Image Processing Reference
In-Depth Information
on two acquisitions of the same image: the so-called double-acquisition methods.
Thereby, the noise variance is, for example, computed by subtracting two acqui-
sitions of the same object and calculating the standard deviation of the resulting
image pixels [40,50,51]. Alternatively, the image noise variance can be computed
from two magnitude MR images as follows.
When two conventional MR images ( K
=
2) are acquired under identical
2 from two equations and two unknowns
using the averaged (averaging is done in K-space) and single images because
imaging conditions, one can solve
σ
N
1
=
m
2
A
2
+
2
σ
2
,
(4.164)
E
s
n
N
n
=
1
N
2
1
σ
=
m
2
A
2
+
2
,
(4.165)
E
a
n
N
2
n
=
1
where denotes the spatial average of the whole image. The subscripts s and a
refer to the single and averaged images, respectively. From Equation 4.165 and
Equation 4.164, an unbiased estimator of the noise variance is derived as
〈〉
2
2
σ
2
=
m m .
(4.166)
s
a
This approach has the following advantages:
It does not require any user interaction, as no background pixels need
to be selected.
It is insensitive to systematic errors such as ghosting, ringing, and
direct current (DC) artifacts as long as these appear in both images. It
is clear that if this type of error appears in only one of the two images,
none of the double-acquisition methods will yield the correct result.
The precision of the noise variance estimator (Equation 4.140) is dras-
tically increased compared to the precision of the estimator given in
Equation 4.130, as all the data points (not only those from the back-
ground region) are involved in the estimation.
It is valid for any SNR of the image.
An obvious disadvantage is the double acquisition itself. However, in MR acqui-
sition schemes, it is common practice to acquire two or more images for averaging.
Hence, those images may be used for the proposed noise estimation procedure,
without additional acquisition time. In addition, the images require proper geomet-
rical registration, i.e., no movement of the object during acquisition is allowed.
 
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