Image Processing Reference
In-Depth Information
Subsection 4.5.3 ). Moreover, if large background areas are available,
which is often the case, many more data points are available for the
estimation of the noise variance than for the estimation of the signal
amplitude. Then, the noise variance can be estimated with much higher
precision. Hence, it might be a valid assumption to regard the noise
variance as known (i.e., to regard the estimated noise variance as the
true noise variance).
If the noise variance cannot be estimated separately (with sufficient
precision), it acts as a nuisance parameter that needs to be estimated
simultaneously with the signal amplitude.
Both cases are discussed in the following subsections.
4.4.3.1
Region of Constant Amplitude and Known
Noise Variance
4.4.3.1.1 CRLB
The Fisher information matrix of the data with respect to the parameter A is given by
ln p
A
2
,
N
A
2
m
I
=−
=
Z
E
(4.78)
σ
σ
2
2
2
with
()
()
A m
I
2
2
m
1
σ
2
Z
=
,
(4.79)
E
σ
2
A m
I
2
0
2
σ
and
) [5]. The
expectation value in Equation 4.79 can be evaluated numerically. Note that I is
in fact a scalar, from which the CRLB can easily be obtained by applying the
inverse operator:
m
a Rician-distributed random variable with true parameters ( A ,
σ
1
σ
2
A
2
CRLB
=
Z
.
(4.80)
N
σ
2
4.4.3.1.2 Conventional Estimation
Usually, Equation 4.18 is exploited for the estimation of the underlying signal A .
Thereby, is estimated from a simple spatial average of the squared pixel
values of the ROI [35-39]:
2
E
[]
m
N
=〈 〉=
1
mm N
2
2
2
[]
.
(4.81)
E
m
n
n
=
1
 
Search WWH ::




Custom Search