TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5408 ~ 54
1
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.521
8
5408
Re
cei
v
ed
No
vem
ber 2
7
, 2013; Re
vi
sed
Jan
uar
y 24, 2
014; Accepte
d
February 1
8
, 2014
A New Digital Image Hiding Algorithm Based on
Wavelet
Packet Transform and Singular Value
Decomposition
Yueli Cui
1
, Shiqing Zhan
g
2
, Zhigang Chen
3
, Wei Zheng
4
1,2,
3
Colle
ge of Ph
y
s
ics & Elec
tronic Eng
i
n
eer
ing T
a
izhou U
n
iversit
y
, T
a
izho
u, Chin
a
4
Colle
ge of Ele
c
tronic an
d Informatio
n
Engi
n
eeri
ng, Heb
e
i
Univers
i
t
y
, Ba
o
d
in
g, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: cui
y
ue
li@tzc.edu.cn
1
, zsq@t
zc.edu.cn
2
, czg@tzc.edu.cn
3
,
w
e
i
z
he
ng
79
9@y
a
ho
o
.
co
m
4
A
b
st
r
a
ct
Th
e
pa
pe
r
p
r
e
s
e
n
t
s a ne
w d
i
g
i
ta
l
ima
g
e
hi
d
i
ng
al
g
o
r
i
t
hm
b
a
se
d
o
n
wa
ve
le
t p
a
c
ke
ts tra
n
s
fo
rm and
sing
ular va
lue
deco
m
positi
on.
T
he low
-
frequency sub-
ba
n
d
of
w
a
velet pa
ckets transform has stron
g
anti-
ja
mmin
g ca
pac
ity an
d the
sin
gul
ar va
lue
h
a
s
very stro
n
g
s
t
ability. Th
e pr
esente
d
a
l
g
o
rit
h
m i
m
p
l
e
m
e
n
t
s
bit
pla
ne dec
o
m
p
o
sitio
n
on the s
e
cret imag
e an
d w
a
vele
t pack
e
t deco
m
p
o
siti
on on the carr
i
e
r image. T
h
e
n
,
it
hid
e
s the
b
i
t
pla
nes w
i
th
i
m
p
o
rtant
infor
m
ati
o
n
into
th
e si
ngu
lar v
a
l
ue
matrix of t
he
low
freq
ue
ncy
coefficie
n
t
mat
r
ix, an
d a
l
so
hi
des th
e
bit p
l
a
nes w
i
th s
e
co
ndary
infor
m
ati
on
into th
e r
e
ma
in
der s
ub-b
a
n
d
matrix
w
i
th hi
g
her e
n
tropy
en
ergy. T
he
hi
din
g
loc
a
ti
o
n
is
a
daptiv
ely
deter
mi
ne
d by t
he c
a
rrier
i
m
ag
e. T
h
e
exper
imenta
l
r
e
sults i
n
d
i
cate
that, the
prop
osed
i
m
a
ge
hi
din
g
a
l
gor
ith
m
has stro
ng r
o
b
u
stness
and
a
n
ti
-
attack, and it al
so has go
od i
n
visibi
lity an
d bi
g capa
bil
i
ty.
Ke
y
w
ords
: i
m
a
ge
hid
i
ng,
sing
ular v
a
l
ue d
e
co
mp
os
iti
on, w
a
vel
e
t packets tra
n
sform, b
i
t p
l
an
e
deco
m
positi
on,
entrogy en
erg
y
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
With the rap
i
d developm
e
n
t of multimedi
a and the i
n
crea
sing b
a
ndwi
d
th of network,
digital ima
g
e
s
a
r
e
be
comi
ng the
main
media fo
rm
o
f
the present
informatio
n society. Howe
ver,
the proble
m
s of informatio
n security su
ch
as
illegal
copyin
g, mod
i
fying and
pirating of
digital
image
s a
r
e i
n
crea
singly
common. T
he
probl
em o
n
h
o
w to
give a
n
effective m
e
thod fo
r ima
ge
encryption ha
s be
come a v
e
ry active re
search fi
eld no
wad
a
ys [1-2].
