TELK
OMNIKA
,
V
ol.
15,
No
.
1,
March
2017,
pp
.
540
548
ISSN:
1693-6930,
accredited
A
b
y
DIKTI,
Decree
No:
58/DIKTI/K
ep/2013
DOI:
10.12928/telk
omnika.v15.i1.3164
540
Ima
g
e
De-noising
on
Strip
Steel
Surface
Def
ect
Using
Impr
o
ved
Compressive
Sensing
Algorithm
Dongy
an
Cui
1,2
,
K
e
wen
Xia*
1
,
Jingzhong
Hou
1
,
and
Ahmad
Ali
1
1
School
of
Electronics
Inf
or
mation
Engineer
ing,
Hebei
Univ
ersity
of
T
echnolo
gy
Tianjin/China/Hebei
Univ
ersity
of
T
echnology
2
School
of
Inf
or
mation
Engineer
ing,
Nor
th
China
Univ
ersity
of
Science
and
T
echnology
T
angshan/China/Nor
th
China
Univ
ersity
of
Science
and
T
echnology
Corresponding
author
,
e-mail:
kwxia@heb
ut.edu.cn
Abstract
De-noising
f
or
the
str
ip
steel
surf
ace
def
ect
image
is
conductiv
e
to
the
accur
ate
det
ection
of
the
str
ip
steel
surf
ace
def
ects
.
In
order
to
filter
the
Gaussian
noise
and
salt
and
pepper
noise
of
str
ip
steel
surf
ace
def
ect
images
,
an
impro
v
ed
compressiv
e
sensing
algor
ithm
w
as
applied
to
def
ect
image
de-noising
in
this
paper
.
First,
the
impro
v
ed
Regular
iz
ed
Or
thogonal
Matching
Pursuit
algor
ithm
w
as
descr
ibed.
Then,
three
typical
surf
ace
def
ects
(scr
atch
,
scar
,
surf
ace
upw
ar
ping)
images
w
ere
selected
as
the
e
xper
imental
samples
.
Last,
detailed
e
xper
imental
tests
w
ere
carr
ied
out
to
the
str
ip
steel
surf
ace
def
ect
image
de-noising.
Through
compar
ison
and
analysis
of
the
test
results
,
the
P
eak
Signal
to
Noise
Ratio
v
alue
of
the
proposed
algor
ithm
is
higher
compared
with
other
tr
aditional
de-noising
algor
ithm,
and
the
r
unning
time
of
the
proposed
algor
ithm
is
only26.6%
of
that
of
tr
aditional
Or
thogonal
Matching
Pursuit
algor
ithms
.
Theref
ore
,
it
has
better
de-noising
eff
ect
and
can
meet
the
requirements
of
real-time
image
processing.
K
e
yw
or
d:
compressiv
e
sensing,
surf
ace
def
ects
,
image
de-noising
Cop
yright
c
2017
Univer
sitas
Ahmad
Dahlan.
All
rights
reser
ved.
1.
Intr
oduction
Image
noise
reduction
is
a
classical
prob
lem
in
image
processing
which
has
o
v
er
50
y
ears
of
research
histor
y[1,
2],
and
stil
l
is
a
hot
topic.
The
str
ip
steel
surf
ace
def
ect
images
in
the
process
of
collection,
acquisition
and
tr
ansmission
will
be
polluted
to
some
e
xtent
b
y
visib
le
or
in
visib
le
noise
,
also
due
to
the
unstab
le
light,
camer
a
vibr
ation
and
other
f
actors
etc.
Theref
ore
,
it
is
necessar
y
to
carr
y
out
the
noise
processing
of
the
collected
images
.
A
large
n
umber
of
studies
ha
v
e
been
carr
ied
out
on
the
surf
ace
def
ect
image
de-noising
at
home
.
In
2008,
Liu
W
eiw
ei,
Y
un
Hui
Y
an
et
al
of
Nor
theaster
n
Univ
ersity
put
f
orw
ard
an
image
de-noising
method
based
on
local
similar
ity
analysis
and
neighborhood
noise
e
v
aluation
[3];
In
2010,
Bo
T
ang
et
al
studied
the
r
ules
of
str
ip
steel
surf
ace
def
ects
image
de-noising
based
on
w
a
v
elet
t
hreshold[4];
In
2012,
Hao
Xu
of
W
uhan
Univ
ersity
of
Science
and
T
echnology
proposed
the
method
of
surf
ace
def
ect
of
str
ip
steel
based
on
mathematical
mor
phology
,
which
could
detect
small
def
ect
edge
under
strong
noise
and
o
wn
strong
noise
imm
unity[5].
