TELKOM
NIKA
, Vol.14, No
.2, June 20
16
, pp. 607~6
1
2
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v14i1.2748
607
Re
cei
v
ed
De
cem
ber 1
3
, 2015; Re
vi
sed
March 19, 20
16; Accepted
April 6, 2016
Multi-source an
d Multi-feature Image Information
Fusion Based on Compressive Sensing
Qingzh
a
o Li
1
,
Fei Jiang
2,3*
1
School of F
o
r
e
ig
n La
ngu
ag
e
s
, Suzhou Un
iv
ersit
y
, Suz
hou
234
00
0, Anhui,
Chin
a
2
Labor
ator
y
of Intelli
ge
nt Information Proc
es
sing,
Suzh
ou U
n
iversit
y
, Suzh
ou 23
40
00, An
hui, Ch
ina
3
School of Infor
m
ation En
gi
ne
erin
g, Suzho
u
Univers
i
t
y
, Suz
hou 2
3
4
000, A
nhu
i, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: fei
w
u
h
an@
1
26.com
A
b
st
r
a
ct
Imag
e fusio
n
is
a compreh
ens
ive infor
m
ation
processi
ng tec
hni
que
and its
purp
o
se is to e
nha
nce
the re
lia
bil
i
ty o
f
the i
m
age
via
t
he
process
i
n
g
of th
e re
du
n
dant
data
a
m
o
ng multip
le i
m
ages, i
m
prov
e the
imag
e defin
itio
n and i
n
for
m
a
t
ion conte
n
t throug
h fusio
n
of the comple
me
ntary in
for
m
ati
on of
mult
ip
l
e
imag
es so
as
to obtai
n the
i
n
formatio
n
of t
he o
b
j
e
ctive o
r
the scen
e
i
n
a
more
accur
a
te, reli
abl
e a
n
d
compre
hens
ive
ma
nn
er. T
h
is
pap
er us
es the sp
arse
r
e
p
r
esentati
on
method
of co
mpressiv
e
sens
i
n
g
theory, prop
os
es a multi-so
ur
ce
and
mu
lti-fe
ature i
m
a
ge i
n
formatio
n
fusio
n
method
base
d
on co
mpr
e
ss
ive
sensi
ng i
n
acc
o
rda
n
ce w
i
th the featur
es of i
m
a
ge fusi
on, p
e
rforms s
parsif
i
catio
n
proc
ess
i
ng o
n
the so
ur
ce
imag
e w
i
th K-SVD alg
o
rith
m and OMP alg
o
rith
m to transfer from spati
a
l
do
ma
in to freq
uency d
o
m
ai
n and
deco
m
poses
in
to low
-
freque
n
cy part and h
i
g
h
-frequ
ency p
a
r
k. T
hen it fuses w
i
th different fusion rul
e
s a
n
d
the ex
per
iment
al r
e
sults
prov
e that
the
met
hod
of th
is
pa
per
is
better th
an th
e tra
d
iti
o
n
a
l
metho
d
s a
n
d
it
can obta
i
n b
e
tter fusion effect
s.
Ke
y
w
ords
: Image Infor
m
ati
o
n F
u
sion, Co
mpressiv
e
Sensi
ng, Sparse D
e
compos
ition
Copy
right
©
2016 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Image fu
sion
is the te
ch
niq
ue to
combi
n
e two
or m
o
re imag
es
of the same
obje
c
tive at
the sa
me tim
e
(o
r differen
t
time) by dif
f
erent
se
n
s
o
r
s throug
h a
spe
c
ific
algo
rithm. This i
s
a
newly-eme
rgi
ng te
chniq
u
e
that integ
r
at
es
se
ns
or,
si
gnal p
r
o
c
e
ssing, imag
e p
r
ocessin
g
a
n
d
artificial
intelli
gen
ce [1]. T
o
gether
with
scientific an
d t
e
ch
nolo
g
ical
prog
re
ss, im
age fu
sio
n
h
a
s
been
wi
dely u
s
ed
in
medi
ci
ne, remote
se
nsin
g, co
mp
u
t
er visi
on,
we
ather fore
ca
st
, military targ
et
identificatio
n
and
other fiel
ds. Ima
ge fu
sion te
chn
o
log
y
bega
n to
draw
attention i
n
the
198
0s,
at
that time, image fusi
on was nothi
ng b
u
t simple
wei
ghted ave
r
ag
e. After that, the technol
o
g
y
grad
ually cau
ght on and p
eople sta
r
ted
to apply
it in the analysi
s
and processing of rem
o
te-
sen
s
in
g multi-sp
ect
r
al ima
ges [2].
