Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
4
,
No
. 5, Oct
o
ber
2
0
1
4
,
pp
. 75
1~
75
7
I
S
SN
: 208
8-8
7
0
8
7
51
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
Satellite Image Denoising Usin
g Local Spayed and Optimized
Center Pixel Weights
P
a
la Ma
h
e
sh
K
u
ma
r
Departement of
ECE, Jawahar
l
al Nehru
Techno
lo
gical University
, H
y
d
e
rab
a
d,
Tel
a
nga
na,
I
n
di
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ju 2, 2014
Rev
i
sed
Sep 3, 20
14
Accepted
Sep 18, 2014
Now a day
’
s dig
ital
image processing app
lic
ation
s
are widel
y
use
d
in variou
s
fields
s
u
ch
as
m
e
dical
, m
i
l
itar
y
,
s
a
t
e
ll
it
e,
rem
o
te s
e
ns
ing
and
even
we
b
appli
cat
ions
als
o
. In an
y
app
lic
ation im
age den
o
is
ing is
a chall
e
nging tas
k
because no
ise re
m
oval will incr
e
a
se the
dig
ita
l q
u
alit
y of
an im
a
g
e and will
improve the perceptu
al visual quality
.
In this
paper we propo
sed a new
me
thod “loc
a
l
spay
e
d
a
nd optimiz
e
d
c
e
n
te
r pixe
l we
ights (LS
O
CPW)
with
non local mean
s” to improve the de
noising p
e
rformance of digital
color
image sequences. Simulation results
show that the proposed method has
given th
e be
tter
perform
ance
when com
p
ared
t
o
the
exis
ting
al
gorithm
s
in
terms of peak signal
to
noise ratio (PSNR) and m
ean
squar
e
error (MSE).
Keyword:
C
e
nt
er pi
xel
w
e
i
ght
s
I
m
ag
e d
e
no
ising
Jam
e
s Stein Estim
a
tor
MSE
PSNR
Copyright ©
201
4 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
:
Pala Mahes
h
kum
a
r,
Depa
rtem
ent of ECE,
Jawa
harl
al
Ne
hr
u Tec
h
nol
ogi
cal
Uni
v
ersi
t
y
,
M
u
m
b
ai
R
o
ad,
K
ukat
p
al
l
y
, H
y
dera
bad
,
Tel
a
nga
na,
I
n
di
a.
Em
a
il: mah
e
shp
a
la25
@g
m
a
il.
co
m
1.
INTRODUCTION
Im
ag
es cap
tu
red
fro
m
b
o
t
h
d
i
g
ital cam
era
s
and
co
nv
en
tio
n
a
l
film
ca
meras
will affect
ed
with
t
h
e
n
o
i
se
fro
m
a variety o
f
sou
r
ces. Th
ese
n
o
i
se ele
m
en
ts
will create so
m
e
seriou
s issu
es
for furth
e
r
p
r
o
cessin
g
of
im
ages in prac
tical applications suc
h
as co
m
put
er vi
si
on
, art
i
s
t
i
c
wor
k
o
r
m
a
rket
i
ng an
d al
so i
n
m
a
ny
fi
el
ds.
There a
r
e m
a
n
y
t
y
pes of noi
ses l
i
k
e sal
t
and
pep
p
e
r
, Ga
ussi
an
, spec
kl
e and pa
ssi
o
n
.
In
sal
t
and
p
e
ppe
r
noi
se
(s
par
s
e l
i
ght
a
n
d
dar
k
d
i
st
urba
nces
),
pi
xel
s
i
n
t
h
e ca
p
t
ure
d
i
m
age ar
e ve
ry
di
f
f
er
en
t
i
n
i
n
t
e
nsi
t
y
f
r
om
th
eir n
e
ibou
ri
ng
p
i
x
e
ls; th
e defin
i
ng
ch
aract
eristic is th
at t
h
e in
ten
s
ity v
a
lu
e o
f
a
noisy picture elem
ent bears
n
o
relation
to
th
e co
lor o
f
n
e
ib
ouring
p
i
x
e
ls. Gen
e
rally th
is typ
e
o
f
n
o
i
se
will o
n
l
y affect a s
m
all
n
u
m
b
e
r o
f
pixels i
n
a
n
i
m
age.
Whe
n
we
viewe
d
a
n
im
age whic
h is affected with salt and
pe
ppe
r
noise, t
h
e im
age
cont
ai
n
s
bl
ack
an
d
w
h
i
t
e
d
o
t
s
,
hence
i
t
t
e
r
m
s as sal
t
and
pep
p
e
r
noi
se
.