F
rom
the
abo
v
e
,
the
e
xisting
str
ip
steel
surf
ace
def
ect
image
de-noising
methods
mainly
f
ocused
on
the
tr
aditional
filter
ing
method.
In
the
e
xisting
theor
y
,
the
or
iginal
signal
is
mostly
pro-
jected
to
a
cer
tain
tr
ansf
or
mation
space
,
and
the
sparsity
of
the
coefficient
in
the
projection
do-
main
is
as
a
fundamental
basis
.
While
the
e
xistence
of
noise
aff
ected
the
sparsity
of
signals
in
the
tr
ansf
or
m
space
.
So
the
optimization
method
is
used
to
restore
the
signal,
if
only
a
single
sparse
constr
aint
pr
inciple
is
used,
it
is
difficult
t
o
accur
ately
reconstr
uct
the
or
iginal
signal.
In
this
case
,
compressiv
e
sensing
theor
y
still
ma
y
tak
e
other
eff
ectiv
e
method
of
reconstr
ucting.
Numerous
studies
sho
w
that
the
reconstr
uction
algor
ithm
based
on
compression
perception
theor
y
is
applied
in
signal
de-noising
can
achie
v
e
good
eff
ect[6]-[8].
Donoho[9]-[1
0],Candes[11]-[13],Romberg[11]-
[13]
and
T
ao[12]-[13]
and
other
scientists
initially
put
f
orw
ard
the
concept
of
compressed
sensing
from
sparse
signal
decomposition
and
appro
ximation
theor
y
in
2004,
f
ollo
w
ed
b
y
a
large
n
umber
Receiv
ed
September
9,
2016;
Re
vised
December
27,
2016;
Accepted
J
an
uar
y
13,
2017
Evaluation Warning : The document was created with Spire.PDF for Python.
TELK
OMNIKA
ISSN:
1693-6930
541
of
rele
v
ant
theoretical
research.
M.A.T
.
Figueiredo
proposed
the
g
r
adient
projection
f
or
sparse
reconstr
uction(GPSR)algor
ithm
based
on
the
L1
nor
m.
The
method
obtaine
d
the
good
eff
ect
of
denoising
[14].
The
compressed
perception
theor
y
is
introduced
into
the
str
ip
steel
surf
ace
def
ect
image
preprocessing,
which
is
r
arely
mentioned
in
the
liter
ature
at
home
and
abroad.
Theref
ore
,
In
this
paper
,
the
impro
v
ed
R
OMP
algor
ithm
w
as
applied
to
the
str
ip
steel
surf
ace
def
ect
image
de-noising,
which
has
better
de-noising
eff
ect
and
shor
ter
r
unning
time
compared
with
tr
aditional
median
filter
ing,
w
a
v
elet
threshold
method
and
tr
aditional
compressed
sensing
algor
ithm.
2.
Resear
c
h
Method
2.1.
Description
of
weighted
R
OMP
algorithm
Needell
et
al
proposed
the
regular
iz
ed
or
thogonal
matching
pursuit
algor
ithm
(R
OMP)
based
on
the
or
thogonal
matching
pursuit
(OMP)[15]-[16].
All
matr
ices
satisfied
the
restr
icted
isometr
y
condition
and
all
sparse
signals
can
be
reconstr
ucted.
The
algor
ithm
w
as
impro
v
ed
based
on
R
OMP
algor
ithm.
The
selection
of
atomic
inde
x
set
f
or
the
first
time
w
as
using
w
eighted
correlation
coefficient,
not
only
consider
ing
the
correlation
coefficient
of
the
current
iter
ation,
also
consider
ing
the
correlation
coefficient
of
the
last
iter
ation,
and
e
xpanding
the
selection
scope
of
inde
x
v
alue
.
W
eighted
f
or
m
ula
is
as
sho
wn
in
(1).
g
t
=
g
+
g
t
1
s:t:g
=
A
T
r
T
1
;
0
<
<
1
;
0
<
<
1
;
+
=
1
(1)
The
pseudo
code
of
algor
ithm
is
as
f
ollo
ws
.
