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ar
e
p
r
o
p
o
s
ed
.
T
h
e
b
asic
an
d
co
m
p
ac
t
w
a
v
elet,
w
h
ich
is
p
r
o
j
ec
ted
b
y
Dau
b
ec
h
ie
s
is
an
o
r
th
o
n
o
r
m
al
w
av
e
lets
,
w
h
ic
h
is
d
ef
i
n
e
d
as
Dau
b
ec
h
ies
w
a
v
elet.
I
t
is
co
n
s
id
er
ed
w
it
h
ex
tr
e
m
e
l
y
p
h
a
s
e
an
d
th
e
h
ig
h
e
s
t
n
u
m
b
er
o
f
v
a
n
i
s
h
i
n
g
m
o
m
e
n
ts
f
o
r
a
g
iv
e
n
s
u
p
p
o
r
t
w
id
th
.
Ass
o
ciate
d
s
ca
li
n
g
f
ilter
s
ar
e
m
i
n
i
m
u
m
-
p
h
ase
f
ilt
er
.
Dau
b
ec
h
ies
w
av
e
lets
ar
e
n
o
r
m
al
l
y
u
s
ed
f
o
r
s
o
lv
i
n
g
f
r
ac
t
al
p
r
o
b
lem
s
,
s
i
g
n
al
d
is
co
n
ti
n
u
i
ties
,
etc.
T
h
e
s
y
m
lets
ar
e
alm
o
s
t
s
y
m
m
etr
ical
w
a
v
elet,
w
h
ic
h
is
p
r
o
j
ec
ted
b
y
Da
u
b
ec
h
ie
s
as
m
o
d
i
f
icat
io
n
s
to
th
e
d
b
f
am
i
l
y
.
Dau
b
ec
h
ies
p
r
o
p
o
s
ed
m
o
d
if
i
c
atio
n
s
o
f
h
er
w
a
v
elet
s
th
at
r
aise
th
eir
s
y
m
m
etr
y
ca
n
b
e
in
cr
ea
s
ed
w
h
i
le
r
etain
i
n
g
g
r
ea
t si
m
p
licit
y
.
T
h
e
s
y
m
le
ts
h
a
v
e
p
r
o
p
er
ties
s
i
m
ilar
to
d
au
b
ec
h
ie
s
[
9
]
[
1
0
]
.
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
I
n
th
is
w
o
r
k
,
t
h
e
m
u
r
al
i
m
a
g
e
is
u
s
ed
f
o
r
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
.
T
h
e
Di
s
cr
ete
w
a
v
elet
tr
an
s
f
o
r
m
b
ased
d
ec
o
m
p
o
s
itio
n
w
a
s
p
er
f
o
r
m
ed
o
n
t
h
e
i
m
a
g
e.
S
y
m
l
et
2
,
co
if
let
2
an
d
d
au
b
ec
h
eis2
ar
e
i
m
p
le
m
e
n
ted
f
o
r
d
ec
o
m
p
o
s
i
n
g
t
h
e
m
u
r
al
i
m
ag
e.
L
ev
els1
,
2
,
3
an
d
4
o
f
d
ec
o
m
p
o
s
i
tio
n
ar
e
ad
o
p
te
d
.
A
f
ter
th
e
d
ec
o
m
p
o
s
itio
n
,
Z
er
o
tr
ee
E
n
co
d
in
g
is
e
m
p
lo
y
ed
.
T
h
e
ca
p
ab
ilit
y
o
f
th
e
co
m
p
r
ess
io
n
alg
o
r
it
h
m
s
is
ev
al
u
at
ed
in
ter
m
s
o
f
MSE
,
P
SNR
,
co
m
p
r
es
s
io
n
r
atio
an
d
B
its
p
er
p
ix
el.
T
h
is
is
tab
u
lated
in
T
a
b
le
1
.
