Databases Reference
In-Depth Information
F I GU R E 13 . 14
Sinan image coded at 0.25 bits per pixel using the JPEG algorithm.
Block
i
-
1
Block
i
+
1
p
q
r
[
] [
] [
] [
Block
i
Block
i
+
2
F I GU R E 13 . 15
Source output sequence.
Let us partition the matrix into two
N
/
2
×
N
/
2 blocks,
A
and
B
. Thus
P
=
[
A
|
B
]
=[
|
]
Let
x
i
p
q
, then the forward transform
Px
i
can be written in terms of the subblocks as
B
]
p
q
=
|
X
i
[
A
The inverse transform matrix
Q
can be represented by an
N
×
N
/
2 matrix, which can be
partitioned into two
N
/
2
×
N
/
2 blocks,
C
and
D
.
C
D
=
Q
Applying the inverse transform, we get the reconstruction values
x
:
ˆ
C
D
[
A
B
]
p
q
CAp
+
CBq
x
i
ˆ
=
QX
i
=
QPx
i
=
|
=
DAp
+
DBq
Repeating the process for block
i
+
1weget
C
D
[
A
B
]
q
r
CAq
+
CBr
x
i
+
1
=
ˆ
QX
i
+
1
=
QPx
i
+
1
=
|
=
DAq
+
DBr
