TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 6088 ~ 6093
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.632
8
6088
Re
cei
v
ed Ma
rch 2
4
, 2014;
Re
vised Ma
y 26, 2014; Accepted June 1
3
, 2014
Film Thickness of Lithium Battery Fast
De-Noising
Based on Atomic Seq
u
ence T
e
mplate Library
Gong Ch
en*,
Xifang Zhu, Qingquan X
u
, Anchen
g Xu, Hui Yang
Cha
ngzh
ou Ins
t
itute of
T
e
chnolo
g
y
, C
h
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: realch
eng
on
g@sin
a
.com
A
b
st
r
a
ct
The natur
al frequency a
nd sc
anning v
i
br
ation fr
equency
of C-dynamic sc
anning syst
em of laser
sensors ar
e a
c
quir
ed for fil
m
thickn
ess of
lithiu
m
b
a
ttery de-no
isin
g b
a
sed o
n
multi-
resol
u
tion w
a
v
e
let
alg
o
rith
m. F
o
r this reaso
n
, fast de-nois
i
n
g
b
a
sed
on
ato
m
i
c
seque
nce te
mp
late l
i
brary
i
s
present. F
i
rs
t,
und
er vari
ous
mo
de
of sca
nni
ng, b
e
st
atomic se
que
nc
e templ
a
te is
built
by spar
se dec
o
m
pos
ition
.
Secon
d
ly, at
the
give
n
mod
e
, fil
m
th
ickne
ss data
is
match to th
e
best
ato
m
ic s
e
q
u
e
n
ce to
de-
nos
i
ng.
Experi
m
ental
r
e
sults s
how
th
at te
mpl
a
te-
m
a
t
ching
p
u
rs
u
i
t (MP) a
l
g
o
r
i
t
hm
i
s
e
ffe
cti
v
e an
d a
l
g
o
r
i
t
hm spee
d
is hig
her tha
n
MP 57 times.
Ke
y
w
ords
: film
thickness
of lithiu
m
battery
；
templ
a
te- ma
tching p
u
rsuit
；
sparse d
e
co
mpositi
o
n
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
Real
-time me
asu
r
em
ent a
u
tomatically
of lithi
um battery thickne
ss can
be reali
z
ed by C-
dynamic sca
nning system
(Figu
r
e1
)b
ased
on
l
a
se
r
sensor, but
scannin
g
pr
oce
ss of
the
sy
stem
is a
c
compa
n
i
ed with
stati
c
an
d dyna
mic e
rro
r in
cluding m
e
ch
anical vibrati
on noi
se
、
sy
st
em
error
of C-dy
namic scanni
ng system
、
d
y
namic erro
r
of differe
nt scannin
g
velo
ci
ty. Performan
c
e
coul
d be ach
i
eved highly accurately ba
sed on m
u
lti-resolution
wa
velet algorith
m
. But natural
freque
ncy
an
d vibratio
n freque
ncy a
r
e
acq
u
ire
d
to
d
e
cid
e
coeffici
ent of wavele
t decompo
siti
on
and re
co
nst
r
u
c
tion coefficie
n
t [1-2].
Sparse
de
co
mpositio
n p
r
o
posed
by Ma
llat and
Zha
n
g
is hot
re
ce
ntly, which h
a
s
bee
n
widely u
s
e
d
i
n
image, vide
o, medi
cal
si
gnal p
r
o
c
e
ssi
ng [3-12]. Sparse de
co
mp
osition
algo
rithm
is ada
pt to choo
se the a
ppro
p
ri
ate ba
sis fun
c
tion
s
to complete
sign
al decom
positio
n on the
con
d
ition of lack of noise
statistical ch
a
r
acte
ri
st
ics, and get natura
l
features
of the origi
nal si
gnal
from redu
nd
ancy di
ction
a
ry [13]. During
i
ndu
strial su
rroun
di
ngs,
spa
r
se
decompo
sit
i
on
algorith
m
reg
a
rd
s actu
al th
ickne
ss a
s
a
part of
the sp
arse co
mpo
n
ent and the vibration n
o
ise as
the resi
dual o
f
film thickne
s
s.
