Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 5
,
O
c
tob
e
r
201
6, p
p
. 2
219
~222
4
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
5.1
164
1
2
219
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Salt and Pepper Noise Remova
l Using Resizable Window and
Gaussian Estimation Function
Suh
ad
A.
Ali,
C. El
af
A.
Ab
bood,
C. S
h
aymaa Abdul
K
a
dhm
Bab
y
lon Univ
ersit
y
,
Scien
c
e
Coll
ege for
W
o
men,
Computer Depar
t
ment, B
a
b
y
lon
,
Iraq
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
n 26, 2016
Rev
i
sed
Au
g 7, 201
6
Accepted Aug 27, 2016
Most t
y
p
e
s of th
e im
ages ar
e cor
r
upted in m
a
n
y
wa
y
s
th
at b
ecau
se expose
d
to d
i
f
f
eren
t ty
pes of
noises.
Th
e
corruptions
happ
en dur
ing
tr
ansmission from
s
p
ace
to ano
t
her
,
during s
t
or
ing
or cap
turing.
Im
age pro
ces
s
i
ng
has
various
techn
i
ques
to pr
oces
s
the im
ag
e.
Before pro
ces
s
the im
age
,
th
ere
is
need t
o
rem
ove nois
e
th
at
corrupt
the
i
m
a
ge and
enh
a
n
ce
it
to
be
as
n
e
ar as
to
the
original image.
This
p
a
per
prop
osed a n
e
w method to
pro
cess
a p
a
rticular
common ty
p
e
o
f
noise.
This method rem
oves s
a
lt
and p
e
pper
noise b
y
using
m
a
n
y
t
echn
i
ques
.
F
i
rs
t,
det
e
c
t
th
e nois
y
pix
e
l
,
th
en in
creas
ing
th
e s
i
z
e
of
th
e
pixel window d
e
pending
on so
me criter
ia to
be enough
to
estimate
the
results.
T
o
estim
ates th
e pixe
ls o
f
im
ag
e, the
Gau
ssian
estim
ation function is
use
d
.
T
h
e re
sult
e
d
i
m
a
g
e
qual
ity
i
s
me
a
s
ure
d
by
t
h
e
st
at
i
s
t
i
c
a
l
qua
ntity
m
eas
ures
tha
t
's
P
eak
S
i
gnal-
to
-Nois
e
Ratio
(
PSNR) and
Th
e Structural
Sim
ilarit
y
(SSIM) m
e
trics.
Th
e
results
il
lustra
te
the
qu
ali
t
y
of
t
h
e
enhanc
ed
im
age
com
p
ared
with
the
oth
e
r
t
r
adition
a
l
t
echni
ques.
Th
e sl
ight
gradu
a
l
of
SSIM metric d
e
scribed
th
e perf
ormance of
th
e
proposed metho
d
with
high
increasing of
noise lev
e
ls.
Keyword:
Gaus
si
an
f
unct
i
on e
s
t
i
m
a
t
i
on
Max
filter
No
ise d
e
tection
PSNR and
SSIM m
e
trics
R
e
si
zabl
e
wi
nd
ow
Sal
t
and
pe
p
p
e
r
noi
se
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
C. Elaf
A
.
Abbo
od
C
o
m
put
er De
p
., Sci
e
nce C
o
l
l
e
ge
fo
r
Wom
e
n
Bab
y
lo
n Un
iv
ersity
Bab
y
lo
n, Iraq
Email: wsci.elaf
.
a
li@uobab
y
lon.edu.iq
1.
INTRODUCTION
Im
age noise c
a
n be catc
h
ing the im
age from
m
a
ny
different noise res
o
urces
. The
s
e resources a
r
e
cont
ai
ni
ng
bi
t
err
o
rs i
n
t
r
a
n
s
m
i
ssi
on, fa
ul
t
y
pi
xel
s
a
nd
da
m
a
ged m
e
m
o
ry
l
o
cat
i
on.
Th
e noi
se t
y
pe
s i
n
cl
u
d
e
Gaus
si
an,
Sal
t
and
pe
ppe
r,
Po
i
sson a
n
d S
p
ec
kl
e n
o
i
s
e. Sal
t
and
pe
ppe
r
des
c
ri
be
d as a w
h
i
t
e
and bl
ac
k
d
o
t
e
s
distributed
on t
h
e im
age in ra
ndom
way with a s
p
ecific le
v
e
l
of
t
h
at
noi
se
[1]
.
