Estimation of Signal and Noise Parameters from MR Data - Advance Image Processing in Magnetic Resonance Imaging - page 91

SNR = 0
SNR = 0.5
SNR = 1.0
SNR = 2.0

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

− 3 − 2 − 1 0 1 2 3

∆φ

(a)

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

2

1.5

1

− 3

− 2

1

−

0.5

0

1

2 0

∆Φ (rad)

(b)

3

FIGURE 4.3 Plot of the phase error PDF as a function of the SNR. (From Sijbers, J., Van
der Linden, A. (2003). Encyclopedia of Optical Engineering , chap. Magnetic resonance
imaging, pp. 1237-1258. Marcel Dekker, ISBN: 0-8247-4258-3.)

• In regions where there is only noise, (i.e., where the SNR is zero),

Equation 4.37 reduces to a uniform PDF:

!
!

1
2

if −<∆< πφπ

π

p ∆ ∆=

φ φ

() (4.38)

0 otherwise.