Some encryption algo
rith
ms
have b
een
freque
ntly cracked
in
re
ce
nt years. Ima
g
e
hidi
ng i
s
an
impo
rtant m
e
thod to
conf
use
illegal de
stro
yer so a
s
to
play a prote
c
ting functi
on.
The main i
d
e
a
of image hi
ding is to hi
d
e
a
se
cret imag
e
into another carrier ima
g
e
[2].
Image hiding meth
o
d
s ca
n be di
vided into either
spatial
-
do
mai
n
or fre
que
ncy-domai
n. The algo
rithm
s
based on
sp
atial-do
main
are di
scu
s
se
d in
the refe
ren
c
e
s
[3-4]. In these
algo
rithm
s
, the hi
dde
n
informatio
n i
s
al
ways sto
r
ed in th
e lea
s
t
signifi
cant bit
s
of the pixel
s
of the
carri
e
r ima
ge. Sp
atial-do
main t
e
ch
niqu
es a
r
e ea
sy reali
z
ed,
but have
po
or
stability.
More
over, hi
dden
inform
a
t
ion is ea
sily
dama
ged
fo
r
spatial
-
dom
ain
techni
que
s. In co
ntra
st, freque
ncy-dom
ain hidin
g
alg
o
rithm
s
are b
e
tter in
term
s of rigidity ro
b
u
st
and cond
uciv
e to ensu
r
ing
se
curity of se
cret info
rmati
on [5-13].
This pa
per
prop
oses a
new an
d eff
e
ctiv
e im
age
hidin
g
al
gorithm. The
propo
sed
method i
s
an
integratio
n of
several te
chn
i
que
s in
cludi
n
g
bit
pl
ane de
comp
ositio
n, sing
ular
valu
e
decompo
sitio
n
and wavel
e
t packet transfo
rm. Th
e experim
en
tal results in
dicate that
th
e
prop
osed
alg
o
rithm h
a
s st
rong
ro
bu
stn
e
ss an
d a
n
ti-attack,
and it
also
ha
s g
o
od invisi
bility and
big capability.
2. The Theor
etical Ba
sis of Propos
ed Algorithm
2.1. Sigular
Value Dec
o
mposition
Takin
g
the i
m
age mat
r
ix
A as
'
M
M
s
non
-n
egative matri
x
, rank
(A
)=
r,
r
，
≤
M
then
resolving this
to Matrix
A
'
s si
ngula
r
value i
s
as follo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A New Di
gital
Im
age Hiding Algorithm
Base
d on Wavelet Packet Tran
sform
and
… (Yueli Cui)
5409
1
r
TT
ii
i
i
A
USV
v
(1)
In the above formul
a,
11
1
...
,
...
,
...
mm
m
uv
UV
S
uv
(2)
The sin
gula
r
value sati
sfie
s the equ
atio
n:
12
1
...
...
0
rr
m
(3)
Non
-
zero
sin
gular value
s
are
equ
al to
matrix’s
ra
nk.
F
r
om
the
above
we
see th
at
the SVD un
it also
satisfies:
ii
i
Av
and
.
TT
ii
i
A
v
Gen
e
rally spea
ki
ng, matrix A
has
many mino
r
sing
ular val
u
es, so the m
a
trix can
us
e
a relatively lowe
r matrix
approximation.
Suppo
sing
kr
, the approximate matrix
~
1
T
k
k
v
A
ii
i
i
,
~
EA
A
(err
or mat
r
ix
). Matrix
A’s si
ngul
ar
value is the
averag
e n
on-negative
real
numb
e
r
and
is al
so
uniq
ue. The
si
ng
ula
r
value
ha
s relative
sta
b
ility
toward
s disturban
ce
and un
chan
geabl
ene
ss towards
mat
r
ix
transfo
rmatio
n. In linear
algeb
ra, the
matrix feat
ure value
sho
w
s th
e matri
x
feature, while
the matrix singula
r
value
is better t
han it
s fe
ature valu
e in
manifestin
g i
t
s feature. Th
e
Image matrix
singula
r
value refle
c
ts the image’
s
＂＂
energy feature
w
hile its corre
s
pon
di
ng
sing
ular ve
ct
or reflect
s
the
image’
s “g
eo
metrical featu
r
e”. Sin
c
e the
image’
s si
ng
ular valu
e is
not
very sensitive to the
ch
ange of image
graynes
s, its very slight alterati
on
will not
affect the i
m
age
vision qu
ality.