T
h
er
e a
r
e
many techni
ques are
use
d
to enha
nc
e the im
age that contam
inate
s
with salt an
d pep
p
e
r
n
o
i
s
e a
nd l
i
m
it
i
ng t
h
e
effect
o
f
i
t
.
St
anda
r
d
Med
i
an
Filter (SMF) is on
e o
f
th
e non
lin
ear filters th
at rem
o
v
e
th
e salt an
d
p
e
p
p
e
r n
o
i
se b
y
fi
n
d
i
n
g
th
e
med
i
an
v
a
l
u
e
of th
e filter
wind
ow t
o
b
e
th
e
p
r
ed
icted
n
e
w
p
i
x
e
l
v
a
lu
e. This filter h
a
s drawb
a
ck
with
t
h
is typ
e
of
n
o
i
s
e t
h
at
i
t
i
s
not
get
a
g
o
o
d
per
f
o
r
m
a
nce
wi
t
h
a
h
i
gh l
e
vel
o
f
t
h
at
n
o
i
s
e;
f
u
rt
herm
ore, i
t
re
m
oves
n
ecessary d
e
tails in
th
e im
a
g
e [2
]. C
o
n
s
eq
u
e
n
tly
, th
e
Weigh
t
ed
Med
i
an
Filter (WMF)
and
R
ecu
rsi
v
e
Weigh
t
ed
Median
Filter (R
WMF)
were i
n
trod
u
c
ed
t
h
at u
s
ed
to in
creasing
th
e qu
ality o
f
resu
lted
im
ag
e b
y
g
e
t
a h
i
g
h
rate to
th
e n
ecessary pix
e
ls in
th
e win
dow th
at
sp
ecified
in
a sp
ecial weig
h
t
[3
].
Bu
t th
e q
u
a
lity o
f
th
e
resu
lted im
ag
e stilled
no
t app
r
op
riate
b
ecau
s
e t
h
ere is
n
o
pred
ict if th
e
p
i
x
e
l is corr
u
p
ted
or
no
t. Th
erefo
r
e,
n
o
i
se d
e
tection
techn
i
qu
es an
d
d
ecision
b
a
sed
algo
r
ithm
s
are p
r
o
posed
to
increase th
e qu
ality
o
f
t
h
e
p
r
o
cessed
im
a
g
e lik
e Ad
ap
ti
v
e
Med
i
an
Filter (AMF) an
d
Progressiv
e
Switch
i
ng
Med
i
an
filter (PSM
F) were
p
r
op
o
s
ed
. Th
ese filters are u
s
ed
no
ise d
e
tectio
n
techn
i
qu
es
t
o
find
th
e no
isy p
i
x
e
ls th
en
pro
cessed
it u
s
in
g
th
e
stan
d
a
rd m
e
d
i
an
filter w
ith
a sp
ecial con
d
itio
n
s
[4
],[5
].
Th
e
p
e
rfo
r
m
a
n
ce of th
ese
filters are in
t
r
oduced
a
g
ood
resu
lts
wi
th
low an
d m
i
d
d
le lev
e
ls
o
f
n
o
ise. Bu
t th
ey
failed
with
h
i
g
h
n
o
i
se's lev
e
ls.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
221
9
–
22
24
2
220
Lately, a d
ecisio
n
b
a
sed
Median
Filter (DB
M
F)
was su
ggested
to
pro
c
essed
the great l
e
v
e
ls
o
f
t
h
at
noi
se
by
re
pl
a
c
i
ng
pi
xel
s
t
h
a
t
reco
gni
ze
d a
s
n
o
i
s
e de
pe
nd
i
ng
on
som
e
cri
t
e
ri
a wi
t
h
t
h
e
val
u
e t
h
at
com
put
e
d
d
e
p
e
nd
ing
o
n
med
i
an
or the
n
e
igh
bor's p
i
xels o
f
th
e
wind
ow. Th
e d
i
sad
v
a
n
t
ag
e of t
h
is filter is th
e
resu
lted
im
age'
s resol
u
t
i
on i
s
dest
r
o
y
e
d as
t
h
e
l
e
ve
l
of
n
o
i
s
e i
s
gr
owt
h
s
[
6
]
.
F
o
r
t
h
at
,
It
has
bee
n
pr
o
p
o
s
e
d
t
h
e
Mo
d
i
fied
Deci
sio
n
Based
Un-symmetric Tr
i
mmed
Med
i
an
Filter (MDBUTMF). Th
e
work
o
f
th
is fi
lter is
su
mm
arized
in
to
two
step
s:
first d
i
stingu
ish
i
ng
th
e no
isy
p
i
x
e
ls, seco
nd
treated
u
s
ing MDBUTM
F.
