TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3509 ~ 35
1
4
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.3533
3509
Re
cei
v
ed
Jun
e
17, 2013; Revi
sed
De
ce
m
ber 10, 201
3; Acce
pted
De
cem
ber 3
0
,
2013
A New Adaptive Threshold Image-Denoising Method
Based on Edge Detection
Bin
w
e
n
Hua
ng*
1
, Yuan Jiao
2
1
Information C
enter, Hai
n
a
n
Vocatio
nal C
o
l
l
ege of Pol
i
tica
l Scienc
e an
d L
a
w
,
No.28
0
, Xi
nD
a
Z
hou Ro
ad, Ha
ikou, Ha
ina
n
, Chin
a, (+
86)08
986
58
559
79
2
Information T
e
chnology
Departmen
t, Haina
n
Medica
l Univ
e
r
sit
y
,
No.3, XueY
uan
Road, Ha
ikou,
Hain
an, Chi
n
a
*
Corres
p
o
ndi
n
g
author, e-ma
i
l
: 6447
13
62@
q
q
.com
A
b
st
r
a
ct
In i
m
a
ge
proc
essin
g
, re
mov
a
l
of no
ise
w
i
thout
bl
urr
i
n
g
t
he
imag
e
edg
es is
a
difficult
pro
b
le
m.
Aiming
at
orthog
on
al w
a
ve
l
e
t transfor
m
and
traditi
on
al
thresh
old
’
s s
hortag
e
, a
ne
w
w
a
velet pa
cket
transform
ad
ap
tive thresh
old i
m
a
ge d
e
-n
oisi
ng
meth
od w
h
i
c
h is bas
ed o
n
edg
e detecti
o
n
is pro
pose
d
. By
edg
e detecti
on
meth
od, the w
a
vel
e
t packet c
oefficie
n
ts corr
espo
ndi
ng to e
dge w
h
ic
h is d
e
tected a
nd ot
he
r
non-
edg
e w
a
v
e
let
pack
e
t coe
fficients ar
e tre
a
ted
by
differe
nt thresh
ol
d. U
s
ing
the
rel
a
tivi
ty amon
g w
a
ve
le
t
packet coeffici
ents and
nei
g
hbor d
e
p
end
e
n
cy relati
on,
a
t
the same ti
me, a
dopti
ng
the new
varia
n
ce
nei
ghb
or esti
mate
meth
od
an
d the
n
the
ad
a
p
tive thres
h
o
l
d
is pro
duc
ed.
F
r
om th
e ex
pe
riment res
u
lt,
w
e
see that co
mp
ared w
i
th tradit
i
on
al
metho
d
s,
this me
th
od c
an not o
n
ly effectively e
l
i
m
i
n
ate nois
e
, but can
also w
e
ll ke
ep
origi
n
a
l
i
m
ag
e
’
s informatio
n
a
nd the q
ual
ity after imag
e de-
n
o
isin
g is very w
e
ll.
Ke
y
w
ords
: i
m
age
de
nois
i
n
g
, w
a
velet p
a
ck
et transfor
m
, e
dge
detecti
on,
nei
gh
bor
dep
end
ency
ad
apt
ive
threshold
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
Wavelet tran
sform i
s
an e
ffective sign
a
l
deno
sin
g
to
ol, it has
sh
o
w
n m
a
ss a
p
p
lication
pro
s
pe
ct in i
m
age
pro
c
e
s
sing, p
a
ttern
recognitio
n
e
t
c. Wavel
e
t transfo
rm h
a
s
multi-re
sol
u
tion
analysi
s
cap
ability as
wel
l
as tim
e
-freq
uen
cy dom
ai
n an
alysis of
sig
nal at th
e
sam
e
time [
1
].