Becau
s
e
of a
larg
e amo
u
n
t
of comp
utation,
the data
measured fro
m
static and dynamic
indu
strial e
n
vironm
ent is trained to g
e
t over-c
om
plet
e diction
a
ry
of atoms b
a
sed on m
a
tchi
ng
pursuit of spa
r
se d
e
compo
s
ition. Then u
nder
vari
ou
s mode of scan
ning, best ato
m
ic se
que
nce
template is
b
u
ilt by spa
r
se de
comp
osit
ion. At
last a
t
the given
mode, film th
ickne
ss
data
is
match
with th
e be
st atomi
c
se
que
nce
to
de-n
o
si
ng. T
he al
gorithm
doe
sn’t ne
ed
to mea
s
u
r
e t
h
e
natural
fre
q
u
ency
and
scannin
g
vibration fr
e
que
ncy
of C-dyna
mi
c
scanni
ng
system an
d
can
adapt to different indu
strial
environ
ment to im
prove the
efficiency of spa
r
se de
co
mpositio
n.
2. Template
-matching Pu
rsuit Spars
e
De-noising
MP algorithm
is an ada
ptive decom
po
sition it
erative algorithm
which
sele
cts t
he be
st
matchin
g
ato
m
from
hig
h
l
y
red
und
ant
over
co
m
p
let
e
di
ctiona
ry
to app
ro
ach
sign
al’s time-
freque
ncy
structure. The
si
gnal i
s
sparse co
mpon
ent
from noi
sy si
gnal, si
gnal
with firm struct
ure
is the
sa
me a
s
atomi
c
pro
p
e
rties,
but n
o
i
s
e
with
rand
o
m
structu
r
e i
s
un
correlate
d
.
If meaningfu
l
atom can b
e
extracted fro
m
the noisy sign
al, t
hen the atom is th
e sign
al. If meanin
g
ful sig
nal
isn’t co
ntinue
to be extracte
d from the sig
nal in re
sidu
a
l
, then the sig
nal in re
sidu
a
l
is noise.
In the p
r
o
c
e
s
s of
iterative,
spa
r
se
deco
m
posit
io
n i
s
t
o
choo
se
the
large
s
t
atom
whi
c
h i
s
the inne
r p
r
o
duct of
sign
a
l
or
signal
re
sidu
al
, sp
arse de
comp
osi
t
ion co
ntinue
s tra
c
king a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Film
Thickne
ss of Lithium
Battery Fa
st De-Noi
sin
g
Base
d on Atom
ic Sequen
ce… (G
ong Chen)
6089
extracting th
e
atom whi
c
h i
s
match to the origi
nal
si
g
nal and
re
sid
ual sig
nal. In the cal
c
ulatio
n of
the inner
pro
duct sele
ctio
n of gabo
r atom, it is very
large, a
nd if the length of t
he input si
gn
al is
too large, the
amount of cal
c
ulatio
n is ev
en more asto
nishi
ng [13].
For a
la
rge
amount of
calcul
ation,
te
mplate
-m
atch
ing
p
u
rsuit sparse de
-noi
sing
is
prop
osed. First, best ato
m
i
c
sequ
en
ce t
e
mplate i
s
bu
ilt by sparse
decompo
sitio
n
und
er va
rio
u
s
mode of
scan
ning. Secondl
y, at t
he given mode, film thickne
s
s dat
a
is mat
c
h to
the be
st atom
ic
seq
uen
ce
to
de-n
o
si
ng. Al
though
be
st
atom is not
e
x
tracted t
o
ca
lculate
by
me
ans of iteratio
n,
the atom is t
o
be the n
e
xt best on
e. Comp
ared
wi
th MP algorit
hm, this alg
o
r
ithm elimin
ate
s
times of iteration. Templat
e
-mat
ching pursuit al
gorithm rai
s
es the
possib
ility of various si
gnal’s
length and g
r
eatly improv
es the perfo
rmance. Figur
e2 is a flow cha
r
t of the fast spa
r
se d
e
-
noisi
ng ba
se
d on template
-matching p
u
rsuit.
