Image Processing Reference
In-Depth Information
100
K = 2
K = 4
K = 6
10
1
1.5
2
2.5
3
3.5
4
4.5
5
SNR
FIGURE 4.8
Relative bias of a simple spatial average estimator for
K
= 2, 4, and 6. The
relative bias is independent of the number of averaged pixels
N
.
unbiased estimator of
A
2
is given by
N
1
∑
2
A
2
=
m
−
K
σ
2
.
(4.125)
n
N
n
=
1
The PDF of
A
2
can be computed to yield
NK
−
2
NAK
A
+
σ
4
A
+
KKA
σ
σ
+
2
2
2
2
2
pA
()
=
p
−
N
2
A
2
2
σ
2
2
2
2
(4.126)
AK A
A
+
2
σ
2
×
I
ε
(
2
+
K
σ
2
).
NK
−
1
σ
2
2
From the unbiased estimator of
A
2
, given in Equation 4.125, a modified RMS
estimator of
A
would be given by
N
1
∑
2
=
m
−
K
σ
2
.
(4.127)
A
n
rms
N
n
=
1
However, root extraction is a nonlinear operation that makes the estimator
biased. Also, the modified RMS estimator is appropriate only when the
argument of the square root operator is nonnegative. A possible, at first sight
A
rms
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