Recently, m
a
in ima
ge denosing
algorithm based on
wa
velet
is
still staying on im
age
decompo
sitio
n
of wavele
t basis, ho
wever, ima
g
e
decompo
sition of wavelet basi
s
o
n
ly
decompo
se l
o
w freque
ncy
part of info
rmation, hi
gh
freque
ncy p
a
rt of inform
ation can’t be
g
o
t
refinem
ent h
andlin
g, this way
ca
uses und
etecte
d
loss p
hen
om
enon
in i
n
formation of
hi
gh
freque
ncy p
a
r
t, wavelet pa
cket ba
sis
ca
n overcom
e
su
ch
sho
r
tag
e
to get bette
r analy
s
is
abi
lity
[2]: Low f
r
eq
uen
cy pa
rt a
nd hi
gh f
r
equ
ency
part
ca
n be
de
com
p
ose
d
at th
e
same
time, t
hus
more hi
gh fre
quen
cy part o
f
information
can b
e
save
d
and got refin
e
ment han
dli
ng.
The m
o
st
widely u
s
ed
wavelet
den
osin
g m
e
tho
d
is n
online
a
r
wavel
e
t tran
sform
threshold
shrink m
e
thod
prop
osed
by Don
oho
et
al [3]. Wavel
e
t thre
shol
d
shri
nk metho
d
cal
c
ulate
s
o
r
thogo
nal
wavelet tran
sf
orm
of noi
se i
m
age,
however, g
e
neral
thresh
old
2
2l
o
g
n
Tn
has
“excessi
v
e killing
”
tenden
cy tren
d
to
wavelet
coeffici
ent, it will ca
use
oscillation lo
cated in vicinity of discontin
ui
ty point and quick ch
an
ge pla
c
e for
denoi
se
d ima
ge
calle
d Gibb
s
phen
omen
on.
Thus, a ne
w
wavelet pa
cket transfo
rm
adaptive thre
shol
d image
de-
noisi
ng meth
od which i
s
b
a
se
d on e
d
g
e
dete
c
tion is prop
osed. Base
d on the
edge info
rma
t
io
n
whi
c
h i
s
effectively detecte
d by thi
s
m
e
thod,
wa
velet
packet i
s
ch
o
s
en
to
decom
pose the
ima
ge.
Usi
ng la
rge
amount
of redu
nda
nt informatio
n
whi
c
h i
s
prod
uced by
wavelet p
a
cket
decompo
sitio
n
and thi
s
kind of redu
ndant info
rm
ation is u
s
ef
ul to find the depe
nde
n
c
y
relation
shi
p
o
f
wavelet co
e
fficients between
i
n
tra
-
scal
e an
d inte
r-scale, th
e
coef
ficient vari
an
ce
estimation
a
c
curacy
ba
sed
on
wavel
e
t coefficient
nei
ghbo
r i
s
gre
a
t
ly improved.
Mean
while, t
h
e
wavelet pa
cket coefficie
n
ts are
divided
into
two cat
egori
e
s, which are
corre
s
pondi
ng to e
dge
and n
on-edg
e wavel
e
t p
a
cket coeffici
ents. Th
es
e
two ki
nd
s of
coeffici
ents are treated
by
different ad
a
p
tive thresho
l
d. This met
hod can
save the origi
n
a
l
image information well and
denoi
se effe
ctively; in addition, it is ve
ry useful to do f
u
rthe
r image
pro
c
e
ssi
ng.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3509 – 35
14
3510
2. Wav
e
let Packe
t Principle
In sho
r
t, the wavelet pa
cket is a family of functions.
The ca
noni
cal orthog
onal
basi
s
libra
ry
of
2
()
LR
is
c
o
ns
truc
ted
by this
family of func
ti
on
s. Form thi
s
li
bra
r
y, many
grou
ps of
can
oni
cal o
r
thogo
nal ba
si
s of
2
()
LR
can be
cho
s
e
n
and
wavelet o
r
tho
gonal b
a
si
s i
s
only on
e
grou
p of them.