N
N
Y
Y
St
a
r
t
Mea
s
u
r
e
d
d
a
t
a
unde
r
st
a
t
ic
ba
c
k
g
r
o
und
S
e
t d
e
c
o
m
p
os
i
t
i
on
p
a
r
a
m
e
t
e
r
s
C
o
ns
tr
uc
t
o
v
e
r
c
o
m
p
l
e
te
d
i
c
t
i
o
na
r
y
S
e
l
e
ct
t
h
e b
e
s
t
at
o
m
S
a
ve
th
e
t
e
m
p
la
t
e
l
i
b
r
a
r
y
C
o
h
e
ren
t
ra
t
i
o
1
e
nd
Mea
s
u
r
e
d
d
a
t
a
u
nde
r
d
i
f
f
e
r
e
n
t
ba
ck
gr
ou
n
d
F
i
nd
t
h
e
be
st
m
a
t
c
h
i
ng
a
t
o
m
se
que
nc
e f
o
r
m
te
m
p
la
te
l
i
br
a
r
y
Me
a
s
u
r
e
d
d
a
t
a
unde
r
dy
nam
i
c
bac
k
g
r
o
und
G
e
t th
e
b
e
s
t
m
a
t
c
h
i
n
g
a
t
o
m
se
que
nc
e
s
C
o
h
e
ren
t
ra
t
i
o
2
Figure 1. Film of Lithium Battery Detectio
n
Fi
gure 2. Flow Ch
art of the Fast Spa
r
se De-
noisi
ng
T
h
e
s
t
ep
s
ar
e a
s
fo
llo
ws
:
Step 1: Train
best atomi
c
seque
nces a
n
d
co
n
s
tru
c
t te
mplate und
er
different mod
e
.
Step 1.1:
De
fine ove
r
-co
m
plete
dictio
nary
{}
(
0
,
1
,
,
1
)
m
r
Dg
m
M
in
Hilbert space,
1
m
r
g
,
m
defines a
s
iteration time
s,
M
defines a
s
iteration te
rmin
ation value.
Step 1.2: Define mea
s
u
r
ed d
a
ta a
s
()
x
n
，
1,
2
,
nN
from st
atic an
d dynami
c
indu
strial env
ironm
ent.
N
defines a
s
lengt
h as si
gnal.
Define
0
()
x
nR
x
，
1,
2
,
nN
，
0
Rx
is
origin
al re
sid
ual sig
nal.
Step 1.3: Sel
e
ct the
b
e
st
atom
o
r
g
D
by MP
algorith
m
to
make
0
0
,
r
Rx
g
maxim
u
m,
get the
re
sid
ual
00
10
0
,
rr
R
x
Rx
Rx
g
g
. Select t
he b
e
st
atom
by MP
algo
rithm, and
get
the
resi
dual
s
1!
21
1
,
rr
R
x
Rx
Rx
g
g
，
,
11
11
,
mm
mm
m
rr
Rx
R
x
R
x
g
g
a
gain.
Step 1.4: De
fine co
he
rent
ratio
()
s
u
p
,
m
r
m
mm
m
r
gD
Rx
R
x
g
R
x
whi
c
h
decre
ases
with
the increa
sin
g
of iteration.
If set to one
conve
r
ge
nce
value, iteratio
n will en
d up
to
M
th and get
1
M
th resi
dual
sign
al
1
,
M
M
MM
M
rr
R
x
Rx
Rx
g
g
.In order to en
sure the coh
e
rent rati
o
rea
c
he
s the set, the iteration value add
s
up to
10
M
times
.
Step 1.5 : Save and
con
s
tru
c
t template lib
rary, the be
st atom de
fines a
s
01
1
0
{,
,
,
}
MM
ll
l
l
lr
r
r
r
Gg
g
g
g
，
1,
2
,
lL
，
L
is the nu
mber of templ
a
te unde
r vari
ous mo
de.
Step 2:De-noi
se un
der give
n surro
undi
ng
.
Step 2.1:Inp
u
t mea
s
ured
data
()
x
xn
，
1,
2
,
nN
und
er
some
kin
d
of mod
e
. Set
0
()
x
xn
R
x
x
。
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
0
46
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 608
8 –
6093
6090
Step 2.2: Select t
he prope
r paramete
r
l
from the temp
late libra
ry an
d get
l
G
. The best
atomic
se
que
nce
s
are
invo
lved in the
ite
r
ation
11
11
,
rr
mm
mm
m
l
l
Rx
x
R
x
x
R
x
x
g
g
,
1,
2
,
mM
M
.
