Information Technology Reference
In-Depth Information
(
)
(
)
multiplying it by
2
, that is,
a
=
x
+
x
/
2
, similarly
a
=
x
+
x
/
2
,
1
1
2
2
3
4
and so on. In a general form, it is given by
=+
, where
m
is the vector size [19]. The other subsignal is known as the fi rst fl uctuation
of the signal
x
and it is denoted as:
a
x
x
2
m
/2
2
m
1
2
m
(
)
1
d
=
d
,
d
,
,
d
and is calculated
by taking the difference between the fi rst pair of values of
x
,
1
2
m
/
2
(
x
−
x
)
/
2
and
1
2
then is multiplied and divided by
2
, and so on. The fi nal expression can
be written as
.
After applying the DWT two vectors are obtained, which are
approxi-
mations
and
details
, with a length of half the original vector. Finally, con-
tinuing the recovery of the vector,
d
=
x
−
x
2
m
/
2
2
m
−
1
2
m
a
+
d
a
−
d
a
+
d
a
−
d
⎧
⎫
[]
f
n
=
1
1
,
1
1
,
,
n
/
2
n
/
2
,
n
/
2
n
/
2
(2)
2
2
2
2
a
d
in Eqs. (6) and (7) can be inter-
We note that the terms
and
ε
=
a
+
+
a
+
d
+
+
d
preted as follows
,
(
)
1
1
1
n
/
2
1
n
/
2
a
d
2
2
f
+
f
f
−
f
f
2
+
2
f
f
+
f
2
2
f
2
1
−
2
f
f
+
f
2
2
⎡
⎤
⎡
⎤
2
1
2
2
(3)
a
+
d
=
1
2
+
1
2
=
1
1
2
+
1
2
=
f
+
f
⎣
⎦
⎣
⎦
1
1
2
2
2
2
and similarly for each set of vectorial
approaches
and
details
[19]. So,
the conservation of energy in wavelets is mentioned, the factor
12
is
mentioned too [20, 21]. By applying the steganographic algorithm, it is
necessary to use a scaling factor, but as the work is with an 8-bit RGB im-
age, this scaling factor is closely related to energy conservation applied to
wavelet theory for grayscale images as shown in most applications. How-
ever, for any space color we propose the following scaling factor [21],
12
j
(4)
where
j
is directly dependent on the number of bits that integrate the image
[20, 21].
The most common approach of the wavelet decomposition is to de-
compose an image to extract energy values for all subbands as features
for the subsequent classifi cation [21]. It is suitable to select a set of sub-
bands for sparse representation in image classifi cation applications. For
a better classifi cation of the results, it is desired that the energy features
Search WWH ::
Custom Search