If t
h
e
ev
en
t th
at th
e
selected
wind
ow is co
rrup
ted as wh
o
l
e,
th
e mean
v
a
lu
e of th
e win
dow will b
e
co
m
p
u
t
ed
and
replace it
with the
processe
d pixel
val
u
e.
This s
o
lution
doe
sn’t get
a
good alterna
tive with high
l
e
vels of
n
o
i
se [7
].
There a
r
e m
a
ny
t
y
pes of es
t
i
m
a
t
i
on fu
nct
i
ons
. O
n
e o
f
t
h
ese f
unct
i
ons
i
s
t
h
e Gaussi
an f
unct
i
o
n
.
Gaus
si
an
f
unct
i
on
i
s
wi
del
y
u
s
ed i
n
st
at
i
s
t
i
c
s w
h
er
e i
t
defi
nes t
h
e
n
o
rm
al di
st
ri
but
i
o
ns
i
n
m
a
ny
appl
i
cat
i
o
n
s
suc
h
as si
gnal
pr
ocessi
n
g
, i
m
age pr
ocessi
ng a
nd m
a
t
h
em
at
i
c
s. Gaussi
an f
unct
i
o
ns c
a
n be
descri
b
e
d by
co
m
b
in
in
g
t
h
e
ex
pon
en
tial fun
c
tio
n with a co
n
c
av
e
qu
adrat
i
c fun
c
tion
.
t
h
e Gau
ssian is the p
r
ob
ab
ility den
s
ity
fu
nct
i
o
n of a
no
rm
al
ly
di
st
ribut
e
d
ra
nd
om
vari
a
b
l
e
and i
t
can be desc
ri
bed i
n
e
quat
i
o
n (1
) i
n
t
h
e t
e
rm
o
f
exponential, m
ean a
n
d standa
rd di
vision val
u
es
[8]:
√
(1
)
Whe
r
e
m
de
not
ed t
o
m
ean val
u
e a
n
d
std
re
fe
r t
o
st
an
dar
d
di
vi
si
o
n
of t
h
e
x
val
u
e.
Thi
s
pa
per
pr
o
pos
ed a ne
w
m
e
t
hod t
o
rem
ove
noi
sy
pi
xe
l
and en
ha
nce t
h
e cor
r
u
p
t
e
d i
m
age by
sal
t
and
pe
p
p
er
n
o
i
s
e. I
n
t
h
e
pr
o
p
o
se
d m
e
t
hod a
n
o
i
s
e
det
ect
i
on t
ech
ni
que
i
s
use
d
t
o
det
e
rm
i
n
e t
h
e
n
o
i
s
y
p
i
xel
.
The
n
fi
n
d
t
h
e
si
ze of wi
nd
o
w
de
pe
ndi
ng
o
n
som
e
st
at
i
s
t
i
cal criteria. Fin
a
lly, th
e p
i
xel v
a
lu
e is estimated
usi
n
g
o
n
e
of t
h
e est
i
m
a
t
i
on f
u
nct
i
o
n
s
.
2.
RELATED WORK
In
rece
nt
t
i
m
e
s, t
h
e
r
e are
m
a
ny
m
e
t
hods t
o
re
d
u
ce Sal
t
and
Pe
ppe
r
no
i
s
e. R
a
kes
h
M
.
R
an
d et
al
.
p
r
op
o
s
ed
a h
y
b
r
i
d
m
e
d
i
an
fil
t
er, th
at d
e
v
e
lop
e
d
the m
e
d
i
a
n
filter app
l
yin
g
cro
ss and
p
l
us tech
n
i
qu
e w
i
t
h
5x5
size windo
w. Ju
st th
e p
i
x
e
ls i
n
cro
s
s an
d p
l
u
s
d
i
rectio
n
s
i
n
5
x5 wi
n
dow will im
p
lica
t
e
in
m
e
d
i
an
filter [9
].
Ism
a
I. and
et
al. in
trodu
ced
a filter with
a
criterio
n
fo
r t
h
e selectio
n
o
f
n
e
igh
boring
p
i
x
e
l u
s
i
n
g th
e l
o
cal and
global occurre
nces of grey
le
vels
to
pre
d
icate
the pixel val
u
e [10].
T
.
