Estimation of Signal and Noise Parameters from MR Data - Advance Image Processing in Magnetic Resonance Imaging - page 131

∧

2 ML from a region of constant amplitude (

MSE σ σ = 1)

1

complex data, identical phases
complex data, different phases 0.9

0.8
0.7

0.6

0.5
0.4
0.3

0.2

0.1

0

0 20 40 60 80 100

N

FIGURE 4.13 MSE for unbiased estimation of the noise variance from a region of con-
stant amplitude for complex data with identical and different phases. (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.)

∧ 2

ML from a region of constant amplitude ( σ = 1, N = 26)

MSE of

σ

0.4

complex data, identical phases
complex data, different phases
magnitude data

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

0 1 2 3 4 5

SNR (A / )

σ

FIGURE 4.14 MSE for unbiased estimation of the noise variance from a region of con-
stant amplitude for complex data with identical and different phases and for magnitude
data. (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.)