By the end of the 1980s, p
eople be
gan
to use it
in co
mmon imag
e
processin
g
such a
s
multi-focus i
m
age
an
d vi
sible
imag
e [
3
]. After the
90s,
hug
e
progre
s
s
had
b
een
mad
e
in
the
resea
r
ch of image fu
sion
due to su
ch multi-resol
u
tion de
com
positio
n algo
rithm and m
u
lti-
resolution fu
sion the
o
ry
as La
pla
c
ian
Pyramid a
nd Gau
s
sian
pyramid, h
o
weve
r, the
s
e
algorith
m
s di
d not d
e
com
pose o
r
tra
n
s
fer
directly
on the i
m
ag
es to
be fu
sed in th
e fu
sion
pro
c
e
ssi
ng, i
n
stea
d, the
fusio
n
p
r
o
c
e
s
sing
was only
co
ndu
cted
in
one
level
[4]. The
em
erg
e
n
ce
of wavelet th
eory an
d co
mpre
ssive se
nsin
g t
heo
ry had p
r
omote
d
a qualitativ
e leap of im
age
fusion
techno
logy. The l
a
tter h
a
s poi
nte
d
it out
th
at compressive
sensi
ng first
requires that t
he
sign
al sh
all be spa
r
se, whi
c
h is the p
r
e
m
ise an
d fou
ndation of thi
s
theory. The
sparse
ne
ss
of
sign
al di
re
ctly affects th
e
desi
gn
of the
mea
s
u
r
eme
n
t matrix a
n
d
the a
c
curacy
of imag
e
sig
nal
recon
s
tru
c
tio
n
[5]. This paper inve
stig
ates the ima
ge fusio
n
method ba
sed
on comp
re
ssive
sen
s
in
g theo
ry in orde
r to
make
mo
st o
f
the f
eature
that this theo
ry has
a lo
w
sampli
ng rate,
exerts the fu
sion
rule
with the com
p
ressive
se
nsi
ng dom
ain, combine
s
com
p
re
ssive
se
n
s
in
g
theory
and
the id
ea
of
wavelet tra
n
sf
orm
and
sea
r
ch
es the
inf
o
rmatio
n fu
si
on field
of m
u
lti-
sou
r
ce and m
u
lti-feature image
s.
Firstly, this p
aper
analy
z
e
s
the th
ree l
e
vels
of m
u
lti-so
urce
and
multi-featu
r
e
imag
e
fusion
and th
e co
mpressiv
e se
nsi
ng the
o
ry ba
se
d on
spa
r
se
rep
r
e
s
entatio
n an
d
introd
uces K
-
SVD dictio
na
ry trainin
g
al
gorithm
and
OMP algo
rith
m. Then, o
n
the above
re
sea
r
ch b
a
si
s,
it
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 2, June 20
16 : 607 – 61
2
608
prop
oses
a
multi-source and
m
u
lti-feature ima
ge informati
on fusi
on
method b
a
sed on
comp
re
ssive sen
s
in
g and
gives the sp
e
c
ific implem
e
n
tation step
s of this algorit
hm. Finally, it is
the simulatio
n
experim
ent
al test and re
sult analy
s
is.
2. Multi-sour
ce and Multi-fea
t
ure Imag
e Fusion
Image fu
sion
is aime
d to
summari
ze t
h
e
multi-ba
nd in
formation
by singl
e sen
s
or or th
e
informatio
n provided by different
sen
s
o
r
s and e
liminat
e the possibl
e redu
nda
ncy
and co
ntradi
ct
s
of multi-sen
s
or i
n
form
atio
n in
orde
r t
o
en
han
ce
t
he tran
spa
r
e
n
cy, a
c
curacy, reliability
and
utilization rat
e
of the information in the image
s and form
a
clear-cut,
com
p
let
e
and accurate
informatio
n d
e
scriptio
n of
the o
b
je
ctive. The fu
se
d im
age
sh
all in
cl
ude
all u
s
eful
inform
ation
wit
h
clea
r fo
cu
s o
f
each
source imag
es
wit
hout lo
si
ng
the texture i
n
formation
of
the imag
e a
nd
maintain th
e
edge
detail
s
and
ene
rgy
so a
s
to
obtai
n a
cle
a
r im
a
ge[6]. The
m
u
lti-feature im
age
fusion i
s
indi
cated as Fig
u
re 1.