Raje
sh a
n
d et al.
discuss
e
d com
p
aris
on
betwee
n four
differe
nt im
age
filtering m
e
thods that are
Bilateral, m
e
dian, ideal an
d Butterworth
filtering, and
th
ey co
n
c
lud
e
d
th
at
m
e
d
i
an
filter g
e
t th
e best resu
lte
d
imag
e th
at co
rrup
ted
in
salt and
p
e
p
p
e
r no
ise[11
].
Othe
rs applied altered m
e
thods to
rem
ove this type of
noi
s
e that corrupt
the rem
o
te satellite im
ages. Yoge
sh
an
d Yog
e
ndra
are ap
p
lied a
no
ise
d
e
tectio
n
t
ech
n
i
q
u
e
to pr
ed
icated
t
h
e
rate o
f
th
e
no
ise
in
satellite i
m
a
g
es. If
n
o
i
se rate is less th
an
p
a
rticu
l
ar th
resho
l
d
v
a
lu
e, th
en
ap
p
l
i
e
d
th
e m
e
d
i
an
filter. Oth
e
rwise, ap
p
l
y th
e adap
tiv
e
weigh
t
alg
o
rith
m
.
Also
, th
ey d
i
scu
ssed
the resu
lted
sa
tellite
i
m
ag
es with
d
i
fferen
t
lev
e
ls of no
ise [12
]
.
V.R
.
Vi
jay
kum
ar i
s
pr
op
ose
d
an al
go
ri
t
h
m
t
o
rem
ove sal
t
and pe
ppe
r n
o
i
s
e i
n
im
ages bas
e
d
on
som
e
statistics, wh
ich
used
t
h
e infl
u
e
n
c
e fu
n
c
tion to
estim
a
t
e
t
h
e resul
t
e
d pi
xe
l
.
The
res
u
l
t
s
of
di
f
f
ere
n
t
st
a
nda
r
d
i
m
ag
es with
differen
t
lev
e
ls
o
f
n
o
i
se are illu
strate
d
[13
]
. Alth
oug
h, th
ere are m
a
n
y
t
ech
n
i
q
u
e
s h
a
d b
een
ap
p
lied to
so
lve th
e salt and
pep
p
e
r
n
o
i
se i
n
th
e im
ag
e, th
ere is n
e
ed
to
d
e
v
e
lop
th
is m
e
t
h
od
s t
o
pro
d
u
c
e m
o
re
enha
ncem
ent and hi
gh
quality im
age. In this
pape
r, a
ne
w
proposed m
e
thod is introduce
d
. That
’s
by ada
p
ted
a devel
o
pe
d t
echni
que t
o
noi
se det
ect
i
on an
d det
e
rm
i
n
e t
h
e si
ze of wi
n
d
o
w
de
pen
d
i
n
g o
n
som
e
cri
t
e
ri
a. Th
e
n
th
e resu
lted
p
i
x
e
l is estim
a
t
e
d
u
s
ing
Gau
s
sian
estim
at
io
n
fun
c
tion
.
In
t
h
e fin
a
l step
, the m
a
x
i
m
u
m
fi
l
t
er is
ap
p
lied on
t
h
e
resu
lted im
ag
e to
g
e
t a b
e
tter reso
lu
tion
and
t
o
im
p
r
ov
ing
the qu
ality.
3.
PROP
OSE
D
METHO
D
In
th
is
p
a
per, t
h
ere is an
in
trod
u
c
ed
for a pro
p
o
s
ed
n
e
w meth
od
to
treat th
e p
a
rticu
l
ar t
y
p
e
o
f
no
ise
that corrupts the im
age in
m
a
ny
way
s
, t
h
at
noi
se i
s
a sal
t
and p
a
pe
r n
o
i
s
e. Fi
g
u
re
1 de
pi
ct
s t
h
e st
eps of t
h
e
pr
o
pose
d
m
e
t
hod
. T
h
e
det
a
i
l
s
o
f
t
h
e
p
r
o
p
o
se
d m
e
t
hod a
r
e e
xpl
ai
ne
d i
n
t
h
e
f
o
l
l
o
wi
ng
st
ep
s:
Step 1
(Noise detecti
o
n):
For each pixel in
the corr
upted i
m
age a(i,j), we
determ
ined if
the pixel is
u
n
c
orru
p
t
ed
, t
h
at m
ean
it is
i
n
th
e
ra
ng
e
0
< a(i,j) <255
, t
h
en
return
t
h
e
sam
e
v
a
lu
e o
f
th
e p
i
x
e
l.