2.2. Wav
e
let Packe
t De
co
mposition
Wavelet
pa
cket
de
comp
o
s
ition
provid
es m
o
re mul
t
i-re
solutio
n
analysi
s
tha
n
wavel
e
t
decompo
sitio
n
. It furthe
r d
e
com
p
o
s
e
s
t
he hi
gh f
r
eq
u
ency
pa
rt. Fi
gure
1
an
d Fi
gure
2
sho
w
the
p
r
oc
es
s
.
Figure 1. Two
Level Wavel
e
t Packet
Decomposition
Figure 2. Dia
g
ram of Wavelet Packet
Decomposition
The lo
w freq
u
ency p
a
rt con
t
ains
the m
a
i
n
energy of image. When
the
se
cret informatio
n
hide
s into
this re
gion, it
ca
n
re
si
st
kind
s
o
f
atta
cks such
as the
filterin
g, crop
ping,
rotating a
nd
so
on, an
d it h
a
s
goo
d
rob
u
s
tne
ss.
The
high frequ
en
cy
part
co
rre
spo
n
d
s
to th
e imag
e d
e
tails.
The hidd
en i
m
age can obt
ain better invi
si
bility, but has poo
r ro
bu
stness.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5408 – 54
13
5410
3. The Propo
sed Algori
t
h
m
Descrip
tio
n
3.1. The Preproces
sing
of Secre
t
Image
Firstly, imple
m
entation of
chao
s en
cry
p
tion
is pro
c
essed on th
e se
cret ima
ge, then
operation
of bit plane
de
compo
s
ition i
s
perfo
rme
d
o
n
the e
n
crypted ima
ge. Th
e si
ze
of pla
n
e
can
not be
co
me greater th
an coefficie
n
t matrix a
fter t
w
o level
wav
e
let packet decom
p
osition of
the carrie
r im
age.
3.2. The Processing o
f
Carrier Image
By implement
ing wavel
e
t p
a
cket de
com
positio
n on th
e ca
rrie
r
ima
ge, we
can g
e
t image
coeffici
ent m
a
trix
t
WP
of 16 different frequ
e
n
cy su
b-band
s as
sho
w
n i
n
Figure 2. Then we take
operation
of
sing
ular valu
e de
com
p
o
s
ition o
n
the
m
a
trix
t
WP
acco
rdin
g to the
form
ula (1),
wh
ere
2
t
=
L
L
2
L
H2
HL
HH2
、、
、
and we ca
n g
e
t the followin
g
formula.
T
tt
t
t
WP
=
U
S
V
(4)
After cal
c
ulati
ng of the ene
rgy entro
py o
f
t
he 12 rema
ining respe
c
tive coefficie
n
t matrix,
then we
sort
them from
larger to
sm
all
accord
ing
to
the ene
rgy e
n
tropy. Fin
a
lly we
can
get
the
sorte
d
coefficient mat
r
ix
,
g
WP
whe
r
e
,
t
=
VV2
V
W
2
F
G2
GG2
、、
、
and satisfie
s
the followin
g
requi
rem
ents
1g
1
2
and
g
g+
1
WP
WP
. It generate
s
a si
gnature vect
or whi
c
h i
s
use
d
to
extract the se
cret ima
ge.