Whe
n
the sig
nal is de
com
posed by wa
velet
packet, many kind
s o
f
wavelet packet ba
si
s
can
be
ado
pt
ed. Acco
rdin
g to the
dem
and
of si
gnal
and
noi
se, th
e be
st b
a
si
s
sho
u
ld
be
ch
ose
n
from them [4]
.
Nowaday
s, Shanno
n ent
ropy is u
s
e
d
more to
search the
be
st b
a
si
s. Thresho
l
d is
the key of wavelet pa
cket denoisi
ng
and t
he adaptive thresh
old whi
c
h is based o
n
edge
detectio
n
is a
dopted by thi
s
pap
er.
3. Edge Dete
ction Algori
t
hm
For
an a
r
bitrary imag
e pix
e
l
(,
)
Pi
j
, the wavel
e
t pa
cket tra
n
sform value
s
of h
o
ri
zo
ntal
and vertical d
i
rectio
n are g
o
t resp
ectivel
y
, they are
1
(,
)
wi
j
,
2
(,
)
wi
j
.
So its modulu
s
is:
22
12
(,
)
(
,
)
(,
)
M
ij
w
i
j
w
ij
(1)
Argume
n
t direction of ima
ge pixel is gradient directi
on, argu
ment
(,
)
A
ij
can be got
from arc tang
ent of
21
(,
)
/
(,
)
wi
j
w
i
j
, and the expre
ssi
on
is:
2
1
(,
)
(,
)
a
r
c
t
a
n
(,
)
wi
j
Ai
j
wi
j
(2)
Argume
n
t
0
(,
)
Pi
j
an
d modulu
s
(,
)
M
ij
of arbitra
r
y image pixel is given, image pixel
pointed by
its
gra
d
ient
di
re
ction can be got
from arg
u
m
ent
(,
)
A
ij
, firstly, image
pixel p
o
int
0
P
is
lighten, then
set the
poi
nt pointed
b
y
argum
ent dire
ction of
image pixel
0
P
as
1
P
, c
o
mpare
modulu
s
of two p
o
ints, li
g
h
ten
1
P
and
extinguish
0
P
if the mod
u
lu
s of
1
P
is l
a
rg
er.
Continue
doing the sa
me handli
ng to
1
P
until modulus of next point is larg
e
r
than or eq
u
a
l to this point.
After traversi
ng all imag
e
pixels, maxi
mum value i
m
age of lo
ca
l modulu
s
is
con
s
i
s
t of all light
points.
Maximum poi
nt of local modulu
s
of ima
ge is
linked a
s
maximum chain; the prin
ciple i
s
that maximu
m point of two mod
u
lus is
adjoin, ta
n
g
e
n
t line di
re
ction is
app
roxi
mate at on
e l
i
ne,
tangent li
ne
dire
ction
is vertical
di
re
ction of
gradie
n
t, and
u
s
e
threshold
to
wipe
off
sho
r
t
maximum value link, in this way, image
(,
)
Pm
n
is margin of original imag
e.
4. Adap
tiv
e
Thresh
old Image De
nosing Bas
e
d on
Wav
e
let Pac
ket Trans
f
orm
an
d
Neighbo
r De
penden
c
y
4.1. Adap
tiv
e
Thresh
old Bas
e
d on Ba
y
esian Estimation [5
]
T
h
r
e
s
h
o
l
d
de
te
r
m
ina
t
io
n
is
ve
r
y
imp
o
r
t
a
n
t s
e
g
m
e
n
t
in th
r
e
s
h
o
l
d
imag
e
de
n
o
s
i
n
g
.
C
h
ang
et
al
u
s
e G
eneralized G
aussia
n
Distribution (G
G
D
) as
p
r
ior model of
wa
velet
co
effici
ent
distrib
u
tion,
by minimum
Bayes ri
sk,
to get a
d
a
p
tive thre
sho
l
d of digital
drive in B
a
yes
frame
w
ork.