MM
is defined a
s
iterative times,
10
MM
M
.
Step 2.3: Fin
a
lly
1
0
()
,
mm
MM
ml
l
M
M
rr
m
yn
R
x
x
g
g
R
x
x
，
1,
2
,
nN
is
got,
Define
()
yn
as
recon
s
tru
c
ted
de-noi
sin
g
si
gnal.
3. Experimental Re
sults
3.1. Simulation of Fas
t
M
P
Signal De-noising
Cons
truc
t s
i
gnal
with nois
e
12
(
)
19
0
s
in
(
2
)
2
00
si
n(
2
)
(
)
ss
xn
f
n
f
n
z
n
in traini
ng
stage,
1
10
s
f
,
2
20
s
f
,
{
0
,0
.
0
0
1
,0
.
0
0
2
,0
.
0
9
9
}
n
,
()
zn
d
e
f
in
es
as g
a
u
ss
ia
n no
is
e wh
ich
c
o
mp
lie
s
with
N(0,10
)
. Set the coh
e
rent ratio 0.3
4
.
Figure 3
(
a
)
i
s
cohe
rent ra
tio conve
r
ge
n
c
e value
wh
e
n
numbe
r of ite
r
ation i
s
chan
ging. Fi
gu
re 3
(
b) i
s
the 9
be
st atomic
se
q
uen
ce
s diag
ram. Figure 3(c)
is sig
nal with
noise, clea
n signal an
d sig
nal after sp
arse de
com
p
o
s
ition.
(a)
(b)
(c
)
Figure 3. Te
mplate Co
nst
r
ucte
d by MP Sparse De
co
mpositio
n du
ring Trai
ning
Best atom seque
nces a
r
e got by template
-MP
while five grou
ps of gau
ssi
a
n noi
se
complying wit
h
N(0,1
0
)
a
r
e
adding to bo
uble-sin
u
soid
al sign
al.
2
4
6
8
10
12
14
16
0
1
2
3
4
5
6
N
u
m
b
e
r
of
i
t
er
at
i
o
n
C
oher
en
t
r
a
t
i
o
0.
3366
0
10
20
30
40
50
60
70
80
90
100
-0
.
4
-0
.
2
0
0.
2
0.
4
0.
6
Sa
m
p
l
i
n
g
v
a
l
u
e
A
m
pl
i
t
ude
be
s
t
at
om
1
be
s
t
at
om
2
be
s
t
at
om
3
be
s
t
at
om
4
be
s
t
at
om
5
be
s
t
at
om
6
be
s
t
at
om
7
be
s
t
at
om
8
be
s
t
at
om
9
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Film
Thickne
ss of Lithium
Battery Fa
st De-Noi
sin
g
Base
d on Atom
ic Sequen
ce… (G
ong Chen)
6091
(a) Five g
r
ou
ps of sig
nal with noise
(b) Five g
r
ou
ps of co
heren
t ratio
(c) Cle
an si
g
nal and
sign
a
l
after MP
(d)
De-noi
sin
g
whe
n
the b
e
st atom und
er
gau
ssi
an noi
se use
d
to others
Figure 4. Fast Sparse
De-noise by Tem
p
late-MP
Table 1. Co
ntrastin
g of Different Me
an Square Error
(MSE)
Table 2. Co
ntrastin
g of both Algorithm
s
M
SE
ga
us
s
i
an
no
i
s
e
gr
ou
p 1
gr
ou
p
2
gr
ou
p 3
gr
ou
p 4
gr
ou
p
5
M
P
7.
536
6
6.
535
6
7.
4
4
3
6
6.
2
3
5
5
7.
6
1
2
3
T
e
m
p
l
a
t
e
-
M
P
7.
187
6
7.
109
9
7.
4
6
4
2
6.
7
6
9
6
7.
1
4
0
4
MP
Te
mp
l
a
t
e
-
MP
t
i
m
e
(
s
)
10.
8
8
0.