Figure 1. Multi-feature imag
e fusion
Gene
rally
sp
eaki
ng, ima
g
e
fusi
on
can
be divid
ed i
n
to pixel lev
e
l, feature
le
vel and
deci
s
io
n level from abstraction. Pixel-level image
fusi
on is the pro
c
e
ss to direct
ly proce
s
s the
data colle
cte
d
from the
se
nso
r
to o
b
tai
n
fuse
d imag
e and it
can
pre
s
e
r
ve a
s
much
ori
g
inal
data
as po
ssible a
nd provid
e ot
her tiny information whi
c
h
can’ be p
r
o
v
ided by other fusi
on lev
e
ls.
Feature-level
image fusio
n
summ
ari
z
e
s
and p
r
o
c
e
s
ses
su
ch feature info
rmation as e
dge
,
sha
pe, texture an
d regio
n
obtain
ed
after p
r
e
p
ro
ce
ssing
an
d feat
ure
extra
c
tio
n
. It can
not
only
maintain sufficient impo
rta
n
t information
,
but also
co
mpre
ss the in
formation, m
a
kin
g
it good
for
real
-time proce
s
sing. Deci
sion
-level
fusio
n
performs combi
national
jud
g
ment on ea
ch
discrimi
nation
re
sult by
si
mulating
hu
man tho
ught
on a
c
cou
n
t of ce
rtain
rules or spe
c
ific
algorith
m
ba
sed on th
e co
mpletion of d
e
ci
sion
or
cla
ssifi
cation ta
sks i
nde
pen
de
ntly on the d
a
ta
c
o
llec
t
ed [7].
3. Compres
s
i
v
e
Sensing
Bas
e
d on Sp
arse Repre
s
enta
tion
The spa
r
se decompo
sitio
n
of
sig
nal refers
to the
acq
u
isitio
n proce
s
s of the
optimum
spa
r
se rep
r
e
s
entatio
n
o
r
sparse
ap
proxi
m
ation
of si
g
nal in
the
ov
e
r
-compl
ete di
ctiona
ry,
that is
to say that, t
he si
gnal
ca
n be
rep
r
e
s
e
n
ted in th
e form of th
e p
r
odu
ct of a
grou
p of
spa
r
se
coeffici
ents
a
nd traini
ng di
ctiona
ry. Accordin
g to
the
spa
r
se repre
s
entatio
n the
o
ry, noisy
sig
nal
contai
ns t
w
o
parts:
useful
sign
al an
d n
o
i
se
s. Usef
ul
signal h
a
s cert
ain
stru
ctural
feature
s
a
nd i
t
s
stru
ctural feat
ure
s
coin
cide
with
atomi
c
stru
cture whil
e the noi
se
s
are i
rrel
e
vant
, therefore, they
have no featu
r
es. Assu
me that image
f
is comp
ri
sed of
two part
s
:
ij
f
ff
(1)
Her
e
,
i
f
rep
r
e
s
ent
s
the
sp
arse rep
r
e
s
e
n
tation com
p
onent of
the
image, name
l
y
the
useful
sign
al of the image and
j
i
f
ff
repre
s
e
n
ts other
co
mpone
nts of the image, n
a
mely
the image noi
se
s [8].