I
n
Gaus
si
an
n
o
i
s
e,
noi
sy
pi
xel
val
u
e
will b
e
a s
m
al
l
ch
ang
e
of orig
i
n
al v
a
lu
e of a p
i
x
e
l. A
h
i
stogram
, a
d
i
screte p
l
o
t
of th
e am
o
u
n
t
of th
e d
i
stortio
n
o
f
i
n
ten
s
ity v
a
l
u
es ag
ain
s
t t
h
e frequ
en
cy
with
wh
ich
it o
c
cu
rs, it shows a
n
o
rm
al d
i
strib
u
tio
n of
n
o
i
se.
Wh
ile
ot
he
r di
st
ri
b
u
t
i
ons a
r
e p
o
ssi
bl
e, t
h
e Ga
ussi
an
(n
orm
a
l
)
di
st
ri
but
i
o
n i
s
us
ual
l
y
a goo
d m
odel
,
due t
o
t
h
e
c
e
nt
ral
li
mit th
eo
rem
t
h
at says th
at t
h
e
sum
of
di
f
f
er
ent
n
o
i
s
es t
e
nd
s t
o
a
p
pr
oach
a
Ga
ussi
an
di
st
r
i
but
i
o
n.
In
sel
ect
i
ng a n
o
i
s
e
re
d
u
ct
i
o
n al
go
ri
t
h
m
,
one m
u
st
consi
d
e
r
several
fact
o
r
s:
A
di
gi
t
a
l
cam
era m
u
st
ap
pl
y
noi
se
re
duct
i
o
n
i
n
a
fract
i
o
n
of
a sec
o
nd
usi
n
g
a t
i
n
y
o
n
bo
ard
C
P
U
,
whi
l
e a
des
k
t
o
p c
o
m
put
er has
m
u
ch
m
o
re po
wer
an
d t
i
m
e
whet
her sac
r
ifi
c
ing s
o
m
e
real detail inform
a
tion is accep
ta
ble if it allows
m
o
re distortion or noise to
be
rem
oved
(h
o
w
agg
r
essi
vel
y
t
o
deci
de
w
h
et
h
e
r t
h
e ra
ndom
variations i
n
the im
age are
noisy or not)
In
real-world
ph
o
t
o
g
rap
h
s
, max
i
m
u
m
v
a
riati
o
n
s
i
n
brigh
t
n
e
ss ("lu
m
i
n
a
n
c
e d
e
tail") will be co
n
s
isted
by
t
h
e
hi
ghest
spat
i
a
l
f
r
e
que
ncy
,
rat
h
e
r
t
h
a
n
t
h
e ra
n
dom
vari
at
i
o
ns i
n
h
u
e
("ch
rom
a
d
e
t
a
i
l
"
). Si
nce
m
o
st
of
noi
se
red
u
ci
n
g
t
echni
q
u
es s
h
oul
d at
t
e
m
p
t
t
o
rem
ove noi
se
with
ou
t d
e
st
royin
g
of real d
e
tail fro
m
th
e c
a
p
t
ured
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
751
–
7
57
75
2
p
h
o
t
ograph
.
In add
itio
n, m
o
st p
e
o
p
l
e find
l
u
min
a
n
ce
n
o
i
se in
im
ag
es less ob
j
ecti
o
n
a
b
l
e
th
an
chro
m
a
no
ise;
th
e co
l
o
red
b
l
o
b
s
are con
s
i
d
ered
"d
ig
ital-lo
ok
ing
"
an
d
artificial, co
mp
ared
t
o
the
mealy appeara
n
ce
of
luminance noi
s
e that som
e
com
p
are to film grain. For
these two
reas
ons
, m
o
st
of
di
gi
t
a
l
im
age noi
se
reduction algorith
m
s
split the
im
age conte
n
t
into c
h
rom
a
and lum
i
nance c
o
m
ponents.
On
e so
lu
tion
t
o
elim
in
ate n
o
ise is b
y
con
v
o
l
v
i
ng
t
h
e
o
r
i
g
in
al im
ag
e with
a m
a
sk
th
at represen
ts
a
lo
w-p
a
ss filter or sm
o
o
t
h
i
n
g
op
eration
.
Fo
r ex
am
p
l
e,
th
e Gau
ssian
m
a
sk
in
co
rp
orates th
e el
e
m
en
ts
det
e
rm
i
n
ed by
a
Ga
ussi
a
n
f
u
nct
i
o
n
.
