Image Processing Reference
In-Depth Information
6.4.3 I
TERATIVELY
C
LUSTERED
I
NTERPOLATION
The ICI algorithm is a gradient-based optimization method, with the initial point for
the optimization generated through an iterative technique [8]. The ICI algorithm is
implemented in the following steps:
Step 1:
Select algorithm parameters
m
,
e
,andk
max
(their meanings and selections
will be discussed shortly). Let
k
¼
0 and assume
the
initial
condition
.
y
(
0
) ¼
C
y
(
0
)
M
y
(
0
)
Y
y
(
0
)
Step 2:
Update y(k) using the recursion formula
) m
q
E
q
y
(
k
)
y
(
k
) ¼
y
(
k
þ
1
(
6
:
36
)
where
q
E
q
y
(
k
)
¼
2J
k
{
P
[
y
(
k
)]
x
}
(
:
)
6
37
Inserting Equation 6.37 into Equation 6.36 results in
) ¼
y
(
k
) m
J
k
{
P
[
y
(
k
)]
x
}
y
(
k
þ
1
(
6
:
38
)
The term J
k
is the 3
3 Jacobian matrix computed at the kth iteration. It is given by
2
4
3
5
q
Py
1
(
k
)
½
q
Py
1
(
k
)
½
q
Py
1
(
k
)
½
q
C
(
k
)
q
M
(
k
)
q
Y
(
k
)
q
Py
2
(
k
)
½
q
Py
2
(
k
)
½
q
Py
2
(
k
)
½
J
k
¼
(
6
:
39
)
q
C
(
k
)
q
M
(
k
)
q
Y
(
k
)
q
Py
3
(
k
)
½
q
Py
3
(
k
)
½
q
Py
3
(
k
)
½
q
C
(
k
)
q
M
(
k
)
q
Y
(
k
)
The Jacobian matrix J
k
is computed numerically at each iteration using the forward
printer map.
Step 3:
Let k
¼
k
þ
1. If E[y(k)]
< e
or k
>
k
max
, then stop; otherwise go to Step 2.
D
E
a
*
and can be selected to be any
arbitrary small number. The index k
max
is the maximum number of iterations. The
algorithm will stop either when
The parameter
e
is the minimum required
D
E
a
*
is less than
m
or when the number of iterations
reaches k
max
. The step size
controls the rate of convergence and should be selected
to achieve fast algorithm convergence and meet accuracy requirements. The upper
bound for parameter
m
m
is derived in the next section.
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