3.3. Hiding Proces
s of th
e Secret Ima
g
e
Step 1:
Hidi
ng the
main
i
n
formatio
n bit
plan
es
B
k
(
)
k=
7
6
5
4
，，
，
into the
sing
ular value
matrix
t
S
as
follows
:
tt
k
t
W=
S
+
B
(5)
Firstly, by modifying the singula
r
va
lue
s
, the transfo
rmation of the modified
t
W
is taken
as
follows
:
T
tt
k
t
1
t
1
t
1
t
W
=
S+
B
U
SV
(
6
)
We can use the new si
ng
ular value m
a
trix
t1
S
to recons
truc
t wavelet c
oeffic
i
ent
'
t
WP
according to the formul
a (4
)
.
'
T
tt
t
1
t
WP
=
U
S
V
(
7
)
Whe
r
e
2
t
=
L
L
2
L
H2
HL
HH2
、、
、
,
'
t
WP
will be used to reconstruct
the carrier image hidden the
se
cret ima
ge.
Step 2: Hidin
g
the se
con
d
a
ry informatio
n bit plane
(3
)
Bk
=
k
，
2
，
1
，
0
into the sing
ular
value matrix
g
WP
as
follows
:
'
gg
k
k
WP
=
W
P
+
B
(
8
)
Whe
r
e
g
=1
,
2
,
3
,
4
Step
3: Wav
e
let
coefficie
n
ts whi
c
h are
obt
ai
ned
from step 1
a
nd step 2
i
s
use
d
to
recon
s
tru
c
t the carrie
r imag
e contai
ns th
e se
cret ima
g
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A New Di
gital
Im
age Hiding Algorithm
Base
d on Wavelet Packet Tran
sform
and
… (Yueli Cui)
5411
3.4. Extrac
tion of the Se
cret Image
Step 1: By ta
king im
pleme
n
tation of 2 le
vel wavelet p
a
cket de
com
positio
n on th
e hidde
n
image,
we
can g
e
t imag
e coefficie
n
t matrix
t
H
WP
,
where parameter t s
a
tis
f
y the following
conditions.
''
2
'
'
'
'
2
'
2
'
'
'
'
'
'
'
'
'
t
L
L
2
L
H
2
H
L
H
H
2
V
V
2
V
W2
WV
WW
N
N
N
M
MN
MM
G
G
G
F
F
G
2
G
G
2
、、
、
、
、
、
、
、
、
、
、
、
、
、
、
Step 2:
Implementation of t
he sin
gula
r
value de
co
mp
osition o
n
co
efficient matri
x
t
HW
P
is
perfo
rmed.
'
A'
'
T
tt
t
t
=U
S
V
(9)
t1
V
and
t1
U
in the formula (6
) is u
s
ed to cal
c
ulat
e the
'
t
W
as
follows
:
''
T
tt
1
t
t
1
W=
U
S
V
(10
)
The followi
ng
formula (1
1)
sho
w
s bit pla
ne matrix extracted.
'(
'
)
/
kt
t
t
BW
S
(11
)
Whe
r
e
''
2
'
'
t
L
L
2
L
H
2
H
L
HH2
、、
、
，
k=
7
6
5
4
，，
，
Step 3: Usin
g
marke
d
ve
ctor a
nd
matrix
to dete
r
min
e
co
efficient m
a
trix
g
HWP
co
ntaini
ng
bit planes. We can get the
rest matrix of the bit
planes by using the formula (8).T
he formula
(1
2)
descri
b
e
s
the
process.
'(
)
/
gg
k
k
B
H
WP
WP
(12
)
Whe
r
e
=
3
,
2
,1
,0
k
Step 4: All th
e bin
a
ry
bit p
l
ane
s i
s
com
b
ined
to
re
co
ver the
g
r
ay i
m
age
an
d to
extract
the se
cret im
age.
4. Experimental Re
sult
Takin
g
512
× 5
12
gray
woma
n im
ag
e a
s
the
carrier im
age,
an
d 12
8×128
g
r
ay ma
p
image a
s
the se
cret ima
ge.
PSRN is u
s
e
d
to
quantitatively measu
r
e
the image hi
dden invi
sible
.
