Biomedical Engineering Reference
In-Depth Information
ʛ
Let us calculate the intensity bias factor
assuming a simple scenario in which
2
2
=
=
|
˃
S
|
=|
˃
T
|
d
1
d
2
d
and
. Under these assumptions, the bias factor is
simplified to
d
2
1
+|
d
|
1
−
1
−|
d
|
|
≥
ʛ
=
d
≥
|
.
(7.28)
1
−|
d
1
+
d
2
+
2
(ˆ)
1
+|
d
The equation above shows how the amount of leakage
|
d
|
affects the bias factor
ʛ
.It
shows that if
|
d
|
is as small as
|
d
|
<
0
.
1, the intensity bias is less than 10%. However,
when
4 and the intensity value of the imag-
inary coherence may have a very large bias. In the following, we introduce a metric
referred to as the corrected imaginary coherence, which avoids this intensity bias.
|
d
|
is as large as 0.4, we have 2
.
3
≥
ʛ
≥
0
.
7.5 Corrected Imaginary Coherence
7.5.1 Modification of Imaginary Coherence
The imaginary coherence can avoid spurious results caused by the algorithm leak-
age. However, its intensity value is affected by the algorithm leakage. In this section,
we introduce a modified form of the imaginary coherence whose intensity values are
unaffected by the algorithm leakage. Let us define the corrected imaginary coherence
as
(ˆ)
ʾ
=
1
2
.
(7.29)
−
(ˆ)
,
ʾ
ʾ
Let us express the estimate of
, such that
˃
T
˃
S
(ˆ)
ʾ
=
1
=
−
˃
T
˃
S
.
−
(ˆ)
2
2
2
|
˃
T
|
|
˃
S
|
Then, considering
˃
T
˃
S
=
d
1
d
2
)
˃
T
˃
S
,
d
1
|
˃
T
|
2
d
2
|
˃
S
|
2
+
+
(
+
1
(7.30)
and using Eqs. (
7.19
) and (
7.20
), we derive
2
−
˃
T
˃
S
−
˃
T
˃
S
=
(
2
2
2
2
|
˃
T
|
|
˃
S
|
1
−
d
1
d
2
)
|
˃
T
|
|
˃
S
|
.
(7.31)