T
h
e
Qu
alit
y
o
f
th
e
r
ec
o
n
s
tr
u
cted
i
m
a
g
e
is
m
ea
s
u
r
ed
in
ter
m
s
o
f
m
ea
n
s
q
u
ar
e
er
r
o
r
(
MSE
)
a
n
d
p
ea
k
s
i
g
n
al
to
n
o
is
e
r
at
io
(
P
SNR
)
r
atio
.
T
h
e
ef
f
ec
tiv
e
n
e
s
s
o
f
t
h
e
co
m
p
r
e
s
s
i
o
n
ca
n
b
e
an
al
y
ze
d
u
s
i
n
g
t
h
e
co
m
p
r
es
s
io
n
r
atio
an
d
b
it
s
p
er
p
ix
el.
T
h
e
MSE
i
s
i
m
a
g
e
g
at
t
h
e
d
ec
o
d
er
is
d
ef
in
ed
as:[1
0
]
.
MSE
=
σ
2
=1
/N
*
s
u
m
m
atio
n
o
f
(
f
[
j
,
k
]
-
g
[
j
,
k
]
)
2
(
1
)
w
h
er
e
th
e
s
u
m
o
v
er
j,
k
d
en
o
tes
th
e
s
u
m
o
v
er
all
p
ix
els
in
t
h
e
i
m
a
g
e
an
d
N
is
th
e
n
u
m
b
e
r
of
p
ix
els
in
each
i
m
a
g
e.
Fro
m
t
h
at
th
e
p
ea
k
s
ig
n
al
-
to
-
n
o
is
e
r
atio
is
d
ef
in
ed
as
th
e
r
atio
b
et
w
ee
n
s
i
g
n
al
v
ar
ian
ce
a
n
d
r
ec
o
n
s
tr
u
ctio
n
er
r
o
r
v
ar
ian
ce
.
T
h
e
P
SNR
is
m
ea
s
u
r
ed
in
ter
m
s
of
d
ec
ib
els
(
d
B
s
)
is
g
iv
e
n
P
SNR
=
1
0
lo
g
10
(
255
2
/MSE
)
(
2)
Gen
er
all
y
w
h
e
n
P
SNR
is
40
dB
or
g
r
ea
ter
,
th
en
th
e
ar
ch
iv
ed
an
d
th
e
co
m
p
r
ess
ed
m
u
r
als
ar
e
v
ir
tu
all
y
in
d
is
ti
n
g
u
is
h
ab
le
by
h
u
m
an
e
y
es.
T
h
e
co
m
p
r
ess
io
n
r
atio
of
t
h
e
i
m
a
g
e
is
g
iv
e
n
by
No
.
of
b
it
s
in
o
r
ig
i
n
al
i
m
a
g
e
/
No
.
of
b
its
in
co
m
p
r
es
s
ed
i
m
a
g
e.
T
h
e
o
r
ig
in
al
m
u
r
al
s
,
co
m
p
r
ess
ed
m
u
r
als
w
i
th
S
y
m
let2
,
le
v
el
1
d
ec
o
m
p
o
s
i
tio
n
an
d
l
ev
el
4
d
ec
o
m
p
o
s
itio
n
ar
e
s
h
o
w
n
in
F
ig
u
r
e
1
an
d
Fig
u
r
e
2
r
esp
ec
tiv
el
y
.
T
ab
le
1
.
P
er
f
o
r
m
a
n
ce
E
v
al
u
ati
o
n
f
o
r
Dec
o
m
p
o
s
itio
n
L
e
v
els
D
e
c
o
mp
o
si
t
i
o
n
L
e
v
e
l
1
T
r
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o
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ms
D
B
2
S
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M
2
C
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2
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R
(
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)
5
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59.
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4
7
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P
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7
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R
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5
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4
1
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6
.
9
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D
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4
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8
4
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4
C
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D
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D
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5
C
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(
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4
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1
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3
.
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4
4
3
.
1
3
M
S
E
2
.
2
2
.