The no
rmali
z
ed cro
s
s-correlation coefficient
(NC) is used to me
asu
r
e the
si
milarity
betwe
en th
e
se
cret
imag
e
and th
e o
r
igin
al secret im
a
ge. It is al
so
use
d
to te
st t
he
robu
stne
ss of
the algo
rithm
unde
r attacki
ng. The o
r
igi
nal va
lue of secret image
PSRN=52.1
7
3
, NC=1
with
out
attacki
ng.
Figure 3 sho
w
s th
e proce
ss
of the hidi
ng and
extra
c
ting alg
o
rith
m. The se
cre
t
image is
resto
r
e
d
with
good robu
stn
e
ss and invi
si
ble witho
u
t attacki
ng.
(a) Car
r
ie
r
im
age
(b) Se
cret image
(c
)
Hid
den im
age
(d) Re
store
d
image
Figure 3. The
Hiding a
nd Restored Imag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5408 – 54
13
5412
With implem
entation of
variou
s
attacki
ngs o
n
the
hidde
n imag
e su
ch a
s
croppi
ng,
filtering, rotati
on and
so on,
the extracted
im
age after a
ttackin
g
is sh
own in Fig
u
re
4.
(
a
)
C
r
op
p
i
ng
1/4
(
b
)
C
r
op
p
i
ng
1/8
(c) Gau
s
sian
noise
(d) Rotation
9
0
0
(e) Rotation
-
9
0
0
(f) Rotatio
n18
0
0
(g) L
o
w
-
pa
s
s
filter
(h) High
-pa
s
s
filter
(i) Medi
an filtering
Figure 4. The
Extracted Image after the
Attacking
4.1. Quantita
tiv
e
Analy
s
is
of Robu
stn
e
ss
In ord
e
r to
evaluate the
robu
stne
ss of
the pro
posed al
gori
t
hm, we im
plement
variou
s
attacking
s
on the
hidde
n
image
and comp
ar
ed with the result
s of Referen
c
e [14] a
nd
Referen
c
e [1
5]. The experi
m
ental re
sult
s are
sho
w
n i
n
Table 1 an
d
Table 2.
Table 1. Co
m
pari
s
on of NC Values bet
ween the Pro
p
o
se
d Algorith
m
and Refe
re
nce [14]
Attacking
Pattern
Proposed
Ref
[14]
Gaussian noise
0.01
1
0.943
Cropping
1/4
0.99697
0.3869
Median filtering
3×3
0.99857
0.9561
Table 2. Co
m
pari
s
on of NC Values bet
ween the Pro
p
o
se
d Algorith
m
and Refe
re
nce [15]
Attacking
Pattern
Proposed
Ref
[15]
Gaussian noise
0.01
1
0.970
Rotation
-90
0.99923
0.943
180 1
0.980
90 0.99948
0.947
Cropping
1/8
0.9992
0.888
1/4 0.99697
0.815
1/2 0.96836
0.701
Median filtering
3×3
0.99857
0.986
5×5 0.99704
0.982
7×7 0.9811
0.965
Lo
w
-
pass filtering
Gauss ambiguit
y
0.99232
0.911
High-pass filtering
Sharpening
0.99471
0.955
Acco
rdi
ng to
the re
sult
s in the a
b
o
v
e tables,
we
can
see
that the p
r
opo
se
d
algorith
m
ha
s better rob
u
st
ness un
der
ki
nds of attacki
ng.
4.2. Quantita
tiv
e
Analy
s
is
of In
v
i
sibility
Another
imp
o
r
tant evalu
a
ting indi
cato
r t
o
mea
s
u
r
e th
e
image
hidi
n
g
effect
is
an
alysis
of
invisibility. From the Tabl
e
3, We can concl
ude that t
he propo
se
d algorith
m
ha
s a highe
r PSRN
value with good invisibility.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A New Di
gital
Im
age Hiding Algorithm
Base
d on Wavelet Packet Tran
sform
and
… (Yueli Cui)
5413
Table 3. Qua
n
titative Evaluation of Pro
p
se
d Algorith
m
Algorithm
Proposed
Ref [14]
Ref [15]
PSRN/DB
52.175
50.7049
30.36
5. Conclusio
n
In the pa
pe
r
a ne
w di
gital
image
hidin
g
algorith
m
ba
sed o
n
wavele
t packet
s
tra
n
sform
and sing
ular value
de
co
m
positio
n
was prop
osed.
