Image Processing Reference
In-Depth Information
lower than the moduli 2
n
-1 and 2
n
+1. Hence, (Molahosseini et al., 2010) have been
substituted 2
2n
+1 with well-formed number 2
2n
+1
-1 that results in introducing the large
dynamic range four-moduli set {2
n
-1, 2
n
, 2
n
+1, 2
2n
+1
-1}. Besides, they have used New CRT-II
to design an efficient reverse converter for this moduli set as described below.
With considering
P
1
=2
n
,
P
2
=2
2
n
+1
-1,
P
3
=2
n
+1,
P
4
=2
n
-1, and the New CRT-II formulas (15)-
(17), we have the following conversion equations (Molahosseini et al., 2010)
nn
21
n
XZ
2(2
1)2(
YZ
)
(42)
2
n
21
Where
nn
1
Zx
22 (
x x
)
n
(43)
1
2
1
21
2
1
n
n
1
Yx
(2
1) 2
(
x x
)
(44)
3
4
3
n
21
Simplified versions of these equations have been computed in (Molahosseini et al., 2010).
Here, we briefly review the final simplified equations. First, (43) can be rewritten as
Zx
2
n
H
(45)
1
Where
Hvv
(46)
1
2
2
21
n
1
vx
xxx
x x
(47)
1
2,
n
1
2,1
2,0
2,2
n
2,
n
1
2,
n
n
n
1
vx
xx
1 1
(48)
2
1,
n
1
1,1
1,0
n
1
n
Next, for simplifying (44) we have
Yx
(2
n
1)
K
(49)
3
Where
Kv v
(50)
3
4
21
n
vxx
xx
(51)
3
4,0
4,
n
1
4,2
4,1
n
if
x
0
xx
xx
3,0
3,
n
1
3,2
3,1
3
,n
v
(52)
n
4
0
if
x
1
111
3
,n
n
1
Eventually, (42) can be computed as below