Input:(1)measurement
matr
ix
y
,
y
2
R
;(2)
M
N
dimensional
sensing
matr
ix
A
=
;(3)
sparsity
le
v
el
K
of
the
signal(the
n
umber
of
nonz
ero
elements
in
x
).
Output
N
dimensional
reconstr
ucted
signal(sparse
appro
ximation
signal)
^
x
2
R
N
.
Initializ
e
r
0
=
y
;
0
=
;
A
0
=
Iter
ation
step(1)Calculate:
g
=
abs
A
T
r
t
1
(which
is:
h
r
t
1
;
j
i
;
1
j
N
);
step
(2)Obtain
u
=
j
g
t
j
according
to
f
or
m
ula
(1),choose
a
set
J
of
the
K
biggest
or
nonz
ero
v
alues
,
which
corresponds
to
the
column
n
umber
of
A
and
constr
uct
a
set
J
;
step
(3)Regular
iz
e:
j
u
i
j
2
j
u
j
j
f
or
all
i;
j
2
J
0
,Among
all
subset
J
0
,choose
J
0
with
the
maximal
energy
P
j
j
u
(
j
)
j
2
;
j
2
J
0
;
step
(4)
t
=
t
1
S
J
0
,
A
t
=
A
t
1
S
j
(f
or
all
j
2
J
0
);
step(5)
Calculate
the
least
squares
solution
of
y
=
A
t
t
:
^
t
=
ar
g
min
t
k
y
A
t
t
k
=
(
A
t
t
)
1
A
T
t
y
;
step
(6)
Update
residual:
r
t
=
y
A
t
^
t
=
y
A
t
A
T
t
A
1
A
T
t
y
step
(7)
t
=
t
+
1
,
if
t
K
,
then
retur
n
step
(1),
if
t
>
K
or
k
t
k
0
2
K
(
k
t
k
0
represents
the
n
umber
of
elements
in
the
set
or
residua
r
t
=
0
,then
the
iter
ation
stop
,
and
enter
step
(7);
step
(8)
^
t
has
nonz
ero
entr
ies
at
t
the
v
alue
is
respectiv
ely
^
t
obtained
from
reconstr
uc-
tion
step
(9)
reconstr
ucted
the
signal
^
x
=
^
.
2.2.
De-noising
Model
Based
On
The
W
eighted
Correlation
R
OMP
Algorithm
Assuming
that
the
receiv
ed
image
signal
is
g
(
x;
y
)
,
which
is
contaminated
b
y
noise
.
The
clean
image
is
f
(
x;
y
)
.
The
additiv
e
noise
is
n
(
x;
y
)
.Then
the
additiv
e
noise
model
is
g
(
x;
y
)
=
f
(
x;
y
)
+
n
(
x;
y
)
.
When
the
signal
is
disturbed
b
y
m
ultiplicativ
e
noise
,
the
model
is
e
xpressed
as
in
(2).
g
(
x;
y
)
=
f
(
x;
y
)
(1
+
n
(
x;
y
))
=
f
(
x;
y
)
+
f
(
x;
y
)
n
(
x;
y
)
(2)
Where
,
the
output
signal
of
the
second
ter
m
is
the
result
of
m
ultiplying
the
noise
,
which
is
aff
ected
b
y
f
(
x;
y
)
.
The
bigger
f
(
x;
y
)
,
the
bigger
the
noise
.
According
to
the
theor
y
of
compres-
siv
e
sensing,
the
f
ollo
wing
results
can
be
obtained,as
in
(3).
g
(
x;
y
)
=
f
(
x;
y
)
+
n
(
x;
y
)
=
(3)
Image
De-noising
on
Str
ip
Steel
Surf
ace
Def
ect
Using
Impro
v
ed
Compressiv
e
...
(Dongy
an
Cui)
Evaluation Warning : The document was created with Spire.PDF for Python.
542
ISSN:
1693-6930
Where
,
is
a
sparse
representation
of
the
tr
ansf
or
med
image
.
In
this
w
a
y
,
w
e
can
reco
v
er
the
or
iginal
image
b
y
estimating
the
sparse
representation
of
the
clean
image
so
as
to
achie
v
e
the
pur
pose
of
remo
ving
the
noise
.
The
de-noising
model
based
on
the
compressiv
e
sensing
model
is
as
in
(4).
=
ar
g
min
k
k
0
;
s:t:
k
g
k
2
2
T
(4)
3.
