TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4794 ~ 4
8
0
1
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.552
4
4794
Re
cei
v
ed
De
cem
ber 3
0
, 2013; Re
vi
sed
March 12, 20
14; Accepted
March 27, 20
14
An Effic
i
ent Imaging Strategy for Single Pixel Camera in
Earth Observation
Chua
nrong Li
1
, Qi Wang
2
, Chang
y
on
g Cao
3
, Lingling Ma*
4
1,2,
4
Ke
y
La
bor
a
t
or
y
of Quantit
ative Rem
o
te Sensi
ng Info
rm
ation T
e
chno
lo
g
y
, Aca
dem
y o
f
Opto-Electron
i
cs,
Chin
ese Aca
d
e
m
y
of Scie
nces
, Beijin
g, 100
0
94, Chi
n
a
2
Universit
y
of Chin
ese Aca
d
e
m
y
of
Scie
nces
, Beijin
g, 100
0
49, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: crli@ao
e.ac.
c
n
1
, w
a
ngq
i_
ao
e@fo
xmai
l.co
m
2
, chang
yon
g
.
cao@n
oaa.
go
v
3
,
llma@
ao
e.ac.cn
4
A
b
st
r
a
ct
Sing
le
pixe
l c
a
mera
is a
n
e
w
imagi
ng
d
e
vice th
at d
e
v
e
lo
ps fro
m
th
e “gh
o
st
” i
m
a
g
in
g a
n
d
compressiv
e
s
ensi
ng th
eory.
F
o
r h
i
gh
res
o
luti
on
i
m
a
g
in
g w
i
th l
a
rge
a
m
o
unt
of d
a
ta
, the pr
ocess
o
f
me
asur
e
m
ent
and rec
onstruc
tion is time-co
n
su
mi
ng, w
h
ic
h li
mits its app
licatio
n to remote sensi
ng ar
ea.
Based
on
the
a
nalysis
of th
e c
onfig
uratio
n
of
the si
ngl
e p
i
xe
l
ca
mera,
an
efficient
i
m
a
g
in
g
strategy thro
ug
h
combi
n
in
g d
i
fferent nu
mbers
of DMD
mirr
or
s and
loc
a
l
i
m
agi
ng w
a
s
pro
pose
d
w
h
ich
is
abl
e to
i
m
ag
e
the
intereste
d
targ
et in high res
o
luti
on w
i
th lo
w
time
cost.
Simulati
on ex
p
e
ri
ment w
a
s carried o
u
t for tw
o
different types
of targets, i.e., th
ree-lin
e target imag
e an
d
the scene co
ns
istin
g
of a ship i
n
the oce
a
n
.
T
h
ree typ
e
s
of
imag
es, in
l
o
w
,
mid
d
le
a
n
d
hi
gh r
e
sol
u
ti
o
n
,
are r
e
constr
ucted r
e
sp
ectively
by th
e c
ontro
l
of
DMD w
o
rking
area a
nd the s
t
rategy to combini
ng
DM
D mirrors. T
he reconstructed i
m
a
ges reac
hed t
h
e
app
licati
on re
q
u
ire
m
e
n
ts at v
e
ry
low
meas
u
r
ement a
nd re
constructio
n
ti
me c
o
st. T
he effectiveness
a
n
d
practica
lity of this strategy co
uld b
e
ap
pli
ed to other co
mpr
e
ssive sens
ing i
m
a
g
i
ng dev
ice
s
.
Ke
y
w
ords
:
singl
e pix
e
l c
a
mera, di
gital
micro
mirr
or devic
e (DMD), earth obs
erv
a
tion, co
mpr
e
ssiv
e
sensi
ng, i
m
ag
e
resoluti
on
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
Single pixel
i
m
aging
is a
new type of
imagi
ng
tech
nique
that d
r
aws m
o
re
an
d mo
re
attention in rece
nt years. It dev
elops from the “g
ho
st” imaging
or
so-call
ed inte
nsity co
rrel
a
tion
imaging
theo
ry [1] an
d
co
mpre
ssive
se
nsin
g the
o
ry. The
first
sin
g
le pixel
cam
e
ra
wa
s re
ali
z
ed
based on di
gital micro m
i
rro
r devi
c
e (DMD) via M
a
rco F. Du
arte et al. in 2006 [2]. Unli
ke
imaging
by
CCD a
rray
in
convention
a
l i
m
aging
syste
m
, the n
e
w i
m
aging
syste
m
empl
oyes
only
s
i
n
g
l
e
-
p
i
xe
l de
te
c
t
o
r
to
c
o
lle
c
t mu
ltip
le
me
a
s
u
r
e
m
e
n
t
s
.
