Digital Signal Processing Reference
In-Depth Information
analysis.
The
objective
quality
measures
are
defined
by
the
following
formulas:
N
M
L
1
NML
F
l
RMSE
=
1
(
F
l
(
i, j
)
−
(
i, j
))
2
,
i
=
1
j
=
1
l
=
(12.83)
i
=
1
j
=
1
l
=
1
(
F
l
F
l
2
(
i, j
)
−
(
i, j
))
NMSE
=
,
i
=
1
j
=
1
l
=
1
F
l
(
i, j
)
2
10 log
,
i
=
1
j
=
1
l
=
1
F
l
2
(
i, j
)
SNR
=
i
=
1
j
=
1
l
=
1
(
F
l
F
l
(
i, j
)
−
(
i, j
))
2
20 log
,
255
RMSE
PSNR
=
(12.84)
F
l
F
l
where
M
,
N
are the image dimensions, and
denote
the
l
th component of the original image vector and its estimation at pixel
position
(
i, j
)
and
(
i, j
)
,respectively. The NCD perceptual measure is evaluated over
the uniform
L
∗
u
∗
v
∗
color space. The difference measure NCD is defined as
(
i, j
)
i
=
1
j
=
1
E
i
=
1
j
=
1
E
∗
L
∗
)
2
u
∗
)
2
+
(v
∗
)
2
]
1
/
2
,
NCD
=
,
E
=
[
(
+
(
(12.85)
2
]
1
/
2
,
2
2
E
∗
=
L
∗
)
u
∗
)
+
(v
∗
)
[
(
+
(
E
is the perceptual color error and
E
∗
is the
norm
or
magnitude
of the
uncorrupted original color image pixel in the
L
∗
u
∗
v
∗
space.
Results obtained using the new filtering techniques are compared with the
filtering algorithms from Table 12.3 in Table 12.4 and Table 12.5. For the de-
noising of both contaminated
LENA
images with the new filtering techniques,
predefined parameter values were used: path length
where
2.
For all evaluated filters, 10 iterations were performed, and the best result in
terms of PSNR is presented in Table 12.4 and Table 12.5.
Figure 12.10 depicts the efficiency of the proposed algorithms (DPAL and
FDPA) in terms of NCD quality measure, as a function of the design param-
eters
η
=
2,
β
=
13,
α
=
1
.
.Itcan be easily noticed that both algorithms yield compara-
ble results with a flat minimum of NCD, which ensures their robustness to
optimal parameter settings. The parameter
α
and
β
ensures quick convergence of
the proposed filters to a stable state, and as can be seen in Figure 12.10, good
results can be obtained for any
α
in the range [1
,
2].
Figure 12.16 presents the efficiency of the DPAL filter applied to a scanned
road map. The new filtering technique was able to remove the raster struc-
ture, while image details such as roads, names, etc. were preserved and
α
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