1
9
e
n
t
h
anc
e 1
5
7
From
Figu
re
3, 4 an
d
Table1, MS
E by templa
te-MP is
clo
s
e to MP
a
l
gorithm.
Perform
a
n
c
e
unde
r g
a
u
ssi
an noi
se
tem
p
late is de
cre
a
sin
g
in
bro
w
n and
0-1 di
stribution
noi
se.
Atom sequ
e
n
ce
sho
w
s the dist
ributio
n
of gau
ss
unde
r ga
ussi
an and
non
-gau
ssi
an noi
se.
Therefore waveform
of sign
al
after de-n
o
isi
ng
d
e
viates from
the actu
al
distrib
u
tion, i
t
is
con
c
lu
ded th
at atomic seq
uen
ce is
sele
ct
ivity under different noi
se environ
men
t
s.
Table
2 pre
s
ents a com
p
a
r
iso
n
of
both
algorit
h
m
s, te
mplate-MP
al
gorithm
is su
perio
r to
MP algorithm
57 times.
3.2. De-n
oising b
y
Template
-MP unde
r Static and
D
y
namic Mo
de
When
C sca
nning
system
is stopp
ed, experim
ent result sho
w
s
MSE of template-MP
and MP
algo
rithm i
s
le
ss than
data
u
npro
c
e
s
sed,
and i
n
crea
si
ng of tem
p
la
te-MP is sli
g
htly
worse th
an
MP, but spe
ed of ope
rati
on of templat
e
-MP is
sati
sfied with me
asu
r
em
ent u
nder
indu
strial surroundi
ng
s.
0
10
20
30
40
50
60
70
80
90
100
-4
00
-3
00
-2
00
-1
00
0
10
0
20
0
30
0
40
0
Sa
m
p
l
i
n
g
v
a
l
u
e
A
m
pl
i
t
ude
gr
ou
p 1
gr
ou
p 2
gr
ou
p 3
gr
ou
p 4
gr
ou
p 5
2
4
6
8
10
12
14
16
0
1
2
3
4
5
6
N
u
m
b
er
o
f
i
t
er
a
t
i
o
n
C
o
h
er
en
t
r
a
t
i
o
gr
o
u
p
1
gr
o
u
p
2
gr
o
u
p
3
gr
o
u
p
4
gr
o
u
p
5
0
10
20
30
40
50
60
70
80
90
100
-400
-300
-200
-100
0
100
200
300
400
S
a
m
p
li
n
g
v
a
lu
e
A
m
p
lit
u
d
e
ori
g
i
n
s
i
gnal
group 1
group 2
group 3
group 4
group 5
0
10
20
30
40
50
60
70
80
90
100
-
400
-
300
-
200
-
100
0
100
200
300
400
S
a
mp
li
n
g
v
a
lu
e
Am
p
l
i
t
u
d
e
o
r
ig
in
s
i
g
n
a
l
0
-
1 di
s
t
ri
but
i
o
n
n
o
i
s
e
br
o
w
n n
o
i
s
e
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 608
8 –
6093
6092
(a) Static o
r
ig
inal film thickness di
stributi
o
n
(b) Five g
r
ou
ps of co
heren
t ratio
Figure 5. Fast Sparse
De-noisi
ng of St
atic Film Thickness by Tem
p
late-MP
Whe
n
scanni
ng, differe
nt
spe
ed
will
ca
use
vario
u
s vibration
noi
se
add
ed in
th
e ori
g
in
thickne
s
s of f
ilm thickne
s
s. Figu
re
6 sho
w
s the
differe
nt amon
g the
v1 (slo
w), v
2
(mi
ddle
)
a
n
d
v3 (fast
)
sca
nning
sp
eed
mode.
Fro
m
the figu
re
, spe
ed of
v1 is
clo
s
e
to v2,distrib
u
t
ion
differen
c
e i
s
n
’
t obvious,
bu
t v3 is fa
ster t
han v1, v2, di
fference a
m
o
ng them
is
no
table. Atoms
of
template lib
ra
ry are
match
to different
scan
ni
ng
sp
ee
d, but data
u
n
match
ed
de
viates from
the
origin
al thickn
ess dist
ributio
n of lithium film.
