Image Processing Reference
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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
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