3.1. Compre
ssiv
e
Sensing Theor
y
Based on Spar
se Rep
r
es
en
tation
K-SVD
dictio
nary
traini
ng method can not
only
pre
s
erve such im
portant info
rmation a
s
the edg
e a
n
d
the texture
and it i
s
e
s
p
e
cially g
ood
at the texture
image. M
o
st
importa
ntly, this
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Multi-source
and Multi-fe
ature Im
age Inform
ation Fusi
on Base
d on
… (Qin
gzh
a
o
Li)
609
method
ha
s excell
ent a
daptability [9
]. K-SVD di
ct
ionary traini
ng al
gorith
m
is
cla
s
sified
as
follows
:
Assu
me that
the ori
g
inal
matrix is
1
N
i
i
Ww
, the re
dun
dant
diction
a
ry i
s
N
DR
,
the
spa
r
se en
cod
i
ng is
1
N
i
i
Ss
and
G
is the uppe
r limit of the number of non
-0 element
s in
i
s
.
The obje
c
tive
equation of
K-SVD dictio
nary lea
r
ning
is rep
r
e
s
e
n
te
d as:
2
0
.
mi
n
.
.
,
i
F
DA
WD
A
s
t
i
a
G
(2)
Step 1: Initialize the di
ction
a
ry
D
, such as
the over-com
plete DCT dictionary.
Step 2: Sparse encodin
g
, use OMP
Algo
rithm on the known dictio
na
ry
D
.
2
2
1
K
j
iT
F
j
F
YD
W
Y
d
W
2
jk
jT
k
T
jk
F
Yd
W
d
W
(3)
In the above
formul
a,
DW
is d
e
c
omp
o
sed int
o
the sum of
matrix with
K
orders which
i
s
1. Assume
t
hat
1
K
items
are fixed, the
rest 1
colum
n
the
th
k
on
e to
be
processe
d an
d
update
d
[10].
Step 3: Upd
a
t
e diction
a
ry
D
. Firstly, assu
me that
the
sparse m
a
trix
W
and di
ction
a
r
y
D
are fixed
an
d that it is to
update th
e
th
k
k
d
in the di
ctiona
ry. Set the correspon
ding
th
k
row
to
k
d
in the c
oeffic
i
ent matrix
W
as
k
T
w
, then:
2
22
2
()
jk
k
k
k
jT
k
T
k
k
k
T
k
R
k
R
F
F
F
jk
F
YD
W
Y
d
w
d
W
E
d
w
E
d
w
(4)
j
T
w
mean
s th
e
th
j
row
of matr
ix
W
. In the a
bove
formula,
DW
is
d
e
com
p
o
s
ed
i
n
to the
sum
of
K
order whi
c
h
is 1. A
s
sume
that th
e
1
K
items
are fi
xed, the
rem
a
ining
1 i
s
th
e
th
k
to
be pro
c
e
s
sed
[11].
Step 4: The
diction
a
ry is
update
d
ro
w
by row. Th
e
spa
r
se matrix
W
and the di
ctionary
D
are fixed. Set the correspo
nding
th
k
row to
k
d
in the c
oeffic
i
ent matrix
W
as
k
T
w
.
Step 5: De
co
mpose
k
R
E
into
kT
R
EU
V
with SVD. Mak
e
k
d
as the fi
rst
colum
n
of
U
and the
n
k
d
is the up
date re
sult of
k
d
. In the mean
while,
update th
e produ
ct of the first
colum
n
of
V
and then use the dictionary
D
to perform
coeffi
cient de
com
positio
n after update i
s
compl
e
ted column by column.
Step 6: Jud
ge
wheth
e
r
the e
s
tabli
s
h
ed iteration
s
or th
e e
r
ro
r rate b
e
twe
en the
recon
s
tru
c
ted
signal an
d the origi
nal si
gnal are
sati
sfied. If it meets the ab
o
v
e terminatio
n
con
d
ition, out
put the final redun
dant di
ctionary
D
, otherwise, turn to Step 2.
3.2. OMP Algorithm
OMP algo
rithm is imp
r
oved from
MP algorith
m
in perfo
rming orth
og
onali
z
ation
pro
c
e
ssi
ng o
n
all atoms
selecte
d
in ev
ery de
comp
o
s
it
ion st
e
p
.