Otherwise,
go
t
o
t
h
e
next
s
t
ep.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
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S
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:
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7
0
8
Sal
t
an
d
Pa
p
p
e
r
N
o
i
s
e Re
m
o
v
a
l
Usi
n
g Resi
z
abl
e
Wi
n
dow
a
n
d
G
a
ussi
a
n
E
s
t
i
m
at
i
o
n F
unc
t
i
on (
S
u
h
a
d
A
.
Al
i)
2
221
S
t
ep
2
(
W
indo
w
s
i
ze
d
e
t
e
rmin
a
t
io
n)
:
i
n
t
h
is step, th
e si
ze of th
e wi
n
d
o
w
is d
e
term
in
ed
d
e
p
e
nd
ing
o
n
t
h
e ratio
of
th
e nu
m
b
er of
th
e un
corrup
ted
p
i
x
e
ls (
nu
pi
x
e
l
) in the
window t
o
the size
of t
h
e whole window
according t
o
the followi
ng equation
(2)
Whe
r
e
N is
re
present t
h
e si
ze
of the c
u
rre
n
t
window.
In th
is
p
a
p
e
r, th
is ratio is com
p
ared
with th
resho
l
d
(its
valu
e is
fix
e
d
to 0
.
3).
If th
e
v
a
lu
e of
ratio
i
s
eq
u
a
l
o
r
m
o
re th
an
t
h
resho
l
d
i
t
will b
e
d
e
p
e
nd
ed. Th
at b
ecau
s
e wh
en
th
e
nu
m
b
er o
f
un
corru
p
t
ed
p
i
x
e
ls is less
th
an
t
h
is
ratio
will b
e
no
t eno
ugh
to estim
a
t
e th
e cu
rr
en
t
p
i
x
e
l, so, th
e
wind
ow
will be d
e
scrib
e
d
as
m
o
stl
y
co
rrup
ted
and
n
o
t
u
tilized
to
p
r
o
cessed
th
e
n
o
i
se. Th
e i
n
itial size o
f
th
e win
d
o
w
will b
e
3
×
3
t
h
en
i
n
creased
t
o
b
e
5
×
5,
7
×
7, an
d so
o
n
. Th
e
max
i
m
u
m
size o
f
th
e
windo
w
will b
e
1
1
×
11
.
St
ep
3
(C
omput
a
t
i
on of
mea
n
and me
dian for e
a
ch window):
com
pute
the m
ean (
m
)
value f
o
r the
wi
n
d
o
w
by
ap
pl
y
i
ng e
q
uat
i
o
n (
3
)
f
o
r t
h
e c
u
r
r
ent
pi
xel
a
n
d fi
nd t
h
e m
e
di
an val
u
e (
md
)
by
so
rt
t
h
e
wi
nd
o
w
'
s
val
u
es
. T
h
e m
e
di
an
val
u
e
wi
l
l
be t
h
e m
i
ddle
value i
n
the s
o
rted wi
ndow'
va
lues.
m
=
∑∑
,
(3
)
Whe
r
e
w
de
not
ed t
o
t
h
e
wi
n
d
o
w
o
f
noi
sy
i
m
age a
n
d
N
d
e
no
ted
t
o
th
e size of
th
e cur
r
e
n
t
w
i
nd
ow
.
Step 4 (Applyi
ng Gaussian
Estima
tion fu
nctio
n
)
:
F
o
r e
a
c
h
unc
or
r
upt
e
d
pi
xel
p
in th
e
wind
ow t
h
at
lies in
th
e
ran
g
e 0
<
p
< 2
5
5
,
d
o
th
e fo
llo
wi
ng
:
St
ep (
4
-1
):
Find
x
wh
ich
is
rep
r
esen
t th
e ab
so
lu
te v
a
l
u
e
o
f
t
h
e di
ffe
rence
between the m
e
dian
value
an
d th
e
p
i
x
e
l
as in
equ
a
tio
n (4
).
|
|
(4
)
St
ep (4
-2
):
Fi
nd
t
t
h
e l
o
cal
st
anda
r
d
di
vi
si
o
n
st
dl
oc
fo
r t
h
e
cu
rre
nt pi
xel.
St
ep (4
-3)
:
Fi
nd t
h
e
Gaus
si
an Est
i
m
a
t
e
d fu
nct
i
on
f
fo
r t
h
e
curre
nt
pi
xel
,
whi
c
h i
s
com
p
ut
ed usi
n
g
equatio
n (1
). Whe
r
e
m
de
n
o
t
e
d t
o
m
ean val
u
e,
st
d
in
th
e eq
u
a
tion
refer to
th
e l
o
cal stand
a
rd
d
i
v
i
sion
s
t
dl
oc
of
t
h
e pi
xel
p
val
u
e a
n
d
x
de
n
o
t
e
d t
o
t
h
e
x
val
u
e t
h
at
c
o
m
put
ed i
n
eq
uat
i
o
n
(4
).
