Digital Signal Processing Reference
In-Depth Information
Z
In the first step, given the reference block
and the candidate match block
x
R
Z
, the SSIM index is defined as
x
R
(2
μμ
+
C
)(
σ
+
C
)
Z
Z
1
Z
Z
2
SSIM Z
(
,
Z
)
=
x
x
x
x
,
R
R
(3)
x
x
2
2
2
2
(
μμ
++
C
)(
σσ
++
C
)
R
Z
Z
1
Z
Z
2
x
x
x
x
R
R
μ
μ
Z
Z
respectively,
σ
where
,
is the mean intensity of
and
,
Z
Z
x
Z
x
R
x
R
x
R
σ
σ
is the standard deviation,
is the correlation coefficient corresponds to
Z
Z
Z
x
x
x
R
μ
Z
-
C
and
Z
μ
the cosine of the angle between the vectors
-
and
,
x
Z
Z
R
x
R
x
2
2
C
are small constants which eliminates unstable results when either
(
μμ
+
)
Z
Z
x
x
R
(
σσ
2
+
2
)
or
is very close to zero.
Z
Z
x
x
R
The SSIM index that values between -1 and 1 achieves its maximum value of 1
only if the two compared blocks are exactly the same. In order to restrict it between 0
and 1, SSIM index is taken by absolute value.
The bigger is the value of SSIM, the structure between the reference patch and its
corresponding ones is more similar. If the SSIM of the neighboring patches is greater
than 0.4, they are allowed to participate in the weighted operation, which is shown as
SSIM Z
(
,
Z
)
>
.4
(4)
x
x
R
For reducing the effect of noise, we propose an operation about weight refinement
based on SSIM, which is written as
−
||
fZ
(
)
−
fZ
(
) ||
2
2
+
SSIMZ Z
(
,
)
x
x
x
x
wi j
( , )
=
exp(
)
R
R
(5)
()
h
δ
2
If the SSIM's value of all neighbourhoods is lower than 0.4, we use the SNIG model
to adjust their coefficients in DT-CWT domain. In order to obtain the patch with less
noise, a Bayesian MAP estimator is developed by adopting the SNIG PDF for
modeling the details of image and using the GGD PDF for modeling the noise. The
SNIG PDF is given by [7]
n
K
(
αδ
δ
2
+
f
2
)
Pf
()
=
A
1
f
(6)
2
+
f
2
αδ
exp(
αδ
)
A
=
K
is the modified Bessel function of the second
where
,and
π
α
δ
kind.
controls the shape of SING model.
is a scale parameter. In [8], the GGD
PDF is expressed as
x
β
GG
,
( )
x
=
C
(
σβ
,
) exp{ [
−
ασβ
(
,
)
] }
(7)
σβ
X
X
x