I
t
sele
ct
s t
he
c
o
lumn of
with
gree
dy iterati
on to make the sel
e
cte
d
colum
n
in
every iteration
clo
s
ely relate
d to the current
redu
nda
ncy
vector to the maximum
extend and
it reduce
s
the relevan
t
part from the
measurement
vector
until the iter
ations
rea
c
h th
e sp
arsene
ss
K
[12]. The p
r
o
c
ed
ure
s
of O
M
P
algorith
m
are
as follo
ws:
(1) Assum
e
that the ove
r-co
m
plete di
ctiona
ry is
12
[,
,
,
,
]
L
Dd
d
d
and the origi
nal
sign
al is
y
, initi
a
lize the
sparseness
S
, the redu
nda
ncy
0
y
, s
u
pport index s
e
t
0
A
and
the initial iteration.
(2)
Cal
c
ulate
and get the sup
port ind
e
x and perfo
rm
signal ap
pro
x
imation and
margin
update
with the lea
s
t squ
a
r
e metho
d
.
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2
610
2
ar
g
m
i
n
WY
W
(5)
(3) Introdu
ce
the sign
al su
pport set.
,
ne
w
YW
(6)
(4)
Upd
a
te the resi
dual e
r
ror.
1
()
ss
s
s
TT
sk
k
k
k
yD
D
D
D
y
(7)
(5) Calculate
the
co
rrelati
on
coeffici
ent
by se
eki
n
g
the
ma
rgin
m
and th
e
ab
so
lute
value of the inner p
r
o
d
u
c
t in the sen
s
in
g
matrix
.
|,
,
1
,
2
,
ii
i
mw
i
N
，
(8)
(6)
Jud
ge wh
ether the iterative termin
a
t
ion con
d
ition
s
are
satisfie
d. If
ne
w
mm
,
make
ne
w
mm
and
1
nn
and turn ba
ck to Step (
2
)
.
(7) If the con
d
itions a
r
e
sa
tisfi
ed, output
the sup
port i
ndex set
1
nn
and
the spa
r
se
coeffici
ent
1
()
mm
m
m
TT
kk
k
k
D
DD
D
y
.
4. The Steps
of Multi-so
u
r
ce Image F
u
sion Algori
t
hm Bas
e
d o
n
Sparse Re
presen
ta
tion
The advanta
ge to apply sparse
representation in im
age fusi
on
is
that it can de
comp
ose
the imag
e int
o
differe
nt freque
ncy d
o
m
ains,
use d
i
fferent sele
ction rule
s in
different d
o
m
a
ins
and obtai
n th
e multi-resolu
tion decomp
o
s
ition of the
f
u
se
d imag
e so as to p
r
e
s
e
r
ve sig
n
ifica
n
t
feature
s
of th
e origi
nal ima
ges i
n
differe
nt freque
ncy
domain
s
in th
e fuse
d imag
e. Acco
rdi
ng
to
the idea of m
u
lti-so
urce im
age fusi
on al
gorithm of
sp
arse re
prese
n
tation co
mpressive se
nsi
n
g,
firstly, perform pre
c
ise g
eometri
c regi
strati
on
on the so
urce i
m
age
s. The
n
take the
over-
compl
e
te dict
ionary DCT
diction
a
ry as the initial dictiona
ry
D
of K-SVD algo
ri
thm. Perform
spa
r
se d
e
co
mpositio
n o
n
the noi
sy
images in the init
ial dictionary
D
with OMP
algorithm [13]. In
th
is
pr
oc
ess
,
ta
k
e
G
a
s
th
e t
e
rmin
ation
co
ndition
of the
iteratio
ns of
OMP alg
o
rith
m, namely
to
r
e
pr
es
e
n
t
th
e ma
ximu
m ite
r
a
t
io
ns
.
2
20
mi
n
,
,
1
,
2
ii
i
y
Dw
w
G
i
N
(9)
Obtain the ne
ce
ssary sparse coefficie
n
t matrix
X
for K-SVD algorith
m
throug
h Fo
rmu
l
a
(9). Th
e algo
rithm pro
c
ed
ure cha
r
t is indi
cated a
s
Figu
re 2.
Figure 2. The
procedu
re of
this pape
r
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TELKOM
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ISSN:
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930
Multi-source
and Multi-fe
ature Im
age Inform
ation Fusi
on Base
d on
… (Qin
gzh
a
o
Li)
611
5. Simulation Experimen
t
al Tes
t
and
Resul
t
An
aly
s
is
The CP
U use
d
in the simul
a
tion experi
m
ent
is Intel(R) Core(TM
)
i3-2370M
@ 2.4
0
GHz
with a memo
ry of 4GB and the prog
ram
m
ing platform
is Matlab 20
11a.