Set:
,,
,
ij
ij
ij
yx
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A New Ada
p
tive Th
re
shol
d Im
age-De
noi
sing Meth
od
Based o
n
Ed
ge Dete
ction
(Binwen Hua
ng)
3511
,
1
,
2
,
...,
ij
N
,
,
ij
y
,
,
ij
x
and
,
ij
mea
n
observed n
o
ise ima
ge, true ima
ge an
d indepe
nde
n
t
identically distributed Ga
u
ssi
an noi
se,
,
ij
obey
s
2
(0
,
)
n
N
distri
bution
.
Set
,,
,
ij
ij
i
j
YX
V
a
s corre
s
po
n
d
ing
wavelet
co
efficient.
Suppo
se if X
and
Y a
s
Gau
ssi
an
d
i
s
tribution, that
is
2
(0
,
)
x
X
,
2
(,
)
x
YX
X
Gene
rali
zed
Gau
ssi
an di
stribution exp
r
e
ssi
on is li
sted
as follows:
,
()
(
,
)
e
x
p
X
XX
GG
x
C
x
.
(4)
x
,
X
,
0
1
,)
[
]
XX
.
(5)
(,
)
(,
)
1
2(
)
X
X
C
.
(6)
1
0
()
ut
te
u
d
u
is gamm
a
function, pa
rameter
X
is st
anda
rd va
ria
n
ce,
is
fo
rm
a
l
para
m
eter. T
hen Bayes
risk is defin
ed a
s
：
22
2
(
)
()
()
(
(
)
)
(
)
XT
YX
rT
E
X
X
E
E
X
X
y
x
p
y
x
d
y
d
x
.
(7)
As to given
para
m
eter, th
e target i
s
to
find the be
st threshold
T
that can
get th
e minimum
B
a
y
e
s ri
sk:
(,
)
a
r
g
m
i
n
(
)
X
T
Tr
T
.
(8)
We can get a
pproxim
ate o
p
timal formul
as of
T
by deriv
ation [5]:
2
()
n
BX
X
T
.
(9)
X
is stan
dard varian
ce of
X
,
2
n
is stan
dard varian
ce of noi
se. This thre
sh
old is Bayes
Shrin
k
threshold.
4.2. Spatial Adap
tiv
e
Thr
eshold for E
dge Wav
e
let Packe
t Coe
f
ficients
This
pape
r u
s
e
s
spatial a
daptive meth
od to
dete
r
m
i
ne ad
aptive
thre
shold
fo
r ea
ch
wavelet coeffic
i
ent, thus
eac
h coefficie
n
t threshold i
s
:
2
(,
)
(,
)
n
B
X
Ti
j
ij
(10)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3509 – 35
14
3512
Noi
s
e varia
n
c
e
2
n
determi
ned by noi
se type, accordin
g to ro
bustn
ess me
dian
estimation p
r
opo
sed by Donoh
o [6], that is,
2
n
is estim
a
ted by subb
a
n
d
1
HH
:
()
0.6745
ij
n
M
ed
i
a
n
Y
,
1
ij
YH
H
(11)
For the ed
ge
pixel, the edg
e pixels which are
a
d
jace
nt have spati
a
l relation. T
herefo
r
e,
one e
dge
pi
xel’s varia
n
ce estim
a
ted
by its adja
c
e
n
t edge
pixel
s
is
more a
c
curate than
the
method e
s
ti
mated by its N nei
ghbo
r pixels. Let
[,
]
P
Y
ij
rep
r
e
s
ent
s the wavel
e
t packet
coeffici
ent rel
a
ted to edge
pixel
(,
)
Pi
j
, so its varian
ce
can b
e
got by the followin
g
form
ula:
22
1
[,
]
[
,
]
21
PP
YY
ij
t
v
L
(12)
(,
)
Pt
v
is the a
d
ja
cent edg
e pix
e
l of edg
e pi
xel
(,
)
Pi
j
. For the
given ed
ge p
i
xel, its
varian
ce i
s
e
s
timated by i
t
s two
side
s
adja
c
ent
L e
dge pixel
s
re
spe
c
tively, that is 2L
+1 e
dge
pixels
in all. Generally speaki
ng,
different value
of L can produce
simil
a
r
result. However, i
t
will
destroy the region
al wh
en
L is
too larg
e and it will a
ffect the cal
c
ulation a
c
curacy wh
en L i
s
too
small.