Result
and
Anal
ysis
Three
kinds
of
str
ip
steel
def
ect
images
(scr
atch,
scar
,
surf
ace
upw
ar
ping)
are
selected
in
this
paper
,and
the
noise
type
is
Gaussian
noise
and
salt
and
pepper
noise
.
3.1.
Sim
ulation
Experiment
1:
Def
ect
ima
g
e
de-noising
polluted
b
y
Gaussian
noise
Firstly
,
the
eff
ect
of
diff
erent
tr
ansf
or
mation
matr
ices
on
the
image
de-noising
processing
is
studied.
Sampling
r
ate
w
as
0.4,
0.5
and
0.4,
respectiv
ely
,as
sho
wn
in
T
ab
le
1.
T
ab
le
1.
Compar
ison
of
diff
erent
sampling
r
ate
and
diff
erent
tr
ansf
or
mation
matr
ices
FFT
FFT
DCT
DCT
D
WT
D
WT
Def
ect
type
M/N
PSNR
time(s)
PSNR
time
(s)
PSNR
time
(s)
scr
atch
0.4
22.4548
3.451
20.6991
3.34
20.9255
0.98
0.5
23.1268
4.891
20.6288
4.703
19.9260
1.282
0.6
23.2428
6.493
20.6907
6.231
19.7568
1.843
scar
0.4
21.7367
3.541
18.7781
3.361
19.7284
0.94
0.5
21.5880
4.932
19.2251
4.671
21.1243
1.361
0.6
21.8828
6.392
19.9448
6.121
19.3047
1.841
surf
ace
upw
ar
ping
0.4
23.0123
3.641
19.9002
3.51
20.8668
1.21
0.5
23.4251
5.323
19.8785
5.044
19.3613
1.469
0.6
23.2042
6.924
20.1599
6.651
19.2570
1.9
F
rom
T
ab
le
1
,w
e
can
get
the
compar
ison
results
of
PSNR
and
r
un
time
under
the
D
WT
and
FFT
,
DCT
tr
ansf
or
m
matr
ix.The
PSNR
v
alue
using
D
WT
tr
ansf
or
mation
matr
ix
to
proce
ss
is
higher
than
that
of
the
DCT
tr
ansf
or
m
matr
ix,
and
is
slightly
lo
w
er
than
that
of
the
FFT
tr
ansf
or
m
matr
ix.
While
the
r
unning
time
of
the
D
WT
tr
ansf
or
m
matr
ix
is
m
uch
shor
ten
than
that
of
the
other
tw
o
.
Ob
viously
,
the
D
WT
tr
ansf
or
mation
matr
ix
can
g
reatly
shor
ten
the
r
unning
time
,
and
it
will
not
reduce
the
image
quality
.
In
this
paper
,
the
D
WT
tr
ansf
or
m
matr
ix
is
applied
in
diff
erent
compression
sensing
algor
ithms
to
process
the
str
ip
surf
ace
def
ect
image
,
so
as
to
achie
v
e
the
pur
pose
of
real-time
processing.
T
ab
le
2
sho
ws
the
de-noising
results
of
three
types
of
def
ects
(scr
atch,
scar
,
f
acial
w
ar
p-
ing)
under
Gaussian
noise
using
OMP
,
Cosamp
,
stomp
and
the
proposed
algor
ithm.
The
sampling
r
ate
is
0.5,
The
tr
ansf
or
mation
matr
ix
is
the
D
WT
matr
ix.
The
Gaussian
noise
mean
is
0
and
v
ar
i-
ance
is
0.1,
0.01,
0.001
respectiv
ely
,
as
sho
wn
in
T
ab
le
2
belo
w
.
F
rom
the
e
xper
imental
data
and
e
xper
imental
results
,
the
PSNR
v
alue
is
higher
than
the
OMP
algor
ithm,
Cosamp
algor
ithm
and
StOMP
algor
ithm
using
the
proposed
method
to
de-noise
the
str
ip
st
eel
surf
ace
def
ect
image
.
Although
the
r
unning
time
is
slightly
higher
than
that
of
the
StOMP
algor
ithm,
b
ut
compared
with
the
OMP
algor
ithm
and
the
Cosamp
algor
ithm,
the
r
unning
time
is
g
reatly
reduced,
about
26.6%
of
the
OMP
algor
ithm
and
41.7%
of
the
Cosamp
algor
ithm.