Simulation e
x
perime
n
t ha
s bee
n mad
e
to the mul
t
i-sou
r
ce ima
ge fusio
n
ba
sed o
n
spa
r
se
rep
r
e
s
entatio
n p
r
o
posed i
n
thi
s
pap
er
and
i
n
orde
r to
co
mpare the
fu
sion
effect
s
of 4
algorith
m
s, we perfo
rm fuzzy pro
c
e
s
sin
g
in the
left side and
right
side of the
source ima
ge,
as
indicated in F
i
gure 3.
(a) O
r
igin
al image
(b)
Right-fo
c
u
s
image
(c) Left-fo
cu
s image
Figure 3. Focus imag
e
In the exp
e
ri
ment, we
u
s
e weighte
d
a
v
erage
meth
od, pri
n
ci
pal
comp
one
nt a
nalysi
s
method
(P
CA), IHS tran
sfo
r
m m
e
thod
a
nd the
met
hod
o
f
th
is
p
a
per
w
i
th
the right-foc
u
s
and left-
focu
s image
s as the so
urce image
s and
obtain t
he fusion results a
s
indi
cated in
Figure 4.
(a) Pri
n
ci
pal compon
ent an
alysis
(b) Weig
hted averag
e
meth
od
(c) IHS trans
f
orm method
(d) T
h
is pa
pe
r method
Figure 4. Fused image
re
sults
It can
be
se
en fro
m
the
above im
age
s that
perfo
rm fusio
n
p
r
o
c
e
ssi
ng
on t
w
o fu
zzy
image
s
which de
scrib
e
th
e sa
me o
b
je
ct and
wh
ich
are fu
zzy in
different
sp
ots by a
dopti
ng
different fu
sion op
erato
r
s throug
h th
e different f
r
equ
en
cy-d
o
m
ain comp
o
nents i
n
ea
ch
decompo
sitio
n
level a
nd
obtain the
fin
a
l fuse
d
wav
e
let pyrami
d. Perform hig
h
-lo
w
fre
que
ncy
fusion
rul
e
a
nd multi
-
scal
e reco
nst
r
u
c
tion o
n
the
fuse
d
wavelet
pyrami
d, th
e reco
nst
r
u
c
te
d
image obtai
n
ed is the fuse
d image.
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Vol. 14, No. 2, June 20
16 : 607 – 61
2
612
It is clear that
the fused im
age ha
s cl
early
shown the feature
s
of the obje
c
t. The metho
d
of this pa
per has
achieve
d
better fu
sio
n
effec
t. The
left and rig
h
t
side
s are very cle
a
r
and
it
pre
s
e
r
ves th
e useful info
rmation of multiple
origin
al image
s and
obtain
s
the fuse
d image
with
clea
r obje
c
tive focu
s. The fuse
d image h
a
s the featu
r
e
s
of both ima
ges.
6. Conclusio
n
Based o
n
the traditional i
m
age fusi
on
framewo
r
k, this pape
r h
a
s propo
se
s a multi-
sou
r
ce and
multi-feature image info
rm
ation fusi
o
n
method ba
se
d on co
mpre
ssive
sen
s
in
g. It
integrate
s
th
e comp
re
ssi
ve sensi
ng sparse re
presentation theo
ry with the idea of wave
let
transfo
rm, ex
plore
s
the fea
s
ibility of the theory to be u
s
ed in the im
age fusi
on an
d make
s ima
g
e
fusion
experi
m
ent ba
sed
o
n
the comp
re
ssive
se
ns
i
n
g
domain. T
h
e
experim
ent result h
a
s
sh
o
w
n
that the method of this p
aper
ca
n accomplish bette
r effect, red
u
c
e si
gnal
sa
mpling rate a
nd
greatly re
du
ce the sampli
n
g
data. It is suitable
for the
image fusio
n
with a large
amount of dat
a.
Ackn
o
w
l
e
dg
ements
This
work wa
s su
ppo
rted
by the University
Natural Scien
c
e Project of Anhui
Province
(Grant No. KJ2014Z
D3
1).
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