Table 3.

Results of the phantom imaging over all 14 vials with different T₁ values for various sampling strategies, where each acquisition was repeated 5 times and K = 11. The ratio of the standard deviation of the T₁ estimator for each proposed sampling strategy and that of the uniform sampling strategy is reported as “precision (prec) with respect to (wrt) uniform.” The points from numerical experiment #3, #4 and #5 show improvement on the standard deviation of the uniform sampling strategy for T₁ values > 600 ms, T₁ values < 1150 ms and all T₁ values, respectively. The theoretical prediction corresponding to the ratios of standard deviations are also reported for each sampling strategy, which are in good agreement with the experimental ratios (P = 0.26, P = 0.09, P = 0.05 for the point selections of different T₁ values of interest respectively) for vials with T1 values in the union of the ranges of optimization.

	uniformly distributed points		points optimized for T = 950 - 1250 ms				po i n t s o pt i mized for T1 = 400 - 600 ms				po i nts o pt imized for T1 = 450 & 1250 ms
Vial	(T1est (ms)	prec (T1est) (ms)	T1est (ms)	prec (T1est) (ms)	prec wrt. uniform	theory prec wrt. uniform	T1est (ms)	prec T1est (ms)	prec wrt. uniform	theory prec wrt. uniform	T1est (ms)	prec (T1est) (ms)	prec wrt. uniform	theory prec wrt. uniform
1	1457 ± 7.7	69.2 ± 6.3	1456 ± 7.4	48.1 ± 5.2	0.70	0.71	1432 ± 12.7	72.0 ± 5.2	1.04	1.01	1450 ± 26.5	48.8 ± 4.4	0.71	0.81
2	1144 ± 14.5	55.7 ± 6.7	1130 ± 7.1	41.0 ± 2.5	0.74	0.76	1127 ± 6.8	54.1 ± 2.7	0.97	0.98	1125 ± 12.9	44.7 ± 2.3	0.80	0.82
3	1151 ± 11.5	53.2 ± 3.8	1155 ± 8.6	43.1 ± 1.4	0.81	0.76	1146 ± 12.2	54.0 ± 6.7	1.02	0.98	1147 ± 20.3	45.3 ± 1.9	0.85	0.82
4	274 ± 5.0	15.3 ± 1.2	275 ± 6.8	23.2 ± 2.5	1.51	1.71	271 ± 7.7	14.7 ± 0.8	0.96	0.99	269 ± 4.5	15.0 ± 0.9	0.98	1.17
5	429 ± 6.6	17.3 ± 1.1	431 ± 2.3	18.8 ± 1.5	1.09	1.11	426 ± 6.8	14.1 ± 1.0	0.81	0.87	426 ± 5.9	15.2 ± 1.0	0.88	0.96
6	729 ± 10.3	31.3 ± 1.2	724 ± 2.1	26.1 ± 3.3	0.83	0.86	724 ± 4.6	29.0 ± 2.6	0.93	0.91	727 ± 13.9	27.7 ± 1.6	0.88	0.87
7	595 ± 6.6	20.0 ± 1.6	599 ± 6.0	18.8 ± 1.6	0.94	0.94	590 ± 11.3	17.8 ± 1.9	0.89	0.89	588 ± 11.8	16.6 ± 1.2	0.83	0.89
8	597 ± 5.0	25.9 ± 0.9	597 ± 5.0	23.3 ± 3.0	0.90	0.94	592 ± 5.3	22.8 ± 1.3	0.88	0.89	594 ± 11.8	23.1 ± 0.3	0.89	0.89
9	980 ± 11.2	34.6 ± 1.2	981 ± 10.4	25.2 ± 0.6	0.73	0.78	971 ± 8.5	29.0 ± 2.5	0.84	0.96	983 ± 13.5	24.2 ± 1.0	0.70	0.84
10	823 ± 13.3	29.8 ± 2.1	822 ± 7.7	24.2 ± 2.0	0.81	0.83	816 ± 8.3	29.0 ± 2.4	0.97	0.93	816 ± 15.0	22.1 ± 1.3	0.74	0.86
11	1148 ± 18.4	52.6 ± 6.4	1144 ± 8.3	37.8 ± 1.5	0.72	0.76	1129 ± 15.5	45.9 ± 2.4	0.87	0.98	1151 ± 18.7	42.0 ± 2.8	0.80	0.82
12	341 ± 4.1	19.4 ± 1.7	342 ± 5.8	22.6 ± 2.4	1.17	1.29	337 ± 7.0	16.3 ± 1.0	0.84	0.89	335 ± 8.7	17.3 ± 0.3	0.89	1.01
13	963 ± 13.8	49.8 ± 3.4	962 ± 6.2	35.4 ± 2.2	0.71	0.79	956 ± 3.7	47.1 ± 5.4	0.95	0.95	964 ± 8.6	37.9 ± 4.1	0.76	0.83
14	1130 ± 10.6	55.8 ± 5.6	1137 ± 10.5	45.0 ± 3.9	0.81	0.76	1121 ± 4.5	52.9 ± 2.2	0.95	0.98	1139 ± 15.8	45.0 ± 1.7	0.81	0.82