Step 5 (E
sti
m
ate the
pi
xel
val
ue
):
Th
e esti
m
a
ted
p
i
x
e
l
v
a
lu
e is co
m
p
u
t
ed
as th
e ratio
b
e
tween
r
1
and
r
2
th
at com
p
u
t
ed
as eq
uatio
n
s
(5
) and
(6) and
th
is v
a
lu
e will b
e
pu
tted
in
th
e cen
t
e
r of th
e wi
n
d
o
w
. The
est
i
m
a
t
e
d pi
xel
val
u
e
i
s
c
o
m
put
ed
usi
n
g
eq
u
a
t
i
on
(7
).
∑
(5
)
An
d
∑
(6
)
Whe
r
e
k
i
s
re
p
r
esent
t
h
e
u
n
c
o
r
r
u
p
t
e
d
pi
xel
s
num
ber i
n
t
h
e
wi
n
d
o
w
.
Thes
e pi
xel
s
den
o
t
e
d as
s(i)
in
eq
uatio
n
(5).
Th
en th
e
resu
lted
p
i
x
e
l
fro
m
th
is step
is
co
m
p
u
t
ed
as:
I
npu
t no
isy
im
age
Noise
d
e
tectio
n
W
i
nd
ow
size
Determ
in
atio
n
Com
pute m
ean
and m
e
dian for
each window
Pix
e
l no
ise
estim
a
tion
App
l
y m
a
x
filter
Out
put
e
n
hanc
ed
im
age
Fi
gu
re
1.
Pr
o
p
o
se
d m
e
t
hod
p
r
oces
sed
st
ages
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
221
9
–
22
24
2
222
B (
i
, j)
= r1 / r
2
(7
)
The ste
p
s
from 1 t
o
5 a
r
e re
pe
ated for eac
h
pi
x
e
l in
the co
rru
p
t
ed
im
ag
e to g
e
t th
e im
ag
e
B
.
Step
6 (Maximum filter
):
App
l
y th
e m
a
x
filter with
win
dow of size
3×3
on
t
h
e resulted
i
m
ag
e
B
.
Thi
s
i
s
d
one
by
re
pl
aci
ng
t
h
e c
e
nt
er
val
u
e
o
f
t
h
e
wi
n
d
o
w
wi
t
h
t
h
e
m
a
xim
u
m
val
u
e.
4.
RESULTS
Th
e pr
opo
sed meth
o
d
u
s
ed
a
r
e
sizab
l
e
w
i
nd
ow
d
e
p
e
n
d
i
ng
on
th
e
am
o
u
n
t
o
f
no
ise in
th
e w
i
nd
ow
,
and
ada
p
t
e
d
t
h
e st
at
i
s
t
i
c
Gau
ssi
an est
i
m
ati
on f
u
nct
i
o
n
t
o
p
r
edi
cat
e t
h
e
pi
xel
s
t
h
at
m
a
ke t
h
i
s
m
e
t
hod
h
a
ve a
go
o
d
per
f
o
rm
ance com
p
ari
n
g
wi
t
h
t
h
e ot
he
r
m
e
t
hods
. Th
e pro
p
o
se
d
m
e
t
h
o
d
i
s
appl
i
e
d
on 8
-
bi
t
s
per
pi
xel
stan
d
a
rd gray
i
m
ag
es with
t
h
e size
5
1
2
x 51
2, fo
r ex
am
p
l
e Go
ld
h
ill, Len
a
and
B
o
at. Th
e
qu
ality o
f
th
e
resulted im
ages is
m
easured
using
PS
NR
and
SS
IM
qu
ality
m
easu
r
em
en
ts th
at illu
strated in
8
an
d
9
eq
uatio
n
s
respectively.
10
∑∑
(8
)
W
h
er
e
th
e v
a
lue
de
not
e
d
t
o
t
h
e rec
o
nst
r
uct
e
d i
m
age pi
xel
s
and
t
h
e
val
u
e
d
e
no
ted to
t
h
e
o
r
i
g
in
al im
ag
e
value. M
x
N i
s
the size
of image
,
(9
)
Whe
r
e
x a
nd
y are the
windows
of
X and Y im
ages
res
p
ectively. µx
and
µy are
re
prese
n
ted the
v
a
lu
es
of
m
e
a
n
fo
r th
e
w
i
ndo
w
s
x
and
y r
e
sp
ectiv
ely.