T
h
i
s
o
p
erat
i
o
n
bri
ngs
t
h
e val
u
e
of e
ach
pi
xel
i
n
t
o
cl
oser
harm
on
y
wi
t
h
the values of its neighbours.
In ge
ne
ral, a sm
oothing f
ilter sets each pixe
l to the
m
ean
value,
or a wei
ghte
d
mean
,
o
f
itself and
its
n
earby n
e
igh
bou
rs;
th
e Gau
ssian
filter is ju
st
o
n
e po
ssib
l
e set
o
f
wei
g
h
t
s.
Howev
e
r,
sp
atial filtering
ap
pro
a
ch
es
lik
e m
ean
filt
ering
or av
erag
e
filtering
, Sav
itzk
y
filteri
n
g
, Med
i
an
filterin
g
,
b
ilateral filter an
d
Wien
er filters h
a
d
b
e
en
su
ffered
with
l
o
o
s
ing
edg
e
s info
rm
at
io
n
.
All th
e filters th
at h
a
v
e
b
een
m
e
n
tio
n
e
d
abov
e
were
g
ood
at d
e
no
ise o
f
im
ag
es but th
ey will p
r
ov
id
e
o
n
l
y low
freq
u
e
n
c
y co
n
t
en
t of
an im
age it doesn’t prese
r
ve t
h
e high
f
r
eq
ue
ncy
i
n
f
o
rm
at
i
o
n. I
n
o
r
de
r t
o
overc
o
m
e
this
issue Non L
o
cal mean
approach has
been int
r
oduced.
More
recently, noise re
duction tec
hni
ques
base
d on t
h
e
“NON-LOC
A
L ME
ANS
(NLM
) ha
d
devel
ope
d t
o
i
m
prove t
h
e
pe
rf
orm
a
nce of
den
o
i
s
i
n
g m
e
chani
s
m
[1]
[4]
[5]
[9]
[
1
5]
. It
i
s
a dat
a
-d
r
i
ven
di
ff
usi
on m
echani
s
m
t
h
at
was introduced
by
Buades
et al.
in
[1
].
It h
a
s
been
pro
v
e
d
th
at it’s a si
m
p
le
an
d
po
we
rf
ul
m
e
t
h
od
f
o
r
di
gi
t
a
l
i
m
age de
noi
si
n
g
.
In t
h
i
s
, a
gi
ven
pi
xel
i
s
de
noi
se
d
usi
n
g a
wei
g
ht
ed a
v
e
r
age
of
ot
he
r pi
xel
s
i
n
t
h
e (
noi
sy
) i
m
age. I
n
pa
rt
i
c
ul
ar,
gi
ve
n a
noi
sy
i
m
age
, and t
h
e de
nois
ed im
age
at
pi
xel
is com
p
uted by
usi
n
g the form
ula
∑
∑
(1
)
Whe
r
e
is so
me weigh
t
assi
gn
ed to
p
i
x
e
l
. Th
e su
m
in
(1)
is id
eally p
e
rfo
r
m
e
d
to
who
l
e
i
m
age to de
noise the
noisy i
m
age.
NLM a
t
large
noise levels
will not
give
accurate
results beca
use the
co
m
p
u
t
atio
n
o
f
weigh
t
s
o
f
p
i
xels will b
e
d
i
fferen
t
for so
m
e
n
e
ibo
u
rh
ood
p
i
x
e
ls
wh
ich
look
s lik
e sam
e
.
Mo
st of th
e stan
d
a
rd
algo
rithm
u
s
ed
to
d
e
no
ise th
e no
isy imag
e and
p
e
rfo
rm
th
e ind
i
v
i
d
u
a
l
filtering
pr
ocess
.
Den
o
i
s
e gene
ral
l
y
reduce t
h
e
noi
se
l
e
vel
but
t
h
e im
age i
s
eit
h
er
bl
ur
red
or o
v
e
r sm
oot
hed d
u
e t
o
losses like edges or lines. In
the recent years
there has bee
n
a fair
am
ount of resea
r
c
h
on
center pi
xel weight
(C
P
W) f
o
r i
m
age de
n
o
i
s
i
n
g [
3
]
,
beca
use C
P
W p
r
o
v
i
d
es an
app
r
o
p
r
i
a
t
e
ba
si
s fo
r sepa
rat
i
ng
n
o
i
s
y
si
gnal
fr
om
the im
age signal. Optim
ized CPW
is
g
ood a
t
energy com
p
action, t
h
e sm
a
ll
coefficient a
r
e m
o
re likely due t
o
noise a
n
d large coefficient
due to im
porta
nt signal feat
ure
[8].
