Digital Signal Processing Reference
In-Depth Information
Assuming that the pixel
F
x
at the position
x
=
p
0
is the pixel under consid-
p
1
, the filter output
F
x
is given
eration, with
F
y
representing the pixel at
y
=
as
p
0
w
∗
p
0
,p
1
·
F
x
=
F
p
0
=
x
w
∗
(
x
w
∗
(
)
·
=
)
·
=
x, y
F
y
x, y
F
y
F
p
1
,
p
1
∼
y
⇔
y
∼
(12.73)
and combining this with Equation 12.72 gives
exp
−
β
·
η
p
0
,p
1
,p
2
,
,p
η
{
W,
...
,p
η
}
p
2
,p
3
,
...
F
x
=
F
p
0
exp
−
β
·
η
p
0
,p
1
,p
2
,
,p
η
·
=
{
F
p
1
W,
...
,p
η
}
p
1
,p
2
,
...
p
1
∼
p
0
p
0
w
∗
p
0
,p
1
·
=
F
p
1
.
(12.74)
p
1
∼
Using the notation from Sections 12.3 and 12.2 and Equation 12.20, we can
formulate Equation 12.74 as
n
F
0
=
1
w
k
F
k
,
(12.75)
k
=
w
k
, the normalized weighting coefficients, play the role of the gener-
alized conductivity coefficients from Section 12.3, and
F
k
are the neighbors of
F
0
, which is the central pixel in the filter mask
W
.
The general form of the AD scheme based on the digital paths can be written
where
as
n
F
0
=
(
−
λ
∗
)
F
0
+
λ
∗
1
w
k
F
k
,
1
(12.76)
k
=
or using the iterative notation, as
n
F
t
+
1
0
−
λ
∗
)
F
t
0
+
λ
∗
1
w
k
F
k
.
=
(
1
(12.77)
k
=
λ
∗
=
λ
k
=
0
c
k
(Equation 12.20), it is possible to obtain
the classical form of the AD scheme defined by Equation 12.15.
Figure 12.9 shows the dependence of PSNR on the
By using the relation
λ
∗
and
K
values for the
color
LENA
image contaminated by impulsive and mixed noise for the classic
multichannel AD scheme and the new DPAF filter defined by Equation 12.75.
Especially interesting is the behavior of the plots as a function of
λ
∗
.Ascan
be seen, for images contaminated by a noise process of high intensity, the
maximum of PSNR is obtained for
λ
∗
very close to 1, which means that it is
favorable to omit the central pixel while calculating the weighted average in
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