L i
s
u
s
ually
ch
ose
n
2
ma
x
(
5
0
,
0
.
0
2
*
)
M
to en
su
re
ade
quate
pi
xels to
estim
a
te its
var
i
anc
e
.
2
[,
]
P
X
ij
is
es
timated as
follows
:
22
2
[,
]
(
,
)
1
[,
]
m
a
x
(
[
,
]
,
0
)
21
PP
XY
n
tv
B
i
j
ij
t
v
L
(13
)
(,
)
B
ij
is the set of 2L adja
c
e
n
t edge pixel
s
of
[,
]
ij
.
4.3. Neighbo
r Depe
nden
c
y
Adaptiv
e
T
h
reshold for Non
-
edg
e
Wav
e
let Packet Coe
fficie
n
ts
Duri
ng th
e va
rian
ce
estima
tion of no
n-e
dge n
o
isy
co
efficients, thi
s
pape
r
con
s
i
ders n
o
t
only intra-su
bban
d but al
so inte
r-scal
e depe
nde
ncy
relativity of wavelet pa
cket coefficien
ts
whi
c
h i
s
diffe
rent f
r
om
pa
st variant
neig
hbor e
s
timati
on. Th
at is th
e relativity be
tween
child
a
n
d
father/brother coefficie
n
t. In scale s an
d dire
ction
o
, the father co
efficient of one co
efficient
(,
)
[,
]
so
Yi
j
is
defined
a
s
(1
,
)
[,
]
so
Yi
j
in
scale
s+1
,
same
di
recti
on
o
and
sam
e
sp
atial lo
cati
on
,
1,
2
,
,
sJ
;
,,
OH
L
L
H
H
H
. The b
r
othe
r coefficie
n
t
of
(,
)
[,
]
so
Yi
j
is
define
d
as
sa
me
scale s, different dire
ction
o
and same sp
atial locatio
n
. So:
1
11
2
3
,
(,
)
(,
)
(
1
,
)
(
,
)
(,
)
(,
)
1
2
22
2
2
,
[
,
]
[,
]
[
,
]
[,
]
ij
so
so
s
o
so
s
o
kl
w
i
n
ij
k
l
ij
ij
ij
Y
NN
YY
Y
Y
(14)
,
ij
win
is squa
re n
e
ighb
or wi
nd
ow centeri
n
g
wavelet coe
fficient
(,
)
[,
]
so
Yi
j
, window
size i
s
NN
, N is po
sitive
odd nu
mbe
r
. The corre
s
p
ondin
g
item o
f
above form
ulas
will be
el
iminated
if there is coefficient that ex
ceeds the
range of wav
e
let subban
d. The windows si
ze will
affect
the estim
a
tio
n
re
sult of va
riance; und
ersized
wi
n
d
o
w
can’t
utili
ze n
e
ighb
or depe
nden
cy
relati
vity
well, ove
r
la
rg
e wi
ndo
w
will
impa
ct the
effect of d
e
n
o
sin
g
. Thi
s
p
aper u
s
e
s
si
ze
33
neigh
bor
window [7].