Table 3. Co
ntrastin
g of Different Me
an Square Error (MSE)
thickness (
μ
m)
group1
group2
group3
group4
group5
group6
group7
original
0.1887
0.1873
0.1993
0.1932
0.1977
0.1936
template-MP
0.1495
0.1789
0.1512
0.1548
0.1971
0.1663
14.1%
MP 0.1522
0.1709
0.1544
0.1556
0.1934
0.1653
14.6%
(a) v
1
(b) v
2
(c
) v
3
Figure 6. Fast Sparse
De-noisi
ng of St
atic Film Thickness by Tem
p
late-MP
0
20
40
60
80
100
120
140
160
180
200
200
200.
2
200.
4
200.
6
200.
8
201
201.
2
S
a
m
p
li
n
g
v
a
lu
e
A
m
pl
i
t
ude
5
10
15
20
25
30
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
N
u
m
b
er
o
f
i
t
er
a
t
i
o
n
C
o
he
r
e
nt
r
a
t
i
o
g
r
ou
p 1
g
r
ou
p 2
g
r
ou
p 3
g
r
ou
p 4
g
r
ou
p 5
0
20
40
60
80
100
12
0
140
16
0
180
20
0
12
0
14
0
16
0
18
0
20
0
22
0
24
0
26
0
S
a
m
p
l
i
ng v
a
l
u
e
A
m
pl
i
t
ude
v
1
ori
g
i
n
s
i
gnal
v
1
te
m
p
l
a
te
-
M
P
v
2
te
m
p
l
a
te
-
M
P
v
3
te
m
p
l
a
te
-
M
P
0
20
40
60
80
10
0
12
0
140
16
0
180
20
0
12
0
14
0
16
0
18
0
20
0
22
0
24
0
26
0
S
a
m
p
li
n
g
v
a
lu
e
A
m
pl
i
t
ude
v
2
org
i
n s
i
gn
al
v
2
te
m
p
l
a
te
-
M
P
v
1
te
m
p
l
a
te
-
M
P
v
3
te
m
p
l
a
te
-
M
P
0
20
40
60
80
100
120
140
160
180
200
120
140
160
180
200
220
240
260
S
a
mp
lin
g
v
a
lu
e
A
m
pl
it
ude
v
1
or
i
g
i
n
s
i
gnal
v
1
te
mp
l
a
te
-
M
P
v
2
te
mp
l
a
te
-
M
P
v
3
te
mp
l
a
te
-
M
P
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Film
Thickne
ss of Lithium
Battery Fa
st De-Noi
sin
g
Base
d on Atom
ic Sequen
ce… (G
ong Chen)
6093
4. Conclusio
n
It is requi
re
d
for re
al-time
,
untouched,
on-lin
e mea
s
ureme
n
t of thickne
ss
of lithium
battery film unde
r ind
u
s
trial
enviro
n
ment, but
multi-re
sol
u
tion wavelet
algorith
m
m
a
ke
s
measurement
complex be
cau
s
e of nat
ural fr
eq
uen
cy and sca
nni
ng vibration f
r
equ
en
cy of C-
dynamic sca
nning system
.
Fast
de-
n
o
i
s
ing
which b
e
st atomic
seque
nce template is built by
spa
r
se d
e
co
mpositio
n
sel
e
cts the
be
st atomic
se
que
nce
to de
-n
o
s
ing. Study
o
f
simulatio
n
d
a
ta
and a
nalysi
s
of indu
strial
su
rro
undi
ng
s sho
w
that
t
he alg
o
rithm
is efficie
n
t to filter noi
se
and
algorith
m
is e
ffective and a
l
gorithm
spe
e
d
is hi
gh
er th
an template
- matchin
g
pu
rsuit 57 times.
Ackn
o
w
l
e
dg
ements
This
wo
rk was fin
a
n
c
ially su
ppo
rted
by the
Jian
gsu
Natural
Scien
c
e
Fo
undati
o
n
(BK2013
024
5
)
, Ch
ang
zh
o
u
Key La
b
o
rato
ry of
Optoele
c
tro
n
i
c
Mate
rial
s and
Devi
ces
(201
306
94).
.
Referen
ces
[1]
Z
hou
JF
.