Exper
iments
sho
w
that,
consider
ing
the
de-noising
eff
ect
and
the
r
unning
time
,
the
perf
or
mance
of
this
algor
ithm
to
handle
str
ip
surf
ace
def
ect
image
Gaussian
noise
pollution
is
optimal.
T
ype
of
e
xper
imen
t
def
ects
respectiv
ely
are
scr
atch,
scar
and
surf
ace
upw
ar
ping.
Gauss
noise
means
is
0,
the
v
ar
iance
is
0.1,
0.02,
0.01,
0.005.
3
*
3
templates
is
selected
in
mean
filter
and
median
filter
f
or
processing.
Figure
1(a)-(g)
to
figure3(a)-(g)
are
respectiv
ely
the
results
of
three
kinds
of
def
ects
when
the
Gaussian
noise
mean
is
0
and
the
v
ar
iance
is
0.01.
T
ab
le
4
sho
ws
the
PSNR
v
alues
of
three
kinds
of
def
ects
using
v
ar
ious
de-
noising
algor
ithms
(Gaussian
noise
with
mean
0
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TELK
OMNIKA
ISSN:
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543
T
ab
le
2.
Gaussian
noise
de-noising
eff
ect
when
the
sampling
r
ate
is
0.5
Def
ect
Gaussian
OMP
OMP
Cosamp
Cosamp
StOMP
StOMP
Propo
sed
Proposed
type
Noise
PSNR
Time(s)
PSNR
Time(s)
PSNR
Time(s)
PS
NR
Time(s)
scr
atch
0.1
15.0269
11.373
11.3264
8.1589
9.6994
1.995
26.
7728
2.9952
0.01
24.1047
11.546
17.9604
7.1916
18.7309
2.139
29.9563
3.0888
0.001
33.4488
11.345
21.1458
7.3788
27.6014
2.124
33.6600
3.0576
scar
0.1
18.3338
11.152
11.4972
7.2696
9.7740
1.58
8
26.
7509
2.9952
0.01
24.0836
11.500
17.4030
7.1760
18.5289
1.907
29.2152
3.0420
0.001
33.1111
11.729
19.9023
7.1760
27.2120
1.484
32.3062
3.1356
surf
ace
0.1
15.1427
11.431
11.3537
7.2384
9.7414
0.856
9
26.
5816
3.1512
upw
ar
ping
0.01
23.7802
11.607
17.0315
7.1448
18.2017
0.3639
29.
3068
2.9952
0.001
32.5775
11.400
19.6132
7.0824
24.7782
0.1734
32.5256
3.0108
and
v
ar
iance
0.01).
Figure
4
(a)-(c)
are
respectiv
ely
the
PSNR
compar
ison
cur
v
e
of
th
ree
kinds
of
def
ects
noisy
images
obtained
b
y
using
v
ar
ious
de-noising
algor
ithms
.
Figure
1.
scr
atch(Gaussian
noise
with
mean
0
and
v
ar
iance
0.01)(a)
the
or
iginal
image
of
scr
atch
(b)
the
image
with
Gaussian
noise
(c)
Median
filter
ing
image
(d)
Mean
filter
ing
image
(e)
W
a
v
elet
de-noising
image
(f)CS
de-noising
image
(g)
de-noising
image
of
the
proposed
algor
ithm
As
sho
wn
in
T
ab
le
3
and
Figure
4,
the
PSNR
v
alues
of
the
v
ar
ious
algor
ithms
are
all
decreased
with
the
increasing
of
the
noise
intensity
.
Compared
with
other
tr
aditional
de-noising
methods
,
the
proposed
method
in
this
paper
has
higher
PSNR
v
alue
,
that
is
,
the
eff
ect
is
better
.
3.2.
Sim
ulation
Experiment
2:
Def
ect
ima
g
e
de-noising
polluted
b
y
salt
and
pepper
noise
T
ype
of
def
ects
are
respectiv
ely
scr
atch,
scar
and
f
acial
w
ar
ping
in
the
e
xper
iment.
Salt
and
pepper
noise
intensity
are
0.1,
0.01,0.005,0.001.
3*3
templates
is
selected
in
mean
filter
and
median
filter
f
or
processing.
Figure
5(a)-(g)
to
figure7(a)-(g)
are
respectiv
ely
the
results
of
three
kinds
of
def
ects
de-noising
images
.