Thus
(,
)
X
ij
is esti
mated as:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A New Ada
p
tive Th
re
shol
d Im
age-De
noi
sing Meth
od
Based o
n
Ed
ge Dete
ction
(Binwen Hua
ng)
3513
22
(,
)
m
a
x
(
(
,
)
,
0
)
XY
n
ij
ij
(15)
4.4. Wav
e
let Packe
t Ada
p
tiv
e
Threshold Algorithm
w
h
ich is
Ba
sed on Edge
Dete
ction
In con
c
lu
sion,
the pro
c
edu
re of th
is algorithm is listed
as follo
ws:
(1)
De
co
mpo
s
ition of
wav
e
let pa
cket of
im
age. Sele
ct a
kind
of wavelet and
d
e
termin
e
layer N of wavelet de
co
mpositio
n, then de
comp
o
s
e wavelet p
a
cket of N layer for ima
ge;
Determine
o
p
timal wavel
e
t pa
cket ba
sis.
Cal
c
ul
ate optimal
wavelet pa
cke
t
basi
s
by g
i
ven
Shanno
n entropy stand
ard.
(2)
Use local modulu
s
max
i
mum value
method to extract the ima
g
e
edge info
rm
ation;
(3) Th
re
shol
d
qua
ntizatio
n
of wavel
e
t pa
cket de
co
mp
osition
coefficient. Fo
r th
e
wavelet
packet
coeffi
cient
s rel
a
ted
to edge,
sp
atial ada
ptiv
e threshold i
s
cho
s
e
n
to d
eal with; for
the
wavelet pa
cket
co
efficient
s relate
d
to homog
ene
ou
s
regi
on
s, ne
ighbo
r d
epe
n
den
cy ad
apti
v
e
threshold i
s
chosen to deal
with.
(4)
Wavelet
packet recon
s
tru
c
tion. Wa
velet packet
recon
s
tru
c
tio
n
of image i
s
do
ne
according to
wavelet p
a
cket decompo
si
tion co
efficie
n
ts of Nth l
a
yer and th
e
coeffici
ents
a
fter
the quanti
z
ati
on han
dling.
5. Experiment Re
sult an
d Analy
s
is
Based
on
the
image
de
no
sing
algo
rith
m mentio
ned
above,
we
u
s
e MA
TLAB
6.5 to d
o
the sim
u
latio
n
expe
riment
. As to
size
512
5
12
’s boat im
age
with
zero m
e
an G
a
u
ssi
an
white
noise, we
u
s
e Win
n
e
r
2 m
e
thod, wavel
e
t packet
met
hod a
nd th
e
method
pro
p
ose
d
in thi
s
p
aper
to do
sim
u
lat
i
on exp
e
rim
e
nt. We
can
get Wi
nne
r2
function
from
MATLAB im
age
processi
ng
tools b
o
x,
33
win
dow i
s
used i
n
this
pap
er.
This
experi
m
ent select
s h
aar
wavel
e
t to do i
m
ag
e
decompo
sitio
n
of 3 laye
rs. As to diffe
re
nt Gau
s
sian
white n
o
ise,
we u
s
e
PSNR (Pe
a
k Sign
al to
Noi
s
e Ratio)
of image as b
enchma
r
k of
deno
sin
g
perf
o
rma
n
ce, it is defined a
s
:
2
,
10
22
((
,
)
(
,
)
)
10
l
o
g
256
ij
Bi
j
A
i
j
PS
N
R
n
(16)
B is denoi
sed
image; A is original n
o
ise-f
r
ee ima
ge.
PSNR (dB) o
f
boat image
is sh
own in T
able 1
in diff
erent n
o
ise intensity and
different
de-n
o
si
ng me
thod. The opti
m
al re
sult is
empha
si
zed i
n
bold.
Re
sult figu
re
of different
deno
sin
g
me
thod of b
oat
image i
s
sho
w
n in
Figu
re
1 while
noise var
i
ance
n
.
