Image Processing Reference
In-Depth Information
Bias of Â
ML
(
σ
= 1, N = 25)
1
complex data, identical phases
complex data, different phases
magnitude data, unknown
2
σ
2
magnitude data, known
σ
0.5
0
−
0.5
0
1
2
3
4
5
SNR (A/
)
σ
FIGURE 4.6
Bias of the ML estimator of
A
for complex data with identical and different
phases and for magnitude data with unknown and known noise variance. (From Sijbers, J.,
den Dekker, A.J. (2004). Maximum likelihood estimation of signal amplitude and noise
variance from MR data.
Magn. Reson. Med.
51(3): 586-594.)
MSE of Â
ML
(
σ
= 1, N = 25)
1
complex data, identical phases
complex data, different phases
magnitude data, unknown
σ
0.9
2
0.8
2
magnitude data, known
σ
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
SNR (A/
)
σ
FIGURE 4.7
MSE of the ML estimator of
A
for complex data with identical and different
phases and for magnitude data with unknown and known noise variance. (From Sijbers, J.,
den Dekker, A.J. (2004). Maximum likelihood estimation of signal amplitude and noise
variance from MR data.
Magn. Reson. Med.
51(3): 586-594.)
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