These
small coeffi
ci
ent
s
can
be t
h
res
h
ol
de
d
with
ou
t affecti
n
g
th
e sign
ifican
t featu
r
es o
f
th
e i
m
age. T
h
e proposed local
spayed a
nd
optim
ized
CPW
cor
r
es
po
n
d
t
o
i
t
s
cont
i
n
u
ous
ver
s
i
o
n sam
p
l
e
d us
ual
l
y
on a dya
d
ic grid, which m
eans
that the scale
s
and
tran
slatio
ns are p
o
wer of two
[5
].
Local spa
y
ed and
optim
ized CPW
is
a sim
p
l
e
non
-l
i
n
ear t
echni
que
, whi
c
h
ope
rates on
one weighted c
o
e
fficient
at a time. Expe
rim
e
n
t
s show the e
f
f
ectiveness
of t
h
e ne
w technique bot
h
in
ter
m
s o
f
peak
sig
n
a
l
-
to-n
o
i
se ratio
(on
si
m
u
lated
n
o
i
sy i
m
ag
es) an
d
o
f
subj
ect
iv
e q
u
a
lity (on
actu
a
l
im
ages).
In th
is letter,
we
d
i
scu
s
s th
e CPW prob
lem
with
NLM
an
d pro
p
o
s
e
new
o
p
tim
ized
so
lu
tion
“l
o
cal
spayed a
n
d optimized CPW
(L
SOCPW)”.
Th
e rest o
f
t
h
is th
esis h
a
s
be
en o
r
g
a
ni
ze
d a
s
:
Sect
i
on I
I
e
x
i
s
t
i
n
g
techniques s
u
c
h
as Savitzky-golay,
m
e
dian, bilateral, wavelet filters, and NLM; Section III disc
usses t
h
e ne
w
opt
i
m
i
zed sol
u
t
i
on o
f
t
h
e C
P
W p
r
o
b
l
e
m
;
Sect
i
on I
V
s
h
o
w
s
expe
ri
m
e
nt
al
com
p
ari
s
on
s f
o
r
vari
ous t
e
c
h
ni
q
u
es
with
th
e n
e
w
so
lu
tion
;
and Sectio
n
V co
n
c
l
u
d
e
s t
h
e th
esis.
2.
E
X
ISTING METHODS
In
t
h
is section
we
d
i
scu
ssed
variou
s sp
atial filters an
d th
eir p
e
rfo
rm
an
ce wh
en
a
no
isy in
pu
t
will b
e
give
n to them
. Here
in t
h
is se
ction
we
had e
xplaine
d a
bout each
filter in detail.
a.
Savitz
ky-Gol
ay Filter
It
i
s
a sim
p
l
i
fi
ed m
e
t
hod and
uses l
east
squa
res t
ech
ni
q
u
e f
o
r cal
c
u
l
a
t
i
ng
di
ffe
re
nt
i
a
t
i
on an
d
sm
o
o
t
h
i
n
g
o
f
d
a
ta. Its co
m
p
u
t
atio
n
a
l sp
eed will b
e
im
p
r
ov
ed
wh
en co
m
p
ared
least-squares techn
i
qu
es. Th
e
maj
o
r
d
r
awb
a
ck
of th
is filter is: So
m
e
o
f
first and
last
d
a
ta p
o
i
n
t
can
no
t sm
o
o
t
h
e
n o
u
t
b
y
th
e
o
r
ig
in
al
Savitzky-Golay m
e
thod.
Ass
u
m
i
ng that,
filter length or
fra
m
e
size (in S
-
G filter
num
b
er of
data sam
p
le rea
d
i
n
t
o
t
h
e
st
at
e
vect
o
r
at
a t
i
m
e)
N i
s
od
d,
N
=
2M
+1
an
d
N
=
d+
1,
w
h
ere
d=
pol
y
n
o
m
i
al o
r
de
r
or
p
o
l
y
nom
i
a
l
degree.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
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:
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8
S
a
t
ellite Imag
e Den
o
i
si
n
g
Usi
n
g Lo
ca
l
Sp
a
y
ed
a
n
d
Op
timized
Cen
t
er Pixel Weig
h
t
s
(
P
al
a
Ma
hes
h
K
u
m
a
r)
75
3
b.