It d
o
e
s
n
o
t a
c
qu
ire
th
e o
b
j
ec
t’s image
throug
h one
exposure, bu
t calcul
ates t
he image fr
o
m
the multiple observation
measure
m
e
n
ts
colle
cted by t
he sin
g
le
-pixel detecto
r a
nd the me
a
s
urem
ent mod
e
reali
z
e
d
(re
c
orded
) by DMD.
The calculati
on algo
rithm
use
d
is the
mathem
ati
c
al
method na
med comp
re
ssive
sen
s
in
g [3].
Since there is only one sensor in the imaging
sy
ste
m
, the archit
ecture of the imaging syst
em
can
be m
u
ch
simpl
e
r tha
n
conve
n
tional
cam
e
ra
s. Th
e sin
g
le-pixel
detecto
r
can
be mu
ch
mo
re
efficient,
le
ss
expen
sive while kee
p
ing
highe
r sen
s
it
i
v
ity, and esp
e
cially
suita
b
l
e
for the
ca
se of
infrared imagi
ng [4].
Earth ob
serv
ation is an i
m
porta
nt app
licati
on a
r
ea
of the single
pixel came
ra and it
usu
a
lly rel
a
te
d to la
rg
e am
ount of
data
volume. Th
e
data a
m
ount
from the
singl
e-pixel
dete
c
tor
is
small
and
thus ea
sy to delive
r
an
d re
co
rd, h
o
w
ever, th
e reco
rd
pro
c
e
s
s of th
e wh
ole
measurement
mode
nee
ds larg
e amo
u
n
t of disk
size, and the
i
m
age
re
con
s
truction
process
also n
eed
s a
m
ount of me
mory si
ze. F
o
r exam
pl
e, to image a
scene of 102
4×1024 pixel
s
with
0.3 sampli
ng
rate, and u
s
e
1 byte short integer
d
a
ta type to store, there ne
ed
s 307GB mem
o
ry
to sto
r
e the
m
easure
m
ent
matrix. If furth
e
r
red
u
ce the
sam
p
ling
rat
e
, the ima
ge
resol
u
tion
wou
l
d
be very low.
Neverth
e
le
ss,
not all targets in the earth
obse
r
vatio
n
scene ne
e
d
to bere
c
on
stru
cted
with high
re
solution. For
e
x
ample, over ocea
n,
only high resolutio
n
of the ship
s in the ima
g
e
scene
are needed, and low resolution
i
m
age of the
sea
surface i
s
su
fficient.In this paper, a new
imaging
strat
egy of the sin
g
le pixel cam
e
ra
suit
able f
o
r re
mote se
nsin
g imagin
g
is propo
sed
.
In
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Efficient Im
aging Strategy for Sin
g
le
Pixel Cam
e
ra in Earth Ob
servatio
n (Ch
uanrong Li
)
4795
Section 2, th
e co
nfiguration of
the
si
ngle pixel
ca
mera
and
co
mpre
ssive se
nsin
g theo
ry is
introdu
ce
d. In Section 3, the DM
D blo
c
k metho
d
to adju
s
t imagin
g
re
solution i
s
presented
and
the simul
a
tio
n
on thre
e-li
n
e
target is
execute
d
to
verify the idea. In Section 4,
the strate
gy to
efficiently im
age the
inte
reste
d
target
in hig
h
re
solution i
s
p
r
opo
sed
and
the sim
u
lati
on
experim
ent to prove the
new
stra
te
gy is execute
d
, and the re
sult is sho
w
n
and an
alyze
d
.
In
Section 5, the
content of this pap
er is
co
nclu
ded.