1
4
2.
1
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8776
IJ
-
I
C
T
Vo
l.
7
,
No
.
3
,
Dec
em
b
er
20
1
8
:
1
46
–
1
48
148
Fig
u
r
e
1
.
Or
ig
i
n
al
i
m
a
g
e
Fig
u
r
e
2
.
I
m
a
g
e
ar
ch
i
v
ed
at
d
ec
o
m
p
o
s
i
tio
n
le
v
el
4
T
h
e
P
SNR
v
a
lu
e
s
ar
e
ap
p
r
o
x
i
m
atel
y
s
a
m
e
an
d
v
er
y
lo
w
,
co
m
p
ar
ed
to
lev
el
s
1
&
2
.
T
h
e
b
its
p
er
p
ix
el
v
alu
e
s
ar
e
also
cr
ea
ted
an
d
th
e
v
ar
iatio
n
s
in
its
v
a
lu
e
s
ar
e
also
f
o
llo
w
in
g
th
e
P
S
NR
v
al
u
e,
s
in
ce
,
it is
r
elate
d
t
o
th
e
P
SNR
.
T
h
e
m
ea
n
s
q
u
ar
e
er
r
o
r
is
also
r
aised
if
th
e
lev
el
o
f
d
ec
o
m
p
o
s
it
io
n
is
i
n
cr
ea
s
ed
.
I
t
is
w
is
e
to
o
b
tai
n
a
least v
al
u
e
o
f
er
r
o
r
,
w
h
ich
i
s
also
g
iv
e
n
b
y
s
y
m
let1
w
it
h
t
h
e
f
ir
s
t le
v
el
o
f
d
ec
o
m
p
o
s
itio
n
4.
CO
NCLU
SI
O
N
T
h
e
m
a
in
o
b
j
ec
tiv
e
o
f
t
h
i
s
p
r
o
p
o
s
ed
w
o
r
k
is
to
ar
ch
i
v
e
a
n
d
co
m
p
r
ess
th
e
m
u
r
al
i
m
ag
e
s
w
i
th
h
i
g
h
q
u
alit
y
,
w
h
ich
i
s
o
b
tain
ed
b
y
th
e
tr
an
s
f
o
r
m
atio
n
o
f
s
y
m
let
w
av
e
let
w
ith
t
h
e
en
co
d
in
g
o
f
E
Z
W
.
I
t
is
also
ac
h
iev
ed
w
i
th
th
e
f
ir
s
t le
v
el
o
f
d
ec
o
m
p
o
s
it
io
n
.
T
h
e
b
its
p
er
p
ix
el
o
f
t
h
e
d
if
f
er
en
t p
r
o
p
o
s
ed
alg
o
r
ith
m
s
ar
e
als
o
d
ec
r
ea
s
ed
if
th
e
le
v
el
o
f
d
ec
o
m
p
o
s
itio
n
is
i
n
cr
ea
s
ed
.
T
h
e
p
er
f
o
r
m
an
ce
s
ar
e
v
ar
ied
,
m
ain
l
y
d
u
e
to
th
e
n
at
u
r
e
o
f
th
e
m
o
t
h
er
w
av
ele
ts
,
u
s
ed
in
t
h
is
w
o
r
k
.
T
h
e
L
ev
el
s
o
f
d
ec
o
m
p
o
s
itio
n
also
p
la
y
s
an
i
m
p
o
r
ta
n
t
r
o
le
in
th
e
s
to
r
ag
e
o
f
m
u
r
als,
w
h
ich
i
s
p
r
o
v
en
b
y
th
e
v
al
u
e
s
o
f
co
m
p
r
ess
io
n
an
d
P
SNR
v
al
u
es
.
RE
F
E
R
E
NC
E
S
[1
]
P
a
n
d
ian
,
R
&
T
.
V
ig
n
e
s
w
a
re
n
.
