000i 		0.0822
0.0914		 0.0603
0.0884		 1.363
1.034
0.0
1.0		 0.000-0.000i
1.000+0.000i 		0.000+0.000i
1.000+0.000i 		0.0822
0.0914		 0.0584
0.0912		 1.408
1.002