T
ab
le
4
sho
ws
the
PSNR
v
alues
of
three
kinds
of
def
ects
using
v
ar
ious
de-noising
algor
ithms
(Salt
and
pepper
noise
intensity
is
0.1).
Figure
8
(a)-(c)
are
respectiv
ely
the
PSNR
compar
ison
cur
v
e
of
three
kinds
of
def
ects
noisy
images
obtained
b
y
using
v
ar
ious
de-noising
algor
ithms
.
As
sho
wn
in
T
ab
le
4
and
Figure
8,
the
PSNR
v
alues
of
the
v
ar
ious
algor
ithms
are
all
decreased
with
the
increasing
of
the
noise
intensity
.
The
median
filter
ing
method
is
v
er
y
eff
ectiv
e
f
or
the
de-noising
of
salt
and
pepper
noise
.
Compared
with
other
tr
aditional
de-noising
methods
,
Image
De-noising
on
Str
ip
Steel
Surf
ace
Def
ect
Using
Impro
v
ed
Compressiv
e
...
(Dongy
an
Cui)
Evaluation Warning : The document was created with Spire.PDF for Python.
544
ISSN:
1693-6930
Figure
2.
scar(Gaussian
noise
with
mean
0
and
v
ar
iance
0.01)(a)
the
or
iginal
image
of
scar
(b)
the
image
with
Gaussian
noise
(c)
Med
ian
filter
ing
image
(d)
Mean
filter
ing
image(e)
W
a
v
elet
de-noising
image
(f)CS
de-noising
image
(g)
de-noising
image
of
the
proposed
algor
ithm
Figure
3.
surf
ace
upw
ar
ping(Gaussian
noise
with
mean
0
and
v
ar
iance
0.01)(a)
the
or
iginal
image
of
surf
ace
upw
ar
ping
(b)
the
image
with
Gaussian
noise
(c)
Median
filter
ing
image
(d)
Mean
filter
ing
image(e)
W
a
v
elet
de-noising
image
(f)CS
de-noising
image
(g)
de-noising
image
of
the
proposed
algor
ithm
the
proposed
method
in
this
paper
has
higher
PSNR
v
alue
,
that
is
,
the
eff
ect
is
better
.
4.
Conc
lusion
F
or
cold-rolling
comple
x
en
vironment,
and
its
image
in
the
acquisition,
acquisition,
tr
ansf
er
process
will
be
polluted
b
y
visib
le
or
in
visib
le
noise
,
w
e
f
ocus
on
de-noising
meth
od
based
on
the
impro
v
ed
compressiv
e
sensing
algor
ithm.
The
conclusions
are
as
f
ollo
ws:
(1)
In
the
compressiv
e
sensing
algor
ithm,
the
image
quality
and
r
unning
time
are
aff
ected
b
y
diff
erent
tr
ansf
or
mation
matr
ix.
Consider
ing
the
tw
o
,
the
D
WT
tr
ansf
or
m
matr
ix
is
the
best.
(2)
Under
the
same
noise
intensity
,
the
proposed
algor
ithm
has
a
little
diff
erence
on
the
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TELK
OMNIKA
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545
T
ab
le
3.
The
de-noising
eff
ect
of
v
ar
ious
algor
ithms
with
diff
erent
intensity
Gaussian
noise
Def
ect
Noise
PSNR0
Median
filter
Mean
filter
w
a
v
elet
CS-OMP
proposed
scr
atch
0.1
12.7296
17.5589
19.0174
24.1869
15.0130
26.7728
0.02
18.6791
24.0706
23.2626
24.0905
20.9537
26.8191
0.01
21.5005
26.7408
24.3423
24.0711
23.8867
29.9563
0.005
24.2483
29.2443
25.2858
24.0755
26.7766
32.6602
scar
0.1
12.9701
17.4094
18.8318
23.8928
15.1302
26.7509
0.02
18.7187
23.8616
22.7633
23.8432
20.9413
26.9985
0.01
21.5438
26.3853
23.7873
23.8198
23.6766
29.2152
0.005
24.1825
28.8335
24.7421
23.8063
26.5264
31.2532
surf
ace
0.1
12.8528
17.1803
18.6847
23.6883
15.0231
26.5816
upw
ar
ping
0.02
18.3413
23.0985
22.4577
23.6199
20.8064
26.8462
0.01
20.8621
25.2768
23.5022
23.6304
23.4988
29.3068
0.005
22.9852
26.9534
24.0940
23.5888
26.1000
32.6708
Figure
4.
the
PSNR
compar
ison
cur
v
e
obtained
b
y
using
v
ar
ious
de-noising
algor
ithms(a)The
PSNR
cur
v
e
of
scr
atch
image
(b)
The
PSNR
cur
v
e
of
scar
image
(c)
The
PSNR
cur
v
e
of
surf
ace
upw
ar
ping
image
de-noising
eff
ect
f
or
diff
erent
kinds
of
def
ects
.