"
A
d
a
p
ti
v
e
wa
v
e
let
p
a
c
k
e
t
b
a
sis
se
lec
ti
o
n
f
o
r
z
e
ro
tree
i
m
a
g
e
c
o
d
in
g
.
"
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
S
i
g
n
a
l
a
n
d
Ima
g
i
n
g
S
y
ste
ms
En
g
in
e
e
rin
g
9
(2
0
1
6
):
3
8
8
-
3
9
2
.
[2
]
P
a
n
d
ian
,
R.
"
Ev
a
lu
a
ti
o
n
o
f
im
a
g
e
c
o
m
p
re
ss
io
n
a
lg
o
rit
h
m
s."
2
0
1
5
IEE
E
U
n
d
e
rwa
ter
T
e
c
h
n
o
l
o
g
y
(
UT)
Ch
e
n
n
a
i
(2
0
1
5
),
1
-
3
.
[3
]
P
a
n
d
ian
R
,
Vig
n
e
sw
a
r
a
n
T
a
n
d
L
a
li
th
a
Ku
m
a
ri
S
Ch
a
ra
c
teriz
a
ti
o
n
o
f
CT
Ca
n
c
e
r
L
u
n
g
Im
a
g
e
Us
in
g
Im
a
g
e
Co
m
p
re
ss
io
n
A
lg
o
rit
h
m
s a
n
d
F
e
a
tu
re
Ex
trac
ti
o
n
,
J
S
CI
IND
RE
S
,
V
o
l
.
7
5
(
2
0
1
6
)
,
7
4
7
-
7
5
1
.
[4
]
Ro
g
e
rl
Cla
y
p
o
o
le et al,
“
No
n
l
in
e
a
r
W
a
v
e
let
tran
sf
o
r
m
f
o
r
ima
g
e
c
o
d
i
n
g
v
ia l
if
ti
n
g
.”
IEE
E
,
2
0
0
3
.
[5
]
A
.
R.
c
a
d
d
e
r
b
a
n
k
,
“
L
o
ss
les
s i
m
a
g
e
c
o
m
p
re
ss
io
n
u
sin
g
in
teg
e
r
to
in
t
e
g
e
r
w
a
v
e
let
tran
s
f
o
rm
s.”
IEE
E
1
9
9
7
.
[6
]
M
in
h
N.
Do
,
“
Co
u
n
t
o
u
rle
t
tr
a
n
sf
o
rm
:
An
e
ff
icie
n
t
d
ire
c
ti
o
n
a
l
mu
lt
i
re
so
lu
ti
o
n
a
l
im
a
g
e
re
p
re
se
n
ta
t
io
n
”
,
2
0
0
5
.
[7
]
G
e
m
m
a
p
a
e
ll
a
,
“
A
d
a
p
ti
v
e
li
f
ti
n
g
sc
h
e
m
e
s c
o
m
b
i
m
in
g
se
m
i
n
o
rm
s
f
o
r
lo
ss
les
s ima
g
e
c
o
m
p
re
ss
io
n
.
”
IEE
E
,
2
0
0
5
.
[8
]
Ch
e
n
w
e
i
De
n
g
,
W
e
isi
L
in
,
Jia
n
f
e
i
Ca
i.
Co
n
te
n
t
-
Ba
se
d
Im
a
g
e
Co
m
p
r
e
ss
io
n
f
o
r
A
rb
it
ra
ry
-
R
e
so
lu
ti
o
n
Di
sp
lay
D
e
v
ice
s
.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
M
u
lt
ime
d
i
a
1
4
(4
):
1
1
2
7
-
1
1
3
9
(2
0
1
2
).