Th
e expe
riment
al re
sult
s a
r
e
sati
sfied
with
good
rob
u
stn
e
ss an
d invisibility. The algorithm
ca
n
effectively
re
sist vario
u
s i
m
age
p
r
o
c
e
s
sing
and attackin
g. The usi
n
g
of chaotic
e
n
cryptio
n
alg
o
rithm imp
r
o
v
es the safe
ty coefficient
of
comm
uni
cati
on and the a
b
ility of anti-attack.
Ackn
o
w
l
e
dg
ements
This
wo
rk is
sup
porte
d by
Nation
al
Nat
u
ral S
c
ien
c
e
Found
ation
o
f
China
un
de
r G
r
ant
No.61
203
257
, Zhejiang
Provinci
al Natural S
c
ien
c
e Fo
und
ation of Chi
n
a unde
r G
r
ant
No.Y111
105
8
，
and the key
proje
c
t of Taizho
u Unive
r
si
ty under Gra
n
t
No. 2011Q
N13 .Than
ks to
Dr Zhi
gan
g Che
n
Dr Shi
q
ing Zha
ng
and from th
e membe
r
s
of image re
search team
for
discu
ssi
on
s a
bout the algo
rithm. Thanks
also
to an
ony
mous
revie
w
ers fo
r their
comment
s.
Referen
ces
[
1
]
Hu Yuc
h
e
n
,
Li
n Min
h
u
i
.
Secu
re I
m
age
Hi
di
n
g
Sch
e
me B
a
s
ed U
p
o
n
Vect
o
r
Quant
iz
at
ion.
Internati
ona
l
jour
nal of p
a
ttern recog
n
itio
n and artific
i
al i
n
telli
ge
nce.
20
04
;
18(6):
111
1-1
130.
[
2
]
Wang H
a
ih
ui.
A Ne
w
m
u
lt
i
w
avel
et
-base
d
A
ppro
a
ch t
o
im
age f
u
s
i
o
n
.
Jo
urna
l of Math
e
m
atic
al
imag
e
and vis
i
on
.
2
0
0
4
;
21(2):
17
7-1
92.
[3
]
D
C
Wu
, WH
T
s
a
i
.
Image
H
i
din
g
In
Sp
ati
a
l D
o
ma
in
Usi
ng
an
Image
Differenc
ing
A
ppro
a
ch.
In
proce
edi
ngs of
conf
erenc
e on
comput
er visi
o
n
,
graph
ics,
an
d imag
e proce
ssing.
19
98;
28
0-28
7.
[
4
]
Bru
y
nd
onck
x
,
Quisqu
at
er,
Macq.
Spatia
l Method for C
opyri
ght La
bel
ing of Di
gital
Imag
es
. I
n
proce
edi
ngs of
t
he I
EEE Workshop o
n
No
nli
near
Si
gn
al an
d I
m
age Proce
ssing.
19
95:
45
6-45
9.
[
5
]
Suni
l Le
e,
Ch
ang
D Yoo,
T
on Ka
lker.
Re
versibl
e
I
m
ag
e
Wat
e
rmarking
Based
on I
n
t
eger-t
o-I
n
t
e
ger
Wa
ve
le
t T
r
a
n
s
fo
rm.
IEEE Tra
n
sactions on Inform
at
ion Forensics And Sec
u
rity
.
2007;
2(
3
)
:
321-33
0.
[6]
PalakK Ami
n
, Ning
Liu, P Subbalakshm
i
.
Sta
t
istica
l Atta
ck R
e
silien
t D
a
ta
H
i
d
i
n
g
. Internat
ion
a
l Jour
na
l
of Network Security
.