Table 1. PSNR (dB)
of Noi
s
y Boat Im
age Usi
ng Different Den
o
isi
n
g
Method
Method
n
Noisy
imag
e
Winner2
Wavelet packet
Proposed b
y
this paper
15
n
24.3892
28.1743
30.3059
33.2671
n
22.5016
26.7738
29.0127
31.8376
n
20.4733
24.5942
26.9548
29.7902
From
experi
ment result, we
see that
this
method
can still effect
ively eliminate noi
se
while noi
se varian
ce i
s
big
and noise po
llution is heav
y. Denoise
d image ha
s cle
a
r margin. Th
is
method ove
r
matche
s tra
d
i
t
ional method
s from PSNR and visu
al effect.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3509 – 35
14
3514
Figure 1. Image De
noi
sing
by Usin
g Different Meth
od
s on a Noisy
Boat Image while
n
6. Conclusio
n
Low fre
que
ncy part and hi
gh frequ
en
cy part can b
e
decompo
se
d at length by wavelet
packet tran
sform that avo
i
d t
he shorta
ge of wavele
t transfo
rm.
The exp
r
e
ssi
on of imag
e
is
redu
nda
nt in
the do
main
o
f
wavelet
pa
cket tran
sform
,
decomp
o
siti
on
coeffici
ent
is
rel
a
tive. T
h
is
pape
r uses lo
cal mod
u
lu
s maximum value method to
extract imag
e edge info
rmation and treat
s
the wavel
e
t coefficient
s which
are relat
ed to e
dge
a
nd ho
mog
e
n
eou
s regio
n
s differently. T
hey
are tre
a
ted b
y
different ad
aptive thre
sh
old. M
ean
whi
l
e, the depen
den
cy relatio
n
shi
p
of wav
e
let
coeffici
ents b
e
twee
n intra-scale and int
e
r-scal
e is
co
nsid
ere
d
ade
quately and then a ne
w imag
e
denoi
sing
m
e
thod i
s
pro
posed. Expe
riment result
indicates th
at this meth
od can n
o
t only
denoi
se effe
ctively, but can also gai
n cle
a
r imag
e margin.
Referen
ces
[1]
Mallat. A th
eor
y for m
u
lti-res
o
lutio
n
d
e
comp
o
s
ition: th
e
w
a
v
e
let shr
i
nk
age.
Biom
etrik
a
. 19
94; 8
1
: 42
5–
452.
[2]
Jintai
Cui.
W
a
vel
e
t Analysi
s Introduction,
F
i
rst Edition.
Xi’
an:
Xi’
an
Jiaoto
ng U
n
iv
ersit
y
Press
.
199
7.13
5-13
7
[3]
Don
oho, M Jo
hnston
e
. Den
o
i
sing
b
y
soft thresh
old
i
n
g
.
IEEE Transactions on Information Theory.
199
5; 41(3): 61
3–6
27.
[4]
Coifma
n RR. Wickerha
u
se
r
MV. Entrop
y
-
b
a
sed a
l
gor
ithm
s for best-basis
selectio
n.
IEEE Trans Inform
T
heory.
199
2; 38(2): 71
3–
718
.
[5]
Cha
ng SG, Yu
B, Martin V. Adaptiv
e W
a
v
e
let
T
h
reshol
di
ng for Imag
e
Den
o
isi
ng a
n
d
Compress
io
n.
IEEE Transactions on I
m
age
Processing
. 20
00; 9 (9): 153
2
–15
46.
[6]
Don
oho
DL, Jo
hnston
e
IM. Ideal s
patia
l a
d
a
p
tation v
i
a
w
a
v
e
let shr
i
nka
ge.
Biom
etrik
a
.
19
94; 81:
425
–
455.
[7]
Chen GY, Bui T
D
,
Krz
y
z
a
k A. Imag
e
De
nois
i
ng
U
s
ing
Ne
igh
b
o
u
rin
g
Wave
let
Co
efficients.
Procee
din
g
s of
IEEE Internati
ona
l Co
nfere
n
c
e on
Acoustic
s
, Speec
h, an
d Sig
n
a
l
Proc
e
ssing.
20
04
;
917
–9
20.
Evaluation Warning : The document was created with Spire.PDF for Python.