Media
n
filter
Th
is
is a non
lin
ear
d
i
g
ital spatial filterin
g
t
ech
n
i
q
u
e
, o
f
ten
u
s
ed
to
remo
v
a
l of n
o
i
se fro
m
d
i
g
ital
i
m
ag
es. Med
i
an
filtering
h
a
s
b
een
wid
e
ly
u
s
ed
in
m
o
st o
f
t
h
e d
i
g
ital
i
m
ag
e p
r
o
cessi
n
g
ap
p
lication
s
. The
m
a
in
id
ea o
f
th
e m
e
d
i
an
filter is to
ru
n
throug
h
th
e i
m
ag
e
en
try b
y
p
i
x
e
l, rep
l
acin
g
each
pix
e
l with
th
e
med
i
an
val
u
e
o
f
nei
g
h
b
o
r
i
n
g pi
xel
s
.
The pat
t
e
r
n
o
f
nei
g
hb
or
s
is called
th
e "wind
o
w",
wh
ich
slid
es, p
i
x
e
l
b
y
p
i
x
e
l,
ove
r t
h
e e
n
tire
im
age.
c.
Bila
tera
l filter
The
bilateral filter is a nonli
n
ear
filter which do
es the
spatial averagi
ng without sm
oothing e
d
ge
s
inform
ation. Because of this
feat
ure it has
been s
h
own that it’s an
effective im
age
denoising algorithm
.
Bilateral filter
is p
r
esen
ted
by To
m
a
si an
d
Man
d
u
c
h
i
in
19
98
.
Th
e con
c
ep
t of th
e
b
ilateral filter was also
p
r
esen
ted
i
n
[8] as th
e SUSAN filter and
in
[3
] as th
e
n
e
igh
borhoo
d
filter. It is
m
e
n
tio
n
a
b
l
e th
at th
e Beltra
m
i
flow algo
rithm
is co
n
s
id
ered
as t
h
e th
eoretical o
r
ig
i
n
o
f
t
h
e b
ilateral
filter
[4
] [5
]
[6
], wh
ich
p
r
o
d
u
ce a
spectrum
of image enhanci
n
g algorith
m
s
ran
g
i
n
g
fr
om
t
h
e l
i
n
ear
di
f
f
us
i
o
n
to
th
e n
on-lin
ear flows. The
b
ilateral filter
tak
e
s a
w
e
igh
t
ed
su
m
o
f
th
e
p
i
x
e
ls i
n
a l
o
cal n
e
igh
borhood
; th
e
w
e
igh
t
s d
e
p
e
nd
on
b
o
th
th
e
sp
atial d
i
stan
ce and
th
e in
ten
s
ity len
g
t
h
.
In
t
h
is way,
edg
e
s are
p
r
eserv
e
d
well wh
ile no
ise
is eli
m
in
ated
ou
t.
d.
Wav
e
let Filtering
Signal
de
noisi
ng
usi
ng t
h
e
DWT [16] consists of
the t
h
ree s
u
cces
sive proce
d
ures,
nam
e
ly, signal
d
eco
m
p
o
s
ition
,
th
resho
l
d
i
n
g
o
f
th
e
DW
T co
efficien
ts, and
sign
al reconstru
c
tion
.
First
l
y, we carry ou
t th
e
wavel
e
t
a
n
al
y
s
i
s
of
a
noi
sy
s
i
gnal
up
t
o
a
c
hos
en
l
e
vel
N.
Seco
n
d
l
y
, we
pe
rf
orm
t
h
res
hol
di
n
g
of
t
h
e
det
a
i
l
co
efficien
ts from lev
e
l 1
to
N. Lastly, we syn
t
h
e
size th
e signal using the s
p
ayed
detail coefficients from
level
1
to
N and
approx
im
at
io
n
co
efficien
ts
o
f
level N.
Howe
ver
,
i
t
i
s
gene
ral
l
y
im
possi
bl
e t
o
rem
ove al
l
t
h
e
noi
se
with
ou
t corruptin
g
th
e si
g
n
a
l. As for th
resho
l
d
i
ng
,
we
can settle eith
er a lev
e
l-d
e
p
e
n
d
e
nt th
resho
l
d v
e
cto
r
of
len
g
t
h N or
a glo
b
a
l thr
e
sh
o
l
d of
a
con
s
tan
t
valu
e fo
r all levels.
e.
Classic
Non l
o
cal me
ans
It
i
s
a dat
a
-d
ri
ven
di
f
f
usi
on
m
echani
s
m
t
h
at
was i
n
t
r
o
d
u
ced by
B
u
a
d
es
et al.
in [1]
.