R
e
se
arch on
errors
ana
l
y
sis an
d p
r
ecis
io
n c
ontro
l
in
hi
gh-
precis
i
on c
onv
e
x
it
y m
easur
ement
w
i
t
h
Las
er for thin Sh
eet. Cha
ngsh
a
: Centra
l South Un
iversit
y
. 20
06: 32-
65.
[2]
Chen G, Zhu X
F
, X
U
QQ, et al
. Multi-resolution
w
a
ve
let in discontinuous coating thickness
measur
ement.
Contro
l Engi
ne
erin
g of Chin
a
. 201
3; 20(1): 17
5-17
8.
[3
]
Ma
l
l
t
S, Zha
ng Z. Ma
tch
i
ng
pu
rsu
i
ts w
i
th
ti
me-frequ
enc
y
dictio
nari
e
s.
IE
EE T
r
ansacti
o
n
s o
n
S
i
gn
al
Processi
ng
. 19
93; 41(1
2
): 339
7-34
15.
[4]
Z
hao RZ
, Liu
XY, LI Ch
in
gC
hun
g, et al.
W
a
vel
e
t den
oisi
n
g
bas
ed o
n
sp
arse repr
ese
n
tation
. Sci
enc
e
in Chi
na: Infor
m
ation Sci
enc
e. 2010; 4
0
(1): 33-4
0
.
[5]
M Plumb
l
e
y
, T
Blume
n
b
a
ch,
L Da
ud
et, R
Gribonv
al.
Sp
arse
re
pres
ent
ations in au
di
o
an
d mus
i
c.
Procee
din
g
s of
the IEEE. 2009.
[6]
R Neff, A Zakhor. Matching
pursuit vi
deo coding: Dic
tionary
approximation.
IEEE Transactions
on
Circuits and Sy
stem
s for VideoTechnology
. 200
2; 12(1): 13
-26.
[7]
M Jalal F
adi
li
, Jean-Luc Starck, Bobin.
Ima
ge Dec
o
mpositi
on an
d Separ
atio
n Using Sp
ars
e
Repr
esentati
o
n
s
: An Overview
.
Proceedi
ngs
of the I
EEE. 2010; 98(6): 9
83-
994.
[8] WANG
CG.
T
he ECG f
e
a
t
ure w
a
ve
de
tection
an
d
d
a
ta co
mpressi
on
bas
ed
on
the s
pars
e
deco
m
positi
o
n
.
Chan
gsh
a
: Na
tiona
l Univ
ersit
y
of Defe
nse T
e
chn
o
lo
g
y
. 200
9: 58-77.
[9]
Liu
H, Ya
ng
J
A
, Hua
n
g
W
J
. Acoustic
sig
n
a
l
de-n
o
isi
n
g
base
d
o
n
par
alle
l s
parse
d
e
comp
ositio
n.
Journ
a
l of Circ
u
its and Syste
m
s
. 20
12; 17(
6
)
; 64-69.
[10]
Li Y, Guo S
X
. A ne
w
meth
o
d
to estimate t
he p
a
rameter
of 1/f Noise of
high
po
w
e
r s
e
mico
nductor
laser d
i
od
e bas
ed on sp
arse d
e
comp
ositio
n.
Journ
a
l of Phy
s
ics
. 2012; 6
1
(3): 1-6.
[11]
D Przem
y
s
l
a
w
, M Nicolas.Greed
y sp
arse
decom
positi
o
n
s
: a comparat
ive stud
y.
TELKOMNIKA
Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2011; 7(1): 3
4
-
40.
[12]
Z
he L,
Xi
ao
XZ
, Co
ng M.
A Nov
e
l Im
age
Rec
onstr
uction
Alg
o
rith
m Based
o
n
Conc
aten
ated
Diction
ar
y.
T
E
LKOMNIKA Indon
esia
n Jour
nal
of Electric
al
Engin
eeri
n
g
. 2
012; 7(2): 4
44-
450.
[13]
W
ang JY, Yin
Z
K
. Sparse signa
l an
d ima
g
e
decom
pos
iti
on an
d Prel
imi
nar
y
App
lic
atio
n. Chen
gd
u:
South
w
e
s
t Jiao
T
ong Univ
ersit
y
press. 2
006:
72-1
16.
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