2007;
5(
1
)
:
112-12
0.
[
7
]
Clif
f
o
rd B
e
rgm
an,
Jen
n
if
er
D
a
vids
on.
Un
itar
y Emb
e
d
d
in
g f
o
r Data
Hid
in
g
w
i
th the SVD.
Procee
di
ngs
of
SPI
E-
T
he Int
e
rnat
i
o
n
a
l So
ciet
y
f
o
r Opt
i
ca
l Engi
neer
in
g.
200
5;
568
1:
61
9-63
0.
[
8
]
Cha
o
chu
n
Liu,
Da
oqi
ng
Da
i,
Ho
ng
Yan.
L
o
cal
discr
imin
ant
w
a
vel
e
t
p
a
cket
co
ord
i
na
t
e
s f
o
r f
a
c
e
re
co
ng
n
i
cition
.
Learn
i
ng r
e
se
arch
.
200
7;
8:
116
5–
119
5.
[
9
]
Wat
s
on AB,
Yang GY,
Solo
mon JA.
Visibi
lit
y
of
w
a
vel
e
t
qua
nt
izat
i
on n
o
ise.
I
EEE T
r
a
n
sact
io
ns
o
n
I
m
age
Process
i
ng.
19
97;
6(8):
1164-
11
75.
[10]
Pi
y
u
T
s
ai, y
u
-c
hen Hu, Hsiu-
L
ien Yeh. Rev
e
rs
ibl
e
image
hidi
ng sc
heme using
predicti
ve codi
ng and
hist
ogr
am shif
t
i
ng.
Sign
a
l pr
oc
essin
g
.
200
9;
89(6):
112
9-1
1
4
3
.
[
11]
Miao Qi,
Y
i
n
g
hua
Lu,
Nin
g
Du.
A n
o
ve
l i
m
age
hi
din
g
a
ppro
a
ch
bas
ed
on c
o
rrel
a
t
i
o
n
an
al
ysis f
o
r
secure mu
lt
imo
dal b
i
omet
rics.
Journ
a
l of
Net
w
o
r
k an
d Com
put
er App
lic
at
ions.
201
0;
33(
3):
247-2
57.
[
12]
Xi
ao
gan
g Wan
g
,
Daomu Zha
o
.
Opt
i
cal ima
ge hi
din
g
w
i
t
h
silhou
et
t
e
re
moval bas
ed
on t
he opt
ic
al
int
e
rf
ere
n
ce pri
n
cipl
e.
Appl
icat
ions-c
entere
d
Rese
arch in o
p
t
ics
.
2012;
51(
6):
686-6
91.
[
13]
Che
ng-Hs
ing
Yang.
I
n
vert
e
d
pat
t
e
rn a
ppr
o
a
ch t
o
im
prove
image
qu
alit
y
of
inf
o
rmat
i
on
hidi
ng
b
y
LS
B
su
b
s
titu
tion
.
Pattern Reco
gn
ition
.
20
08;
41(
8
)
:
2674-2
6
8
3
.
[
14]
Zhang
X,
Zha
ng Guica
ng.
A
n
Adapt
iv
e Di
g
i
t
a
l Wat
e
rmarki
ng Alg
orit
hm
Based o
n
Wavelet
Packet
s
T
r
a
n
s
fo
rm.
Journal of co
mp
uter-aid
ed d
e
si
g
n
&co
m
puter g
r
aph
ics
.
Chin
a.
2007;
1
9
:
931
–93
4.
[
15]
Zhang
Yi,
C
h
e
n
Li-P
in
g,
T
ang
Xi
ang-
ho
ng.
A Di
git
a
l
Wat
e
rmarkin
g
A
l
g
o
rit
h
m B
a
sed
on DWT
an
d
SVD.
Jouna
l of
Hang
z
h
o
u
Dia
n
z
i
Univ
ersity
.
200
7;
27(2).
Evaluation Warning : The document was created with Spire.PDF for Python.