It has be
e
n
pr
o
v
ed t
h
at
i
t
’
s a sim
p
l
e
and
po
we
rf
ul
m
e
tho
d
fo
r di
gi
t
a
l
im
age den
o
i
s
i
n
g.
In t
h
i
s
, a
gi
ven
pi
xel
i
s
de
noi
se
d
usi
n
g
a
wei
g
ht
ed a
v
e
r
age
of
ot
he
r
pi
xel
s
i
n
t
h
e
(
n
oi
sy
) i
m
age.
I
n
pa
rt
i
c
u
l
ar,
gi
ve
n
a
n
o
i
sy
im
age
, a
n
d the
d
e
no
ised
im
ag
e
at
pi
xel
i
s
com
put
ed
by
u
s
i
ng t
h
e
fo
rm
ul
a
∑
∑
(1
)
Whe
r
e
is so
me weigh
t
assi
gn
ed to
p
i
x
e
l
. Th
e su
m
in
(1)
is id
eally p
e
rfo
r
m
e
d
to
who
l
e
i
m
age to de
noise the
noisy i
m
age.
NLM a
t
large
noise levels
will not
give
accurate
results beca
use the
co
m
p
u
t
atio
n
o
f
weigh
t
s
o
f
p
i
xels will b
e
d
i
fferen
t
for so
m
e
n
e
ibo
u
rh
ood
p
i
x
e
ls
wh
ich
look
s lik
e sam
e
.
,
/2
∈
(2
)
In
t
h
i
s
eac
h
we
i
ght
i
s
c
o
m
put
ed
by
si
m
i
l
a
ri
ty
qua
nt
i
f
i
cat
i
o
n
bet
w
ee
n t
w
o
l
o
cal
pat
c
hes a
r
o
u
n
d
n
o
i
s
y
pi
xel
s
and
as shown
in
eq.
(2
).
Her
e
,
i
s
a
Gaus
si
an
wea
k
l
y
sm
oot
h
ker
n
el
[1]
a
n
d
d
e
no
tes th
e
l
o
cal
pat
c
h, t
y
p
i
cal
l
y
a squa
re
cent
e
re
d at
t
h
e
pi
xel
and
i
s
a t
e
m
p
erat
ur
e
par
a
m
e
t
e
r cont
rol
l
i
ng t
h
e
beha
vi
or
of
t
h
e
wei
g
ht
f
unct
i
o
n.
3.
PROP
OSE
D
LOCAL
SP
A
Y
ED
A
N
D
O
P
TIMIZ
E
D C
P
W
ALGO
RI
THM
a.
Ex
isting
Center Pix
e
l Wei
g
hts
The
CPW i
n
the
classic
NL
M is
unitary, because
(2)
im
plies
,
1
fo
r
all
∈
1
. H
o
we
ve
r,
i
t
has
b
een repo
rted
th
at th
is
un
itary CPW
will no
t p
e
rform
we
ll in
m
a
n
y
ev
en
ts [7
].
In
d
e
ed, if an im
ag
e will b
e
affect
ed
wi
t
h
hi
g
h
er l
e
vel
s
of
noi
se i
t
gi
ves p
o
o
r
per
f
o
rm
ance whe
n
t
h
e noi
sy
pi
xel
dom
i
n
at
es i
n
t
h
e
reco
vere
d pi
xe
l
.
In i
m
prove
r t
o
t
h
i
s
C
P
W
,
s
e
veral
ot
her C
P
W
s
h
a
d
been
pro
p
o
se
d an
d
m
e
rged wi
t
h
i
n
t
h
e
NLM comm
unity to enhance
the syste
m
perform
a
nce. The
s
e in
clude the
zero CPW
(3),
the Stein CPW (5),
and t
h
e m
a
x CP
W
(
6
)
.
Th
ese
C
P
W
s
are
of
t
w
o g
r
ou
ps:
gl
obal
C
P
Ws (
3
)
,
(4
) an
d l
o
cal
C
P
W
s
(
5
)
,
(
6
)
.
The
g
l
ob
al CPWs
use a co
n
s
tan
t
cen
t
er
p
i
x
e
l
wei
g
h
t
s fo
r ev
ery
p
i
x
e
l,
wh
ile the lo
cal will
v
a
ry for all p
i
x
e
ls.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
751
–
7
57
75
4
In
t
h
e
fu
rt
he
r
sect
i
on,
we
wi
l
l
sho
w
t
h
at
al
l
of
t
h
e a
b
ove
m
e
nt
i
oned C
P
W
s
ha
d
fai
l
e
d t
o
t
a
ke
al
l
vari
a
b
l
e
s i
n
t
o
c
onsi
d
erat
i
o
n
an
d t
h
e
r
ef
ore we exagge
rate
the CPW
problem
.