σ
,
σ
are de
n
o
t
e
d t
o
t
h
e x a
n
d y
st
a
nda
r
d
de
vi
at
i
o
n
respectively.
σ
refer to t
h
e cr
os
s-co
rrelatio
n
of the m
ean shifted im
ages x
−
µx and y
−
µy, and the di
for i
= 1,
2 are small p
o
sitiv
e con
s
tan
t
s. Th
ese con
s
ta
n
t
s
av
oid
d
i
v
i
d
e
d b
y
zero
issu
es wh
en
eith
er (
μ
μ
) ,
(
σ
σ
) or (
σ
σ
) is clos
e to zero. The
global
SS
I
M
qu
ality i
m
ag
e th
at refer to
th
e i
m
ag
es x
and
y can
b
e
calculated
by a
v
era
g
ing t
h
e
SS
I
M
val
u
es c
o
m
puted for
small spatial windows
of t
h
e two im
ages.
Figures (2), (3)
an
d
(4) illustrated the
propose
d m
e
thod'
s eff
ect on Goldhill,
Boat
and Lena
im
ages
th
at h
a
v
e
salt an
d p
e
pp
er no
ise with
rate
4
0
%,
6
0
%
and
90% resp
ectiv
ely.
(a)
Orig
in
al
Go
l
d
h
ill im
ag
e
(b
) d
i
st
o
r
ted
Go
l
d
h
ill im
a
g
e
(c)
Treated
imag
e
Fi
gu
re
2.
Pr
o
p
o
se
d M
e
t
h
od
e
ffect
on
G
o
l
d
hi
l
l
im
age 40%
S
a
l
t
and
pe
pp
er
noi
se
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Sal
t
an
d
Pa
p
p
e
r
N
o
i
s
e Re
m
o
v
a
l
Usi
n
g Resi
z
abl
e
Wi
n
dow
a
n
d
G
a
ussi
a
n
E
s
t
i
m
at
i
o
n F
unc
t
i
on (
S
u
h
a
d
A
.
Al
i)
2
223
(a)
O
r
igi
n
al Boat im
age
(
b
)
dist
ort
e
d B
o
at im
age
(c)
Treate
d
im
age
Fi
gu
re
3.
Pr
o
p
o
se
d M
e
t
h
od
e
ffect
on
Boat i
m
age 60% salt
and pe
pper noi
s
e
(a)
O
r
igi
n
al Le
na im
age
(b
) di
st
or
t
e
d
Le
na
im
age
(c)
Treate
d
image
Fi
gu
re
4.
Pr
o
p
o
se
d M
e
t
h
od
e
ffect
on
Le
na i
m
age 9
0
%
Sal
t
an
d
pep
p
e
r
no
i
s
e
Tab
l
e 1
sh
ows SSIM and
PSNR resu
lts for Go
ldh
ill,
Bo
at
an
d
Len
a
im
a
g
es with
d
i
fferen
t
salt an
d
pep
p
e
r
'
s
l
e
vel
noi
se
by
a
p
pl
y
i
ng
o
u
r
pr
op
ose
d
m
e
t
hod.
To s
h
ow the e
fficiency
of
our
p
r
op
osed
m
e
th
od
, th
e pr
op
o
s
ed
al
g
o
rithm (PA) is com
p
ared
with
v
a
ri
o
u
s
al
g
o
rith
m
s
lik
e Stan
dard
m
e
d
i
an
filter (SMF),
Ad
ap
tiv
e m
e
d
i
an
filter (AMF), Prog
ressiv
e
switch
i
ng
med
i
an
filter (PSMF), Decisio
n
b
a
sed
med
i
an
al
g
o
rith
m (DBMF), an
d
Mod
i
fied
Decision
Based
Un
symm
etrica
l Trimmed
Med
i
an
Filter (M
DBUT),
as com
p
u
t
ed
in
[7
].
Th
e co
m
p
arison
is
do
n
e
u
s
i
n
g PSNR
measure as
shown in
Table
2. These
res
u
lts
are c
o
m
puted
f
o
r
Lena
st
an
da
rd
i
m
age for
di
ffe
rent
l
e
vel
s
o
f
sal
t
an
d p
e
pp
er no
i
s
e.
Tabl
e 1. Il
l
u
st
r
a
t
i
on of
SS
IM
and
PS
NR
fo
r cor
r
up
ted im
ag
es with d
i
fferen
t lev
e
ls
o
f
no
i
s
e
Noise Levels
Goldhill
Boat
Lena
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
10%
0.