(3)
Compared
with
the
tr
aditional
algor
ithm
such
as
median
filter
ing,
mean
filter
ing,
w
a
v
elet
de-noising
and
con
v
entional
compression
sensing
method
,the
proposed
method
has
better
de-
noising
eff
ect.
Ac
kno
wledg
ement
This
w
or
k
w
as
suppor
ted
b
y
the
National
Natur
al
Science
F
oundation
of
China
(No
.
51208168),
and
Hebei
Pro
vince
Natur
al
Science
F
oundation
(No
.
E2016202341).
Ref
erences
[1]
Zhang
Y
e
,
Jia
Meng,
”Underg
round
Image
Denoising”
TELK
OMNIKA
Indonesian
Jour
nal
of
Electr
ical
Engineer
ing
,
v
ol.
12(6),
pp
.4438-4443,
2014.
[2]
W
ANG
Jianw
ei,
”A
Noise
Remo
v
al
Algor
ithm
of
Color
Image”
TELK
OMNIKA
Indonesian
Jour
nal
of
Electr
ical
Engineer
ing
,
v
ol.
12(1),
pp
.565-574,
2014.
[3]
W
eiw
ei
Liu,
Y
an
Y
un-hui,
Sun
Hong-w
ei
et
al.,
”Impulse
noise
reduction
in
surf
ace
def
ect
of
steel
str
ip
images
based
on
neighborhood
e
v
aluation,
”
Chinese
Jour
nal
of
Science
Instr
u-
ment
,
V
ols
29,
pp
.
1846-1850,
2008.
[4]
Bo
T
ang,
K
ong
Jian-yi,
W
ang
Xing-dong
et
al.,
”W
a
v
elet
threshold
denoising
f
or
steel
str
ip
surf
ace
def
ect
image
,
”
Jour
nal
of
W
uhan
Univ
ersity
of
Science
and
T
echnology
,
V
ols
33,pp
.
Image
De-noising
on
Str
ip
Steel
Surf
ace
Def
ect
Using
Impro
v
ed
Compressiv
e
...
(Dongy
an
Cui)
Evaluation Warning : The document was created with Spire.PDF for Python.
546
ISSN:
1693-6930
Figure
5.
scr
atch(Salt
and
pepper
noise
intensity
is
0.1)(a)
the
or
iginal
image
of
scr
atch
(b)
the
image
with
Gaussian
noise
(c)
Median
filter
ing
image
(d)
Mean
filter
ing
image
(e)
W
a
v
elet
de-
noising
image
(f)CS
de-noising
image
(g)
de-noising
image
of
the
proposed
algor
ithm
Figure
6.
scar(Salt
and
p
epper
noise
intensity
is
0.1)(a)
t
he
or
iginal
image
of
scar
(b)
the
image
with
Gaussian
noise
(c)
Median
filter
ing
image
(d)
Mean
filter
ing
image(e)
W
a
v
elet
de-noising
image
(f)CS
de-noising
image
(g)
de-noising
image
of
the
proposed
algor
ithm
38-42,2010.
[5]
Hao
Xu,
”Image
processing
and
identification
of
str
ip
steel
surf
ace
def
ects
based
on
machine
vision,
”
Thesis
f
or
master’
s
deg
ree
of
W
u
Han
Univ
ersity
of
science
and
technology
,2012.
[6]
Amin
T
a
v
ak
oli,
Ali
P
our
mohammad,
”Image
Denoising
Based
on
Compressed
Sensing,
”
In-
ter
national
Jour
nal
of
Computer
Theor
y
and
Engineer
ing
,V
ols
4,pp
.
266-269,2012.
[7]
Shunli
Zhang,
”Compressed
Sensing
Method
Applicatio
n
in
Image
Denoising,
”
Inter
national
Jour
nal
of
Signal
Processing,
Image
Processing
and
P
atter
n
Recognition
,V
ols
8,pp
.