0
(3
)
1
(4
)
e
x
p
|
|
/
(5
)
m
a
x
,
(6
)
b.
Shrinka
g
e
Estima
to
r
To
fu
lly ex
po
se th
e CPW
prob
lem
,
we sep
a
rate th
e
c
ont
ri
b
u
t
i
o
n
s
of t
h
e c
e
nt
er a
n
d
of
t
h
e n
o
n
-
ce
nt
er
pixels i
n
the
Non L
o
cal Means de
noised
pixel
in
(2)
(7
)
Whe
r
e
is th
e su
m
all n
o
n
-center p
i
x
e
ls
,
∈
\
(8
)
and
i
s
t
h
e de
n
o
i
sed
pi
xel
by
u
s
i
n
g
al
l
n
o
n
-
ce
nt
er
wei
g
ht
s.
,
/
∈
\
(9
)
If we
a
r
e
give
n an
optim
ized
and
s
o
lve
fo
r
,
we can see th
at
th
e
o
p
tim
ized
is a
f
u
n
c
tion of
,
,
. Thu
s
a Cen
t
er
p
i
x
e
l
weigh
t
s do
es
no
t co
nsid
er all
t
h
e va
riables. He
re we notice
t
h
at the
gl
obal
C
P
Ws
neglect all thre
e va
riables
form
the CP
W fun
c
tio
n,
wh
ile t
h
e lo
cal C
P
W
n
e
g
l
ects
.
Let
be a
f
r
act
i
o
n
of
t
h
e c
o
nt
ri
b
u
t
i
o
n
o
f
t
h
e ce
nt
er
pi
xel
in
, nam
e
ly
⁄
(1
0)
Accord
ing
l
y, th
e
NLM-CPW prob
le
m
in
(7) can
b
e
rewritten
as
1
(1
1)
Eq. (
1
1) i
s
so
cal
l
e
d shri
n
k
a
g
e est
i
m
a
t
o
r, whi
c
h can be
an im
pro
v
e
d
v
e
rsi
o
n o
f
exi
s
t
i
ng est
i
m
at
ors by
usi
n
g
th
e inp
u
t
d
a
ta.
c.
The James
-Stein Center Pi
xel Weight
Th
is is a classic so
l
u
tio
n wh
ich
m
i
n
i
mizes th
e risk of estim
a
tio
n
in term
s o
f
th
e erro
r and
t
h
e
cor
r
es
po
n
d
i
n
g
new
est
i
m
at
or
i
s
deri
ved
as
fo
l
l
o
ws
1
̂
(1
2)
Whe
r
e,
1
2
/
‖
̂
‖
(1
3)
d.
Prop
osed
L
o
c
a
l
Sp
a
y
ed
an
d
op
timiz
e
d Ce
nter Pi
xel Wei
g
hts
Alth
oug
h
th
e
Jam
e
s-Stein
C
P
W
con
s
id
ers
all th
e v
a
riab
les in
th
e CPW
fun
c
tion
,
it stil
l a
g
l
o
b
a
l
CPW
and will gives a
m
onovula
r
weight
to all pixels. Howe
ver, instead
of
unbiased for each pi
xel the
d
e
no
ised
p
r
o
c
ess will b
e
always b
i
ased. Thus, id
eally
we
wan
t
a lo
cal spayed
and
op
timized
CPW
for ev
ery
pixel.
One possible sol
u
tion is to re
place
the
‖
̂
‖
in
(12) with
‖
̂
‖
, bu
t it leads to
an
un
stable
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
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7
0
8
S
a
t
ellite Imag
e Den
o
i
si
n
g
Usi
n
g Lo
ca
l
Sp
a
y
ed
a
n
d
Op
timized
Cen
t
er Pixel Weig
h
t
s
(
P
al
a
Ma
hes
h
K
u
m
a
r)
75
5
so
lu
tion
,
b
e
cau
s
e of th
e faulty p
o
i
n
t
-wise esti
m
a
tio
n
.
Altern
ativ
ely, we can
d
i
v
i
d
e
t
h
e in
pu
t i
m
ag
e in
to
several bl
ocks
and thus the J
S
CPW
(13) wi
ll be co
m
put
ed for each local
block whic
h i
n
terns a local spayed
an
d op
timized
CPW
will b
e
ad
ap
ted
to every p
i
x
e
l.