984
39.
217
0.
987
38.
552
0.
992
41.
239
20%
0.
966
36.
146
0.
976
35.
624
0.
984
38.
702
30%
0.
946
34.
135
0.
963
33.
599
0.
974
36.
355
40%
0.
922
32.
516
0.
946
31.
862
0.
961
34.
260
50%
0.
894
31.
086
0.
926
30.
169
0.
945
32.
607
60%
0.
856
29.
573
0.
896
28.
455
0.
918
30.
515
70%
0.
794
27.
603
0.
844
25.
932
0.
874
28.
111
80%
0.
708
25.
733
0.
77
23.
728
0.
799
25.
404
90%
0.
626
24.
388
0.
691
22.
194
0.
731
23.
63
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
221
9
–
22
24
2
224
Tabl
e
2. C
o
m
p
ari
s
o
n
i
n
PS
N
R
bet
w
ee
n t
h
e
pr
o
pose
d
al
go
r
i
t
h
m
and
ot
her
m
e
t
hods
Noise Levels
SMF
AMF
PSMF
DBMF
MDBUT
M
E
PA
10%
28.
49
36.
30
30.
86
36.
98
36.
67
41.
239
20%
25.
75
29.
20
28.
28
33.
22
32.
65
38.
702
30%
21.
85
23.
72
25.
26
30.
38
30.
19
36.
355
40%
18.
41
18.
60
22.
36
28.
23
28.
32
34.
260
50%
14.
73
15.
33
19.
18
26.
49
26.
62
32.
607
60%
12.
23
12.
20
12.
15
24.
72
24.
73
30.
515
70%
9.
98
9.
95
9.
76
22.
66
22.
38
28.
111
80%
8.
02
8.
26
8.
09
20.
42
20.
07
25.
404
90%
6.
58
6.
65
6.
62
17.
23
17.
39
23.
63
5.
CO
NCL
USI
O
N
Thi
s
pa
per i
n
t
r
od
uce
d
a deve
l
ope
d al
go
ri
t
h
m
t
o
enhance t
h
e cor
r
upt
e
d
i
m
age wi
t
h
sal
t
and pe
pp
e
r
n
o
i
se. Th
is meth
od
i
n
tr
odu
ced
a goo
d r
e
su
lts co
m
p
ar
ed
wi
t
h
t
h
e
ot
he
r al
g
o
ri
t
h
m
s
. Thi
s
m
e
t
hod
use
d
a
r
e
sizab
le
w
i
ndo
w sch
e
m
a
to
g
e
t th
e
app
r
opr
iated
size
o
f
w
i
nd
ow
t
h
at hav
e
a
nu
m
b
er
o
f
un
co
rr
up
ted p
i
x
e
ls
t
h
at
im
port
a
nt
i
n
est
i
m
a
ti
on p
r
oces
s. The
usi
ng
of Ga
ussi
a
n
est
i
m
a
t
i
on fu
n
c
t
i
on i
n
st
at
i
s
t
i
cal
m
e
t
hod l
e
d
t
o
a
g
ood
qu
ality an
d
im
ag
e en
h
a
n
cem
en
t. Th
e
PSNR m
e
tric i
llu
strated
in
Tab
l
e 1
rang
ed
fro
m
2
3
to
41
alo
ng
wi
t
h
di
ffe
rent
noi
se l
e
vel
s
.
Al
t
h
o
u
g
h
,
t
h
e
hi
g
h
di
ffe
re
nce in
no
ise lev
e
l, th
e SSIM
m
e
tric h
a
v
e
a slig
h
t
changing a
nd
have a
n
acce
pted res
u
lts with high levels
of noise like 80% and
90%. In the ot
her
words
,
the
g
ood
resu
lts
o
f
SSIM m
e
tric d
e
no
ted th
at the p
r
op
osed
m
e
t
h
od
h
a
v
e
a
g
ood
p
e
rform
a
n
ce an
d a v
i
su
al
q
u
ality,
whe
r
e
SSIM
m
o
ti
vat
e
d
by
t
h
e
o
b
ser
v
at
i
o
n
t
h
at
nat
u
ral
i
m
ages ha
ve
hi
ghl
y
st
ruct
ure
d
si
gnal
s
wi
t
h
st
r
o
n
g
neighborhood depe
ndencies
. These depe
nde
n
cies
carry use
f
u
l
inform
atio
n
ab
ou
t th
e st
ructures of
the objects
in the
vis
u
al sc
ene.
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