203-
212,2015.
[8]
M.
T
.
Alonso
,
P
.
L.
Dekk
er
and
J
.
J
.
Mallorqui,
”A
No
v
el
Str
a
tegy
f
or
Radar
Imaging
Based
TELK
OMNIKA
V
ol.
15,
No
.
1,
March
2017
:
540
548
Evaluation Warning : The document was created with Spire.PDF for Python.
TELK
OMNIKA
ISSN:
1693-6930
547
Figure
7.
surf
ace
upw
ar
ping(Salt
and
pepper
noise
intensity
is
0.1)(a)
the
or
iginal
image
of
surf
ace
upw
ar
ping
(b)
the
image
with
Gaussian
noise
(c)
Median
filter
ing
image
(d)
Mean
filter
ing
image(e)
W
a
v
elet
de-noising
image
(f)CS
de-noising
image
(g)
de-noising
image
of
the
proposed
algor
ithm
T
ab
le
4.
The
de-noising
eff
ect
of
v
ar
ious
algor
ithms
with
diff
erent
intensity
Salt
and
pepper
noise
Def
ect
Noise
PSNR0
Median
Mean
w
a
v
elet
CS-OMP
Proposed
scr
atch
0.1
17.5990
31.5663
22.3715
23.4050
20.1083
31.5687
0.01
26.7632
36.4494
26.3376
30.6689
32.4924
37.3122
0.005
28.6169
36.4548
26.7347
33.5300
35.9337
42.4640
0.001
32.2959
36.4613
26.9791
37.1267
41.6660
48.3173
scar
0.1
17.3623
29.7687
21.9811
22.9747
19.7776
30.1205
0.01
26.5068
34.8033
25.2883
29.3508
30.9695
36.5890
0.005
28.4849
34.8155
25.6405
31.6003
34.4295
40.7194
0.001
32.0367
34.8203
25.8779
35.0911
38.5237
45.1762
surf
ace
0.1
17.0
655
28.1653
21.9634
23.1624
19.8053
29.2302
upw
ar
ping
0.01
24.3441
29.7292
24.5819
28.2800
30.6486
34.7397
0.005
25.7489
29.7268
24.8582
30.2394
32.7035
38.1562
0.001
26.9719
29.7334
25.0317
32.4196
36.0263
42.2687
Figure
8.
the
PSNR
compar
ison
cur
v
e
obtained
b
y
using
v
ar
ious
de-noising
algor
ithms(a)The
PSNR
cur
v
e
of
scr
atch
image
(b)
The
PSNR
cur
v
e
of
scar
image
(c)
The
PSNR
cur
v
e
of
f
acial
w
ar
ping
image
on
Compressiv
e
Sensing,
”
IEEE
T
r
ans
.
Geoscience
and
Remote
Sensing
,V
ols
48,pp
.
4285-
4295,2010.
[9]
D
Donoho
,
”Compressed
sensing,
”
IEEE
T
r
ans
,
on
Inf
or
mation
Theor
y
,V
ols
52,pp
.
1289-
Image
De-noising
on
Str
ip
Steel
Surf
ace
Def
ect
Using
Impro
v
ed
Compressiv
e
...
(Dongy
an
Cui)
Evaluation Warning : The document was created with Spire.PDF for Python.
548
ISSN:
1693-6930
1306,2006.
[10]
D
Donoho
,
Y
Tsaig,
”Extensions
of
compressed
sensing,
”
Signal
Processing
,V
ols
86,pp
.
533-
548,2006.
[11]
E.
Candes
,
J
.
Romberg,
”Sparsity
and
incoherence
in
compressiv
e
sampling,
”
In
v
erse
Prob
,V
ols
23,pp
.
969-985,2007.
[12]
E.
Candes
,J
.
Romberg,
T
.
T
ao
,
”Rob
ust
uncer
tainty
pr
inciples:
Exact
signal
reconstr
uction
from
highly
incomplete
frequency
inf
or
mation,
”
IEEE
T
r
ans
.
Inf
or
m.
Theor
y
,V
ols
52,pp
.
489-
509,2006.
[13]
E.
Candes
,J
.
Romberg,
T
.
T
ao
,
”Stab
le
signal
reco
v
er
y
from
incomplete
and
inaccur
ate
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