1
|
|
2
/
‖
̂
‖
(1
4)
In this way, we derive
d and constructe
d a new local
spaye
d
and optim
i
ze
d CPW
at each and eve
r
y pixel, and
th
u
s
th
e
p
i
x
e
ls
will b
e
d
e
no
ised
b
y
u
s
i
n
g
LAOCPW, it can
b
e
written
as
1
̂
(1
5)
4.
R
E
SU
LTS AN
D ANA
LY
SIS
All th
e fo
llowi
n
g
sim
u
latio
n
s
are do
n
e
un
d
e
r th
e MATLAB R2
01
4
a
env
i
ron
m
en
t with
In
tel Co
re i3
CPU at 4.0
GHz.
We c
o
m
p
ared t
h
e pe
rformance eval
u
a
ti
o
n
of ex
isting
CPW
s
with
the p
r
op
o
s
ed
LAOCPW
al
go
ri
t
h
m
unde
r t
h
e cl
assi
c
N
o
n
-
L
o
cal
M
ean
s fram
e
wo
rk
(
o
nl
y
t
h
e C
P
W i
s
cha
nge
d)
.
In
p
a
rt
i
c
ul
ar,
we se
t
t
h
e
search
re
gi
o
n
t
o
30×
3
0
s
qua
r
e
, an
d
14
x
1
4
B
cent
e
re
d
on
t
h
e l
o
cal
pi
xel
,
an
d t
e
st
pe
rf
o
r
m
a
nce fo
r 3
x
3
,
5
x
5
an
d 7x7
p
a
tches, r
e
sp
ectiv
el
y. H
e
re
gray s
cale and col
o
red im
ages both
have
bee
n
t
a
ken
i
n
t
o
co
nsi
d
erat
i
o
n
with
add
itiv
e
Gau
s
sian
n
o
i
ses. Th
en
the d
e
n
o
i
si
n
g
p
e
rfo
rman
ce will b
e
ev
alu
a
ted
b
y
calcu
l
atin
g
th
e
PSNR
,
wh
ich
is
u
s
ed
t
o
m
easu
r
e th
e
q
u
a
lity of th
e reco
v
e
red
im
ag
e after
d
e
n
o
i
si
n
g
op
eratio
n
F
i
gure 2.
P
e
rfor
m
ance r
e
s
u
lts
of
exis
ting
and p
r
o
pos
ed CP
W
s
for “
l
ena”
F
i
gure 3.
P
e
rfor
m
ance r
e
s
u
lts
of
exis
ting
and p
r
o
pos
ed CP
W
s
for “
v
egetabl
e
”
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
751
–
7
57
75
6
Fig
u
re
4
.
Perform
an
ce resu
lts
o
f
ex
isting
an
d propo
sed CPWs
for “satellite”
(a)
(
b
)
(c)
Figu
re
6.
(a
) (
b
) a
n
d
(c
) Com
p
ariso
n
of
PS
N
R
values
f
o
r
ex
isting a
n
d
p
r
o
p
o
se
d CP
Ws
fo
r
3 test im
age
5.
CO
NCL
USI
O
N
In t
h
i
s
l
e
t
t
e
r, a
sim
p
l
e
and un
i
que m
e
t
hod h
a
s been
pr
o
pos
ed t
o
ad
dre
ss t
h
e i
ssue o
f
i
m
age rec
ove
ry
fro
m
its n
o
i
sy
co
un
terp
art.
It is b
a
sed
on
the lo
cal sp
ayed an
d
op
timized
cen
ter p
i
x
e
l
weigh
t
alg
o
rith
m
an
d
o
v
e
rco
m
es
th
e ex
istin
g
CPW
p
r
ob
lem wh
ich o
ccurs in
cl
assical NLM filtering and
shrinkage estim
ator. This
propose
d
m
e
thod of de
noise
algorithm
produce overall be
tter psnr
res
u
lt com
p
ared wit
h
ot
her tra
d
itional
denoises
a
p
proaches unde
r va
rious
large noise
levels.
28.5
29
29.5
30
30.5
31
Lena
Lena
26.2
26.4
26.6
26.8
27
27.2
27.4
V
e
git
a
ble
Vegitable
28.5
29
29.5
30
30.5
31
31.5
32
Sa
t
e
llit
e
Satellite
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
S
a
t
ellite Imag
e Den
o
i
si
n
g
Usi
n
g Lo
ca
l
Sp
a
y
ed
a
n
d
Op
timized
Cen
t
er Pixel Weig
h
t
s
(
P
al
a
Ma
hes
h
K
u
m
a
r)
75
7
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