[9
]
M
A
Ho
n
g
-
we
i,
WA
N
G
Bin
,
Ap
p
li
c
a
ti
o
n
o
f
W
a
v
e
let
T
r
a
n
sf
o
rm
to
S
ig
n
a
l
d
e
-
n
o
isi
n
g
in
Ultra
so
n
ic
T
e
stin
g
,
ND
T
,
V
o
l
u
m
e
2
6
Nu
m
b
e
r
2
,
F
e
b
2
0
0
4
,
P
6
8
-
71
[1
0
]
Zh
o
u
W
e
i,
A
d
v
a
n
c
e
d
T
e
c
h
n
o
l
o
g
y
o
f
W
a
v
e
let
An
a
lys
is
B
a
se
d
o
n
M
AT
L
AB
,
P
u
b
li
s
h
e
d
b
y
X
i
Dia
n
Un
iv
e
rsity
P
re
ss
,
X
i’an
,
2
0
0
6
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
S
.
La
li
th
a
K
u
m
a
r
i
h
a
s
c
o
m
p
lete
d
g
ra
d
u
a
ti
o
n
f
ro
m
Bh
a
ra
th
id
a
sa
n
U
n
iv
e
rsity
,
T
h
iru
c
h
irap
p
a
ll
i
(1
9
9
3
)
i
n
El
e
c
tro
n
ics
a
n
d
Co
m
m
u
n
ica
ti
o
n
En
g
in
e
e
rin
g
Disc
i
p
li
n
e
.
S
h
e
o
b
t
a
i
n
e
d
h
e
r
p
o
st
G
ra
d
u
a
ti
o
n
i
n
P
o
w
e
r
El
e
c
tro
n
i
c
s
f
ro
m
Bh
a
ra
th
id
a
sa
n
U
n
iv
e
rsity
,
T
h
iru
c
h
irap
p
a
ll
i
(1
9
9
9
).
P
re
se
n
tl
y
sh
e
is
w
o
rk
in
g
a
s
a
n
A
ss
t.
p
ro
f
e
ss
o
r
i
n
t
h
e
De
p
a
rtm
e
n
t
o
f
E
IE
o
f
S
a
t
h
y
a
b
a
m
a
Un
iv
e
rsit
y
,
Ch
e
n
n
a
i.
S
h
e
is
a
ls
o
p
u
rsu
i
n
g
h
e
r
Do
c
to
ra
te
a
t
S
a
t
h
y
a
b
a
m
a
Un
iv
e
rsit
y
,
Ch
e
n
n
a
i.
.
He
r
re
se
a
rc
h
in
tere
st i
n
c
l
u
d
e
s S
ig
n
a
l
P
ro
c
e
ss
in
g
a
n
d
S
o
f
t
Co
m
p
u
ti
n
g
.
R.P
a
n
d
ia
n
h
a
s
c
o
m
p
lete
d
g
ra
d
u
a
ti
o
n
f
ro
m
M
a
d
ra
Un
iv
e
rsity
,
Ch
e
n
n
a
i
(
1
9
9
9
)
i
n
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
ri
n
g
Disc
ip
li
n
e
.
h
e
o
b
tai
n
e
d
h
e
r
p
o
st
G
ra
d
u
a
ti
o
n
in
A
p
p
li
e
d
El
e
c
tro
n
ics
f
ro
m
A
n
n
a
Un
iv
e
rsit
y
,
Ch
e
n
n
a
i
(2
0
0
7
)
.
P
re
se
n
tl
y
sh
e
is
w
o
rk
in
g
a
s
a
n
A
s
st.p
ro
f
e
ss
o
r
in
t
h
e
De
p
a
rtm
e
n
t
o
f
EIE
o
f
S
a
th
y
a
b
a
m
a
Un
iv
e
rsit
y
,
Ch
e
n
n
a
i.
He
is
a
lso
p
u
rs
u
in
g
h
e
r
Do
c
to
ra
te
a
t
S
a
th
y
a
b
a
m
a
Un
iv
e
rsit
y
,
Ch
e
n
n
a
i.
His res
e
a
rc
h
in
t
e
re
s
t
in
c
l
u
d
e
s Im
a
g
e
P
ro
c
e
ss
in
g
.
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