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In-Depth Information
1
2
min
ʻ
WWQ
+
−
2,1
2
F
W
W
, then the i-th column of
W
is
is
q
−
ʻ
i
qif
,
ʻ
<
q
i
i
*
Wi
(:, )
=
q
i
0,
otherwise
.
Algorithm 1.
Solving Eq.(2) by Inexact ALM
Input:
data matrix
X
, parameter
ʻ
Initialize:
ZJ
==
0
,
E
=
0
,
Y
=
0
,
Y
=
0
,
1
2
−
6
10
μ
=
10
max
=
10
ˁ =
1.1
ʵ
=
10
−
8
,
,
,
.
u
while
not converged do
1.
fix the others and update
J
by
1
1
2
(
)
J
=argmin
J
+−+
J
Z
Y
μ
2
μ
*
2
F
2.
fix the others and update
Z
by
(
)
(
)
−
1
(
)
t
t
t
t
Z
=+
I XX
XX
− ++ −
XE J
XY Y
μ
1
2
3.
fix the others and update
E
by
ʻ
1
(
)
2
E
=
arg min
E
+
E
−
X
−
XZ
+
Y
μ
1
2,1
μ
2
F
4.
update the multipliers
(
)
YY
=+ − −
μ
X ZE
1
1
(
)
5.
update the parameter
YY
=+ −
μ
ZJ
2
2
(
)
by
μ
=
min
ˁμ
,
max
μ
u
6.
check the convergence conditions
XXZE
ʵ
∞
−− <
and
ZJ
−<
ʵ
end while
3
The Proposed Method
Given a pair of multi-temporal remote sensing images
X
and
X
, we denote it as
2
[
]
12
Xxx
=
,
.Both
x
and
x
are column vectors which are reshaped by
X
and
X
. For change detection, the majority of the images
X
and
X
is usually the
unchanged areas, and thus the data of unchanged areas is low-rank. Moreover, the
data of changed areas can be viewed as sparse. Therefore, we use LRR to decompose
2
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