2. Introducti
on of Single Pixel Camer
a
and Compr
e
ssiv
e
Sensing
Figure 1
sho
w
s th
e
config
uration
of the
singl
e pixel
came
ra. T
h
e
main
comp
on
ents of
the device a
r
e an imagin
g
lens, DM
D an
d it
s cont
rol b
o
ard a
nd the
singl
e se
nsor.
(a)
(b)
Figure 1. (a)
The sc
hematic
of
s
i
ngle pixel c
a
mera (pic
ture fr
om http://ds
p
.ric
e.edu/cs
camera)
(b) T
he expe
rimental app
aratus of sin
g
le
pixel came
ra
The pivotal
d
e
vice in
the
system to
reali
z
e
ran
dom
m
easure
m
ent i
s
the
DM
D,
which
is
a
planar array
of millions
of micr
o mirrors in the
size of mi
cr
ometers. Each mirror
can be
controlled to
rotate to two
dire
ction
s
, ca
lled “o
n”
a
nd
“off”, so that
the light goe
s into the DM
D
can b
e
refle
c
ted to two different di
re
ctio
ns. T
he obj
ect is imaged o
n
the DMD first and then
DMD
reflect
differe
nt part
s
of th
e obje
c
t to di
fferent di
recti
o
ns. An im
ag
ing len
s
i
s
pl
ace
d
on th
e “on”
dire
ction to
focu
s o
n
th
e dete
c
tor.
One ty
pe
of DM
D
confi
guratio
n i
s
related to
on
e
measurement
value. If changing the p
a
ttern on t
he DMD,
more
measure
m
ent values coul
d
be
acq
u
ire
d
. Th
e pattern fo
r one me
asurement is
call
ed a fram
e, and the n
u
m
bers of fram
es
need
ed to fully recon
s
tru
c
t
the image is decide
d
by the dimen
s
io
n
of the image sce
ne and t
h
e
spa
r
sity of the obje
c
t.
The equ
ation
for DM
D is ex
pre
s
sed by:
m
i
n
j
ijt
ij
t
x
y
11
.
(1)
W
h
er
e
m
,
n
is
th
e
s
i
ze
o
f
D
M
D ar
ra
y,
x
ij
is th
e
obje
c
t
’
s
refle
c
tion i
n
tensity o
n
p
o
sition
(i, j
)
, a
n
d
Φ
ijt
is the
stat
us of th
e mi
rror o
n
corr
e
s
p
ondin
g
po
siti
on, eithe
r
0
o
r
1. y
t
is t
he
measurement
of
t
-
th time. For
M
times
meas
urements
,
t
=1,2,…,
M
.
Comp
re
ssive
sen
s
ing th
eo
ry can b
e
ad
opted to
solve Equation
(1
). The theo
ry prove
s
that sp
arse
signal
s
can
be
well
re
co
nst
r
ucted
from
in
coh
e
re
nt me
asu
r
em
ents
at the
sampli
ng
rate b
e
yond
Nyqui
st limit. Assu
ming
x
N×
1
is
the one d
i
mensi
on expansi
o
n
of
x
ij
and in
Equati
o
n
(1),
wh
er
e
N
=
mn
.
Φ
M×N
(
M
<
N
) i
s
th
e
measurement
matrix th
at
each
ro
w ve
ctor is the
o
ne
dimen
s
ion
ex
pan
sion
of th
e patte
rn
at
one f
r
ame.
y
M×
1
is the
me
asu
r
em
ents
of
M
times
.
The
ratio
M/N
i
s
calle
d the sa
mpling
rate. To solve th
e
unde
rdete
r
mined e
quati
on, x shoul
d
be
sufficie
n
tly sp
arse a
nd th
e
spa
r
sest ve
ct
or a
m
ong
the
sol
u
tion
set
of the eq
uati
o
n i
s
the
co
rrect
one. The line
a
r equ
ation can be tran
sfo
r
med into
su
ch optimizatio
n probl
em:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4794 – 4
801
4796
.
.
.
min
arg
ˆ
0
y
x
t
s
x
x
(2)
The L0-no
rm
in Equation (2) indi
cate
s
t
he numbe
r of nonze
r
o el
ements. Whil
e many
sign
als like e
a
rth
observat
i
on o
b
je
ct
s a
r
e non
-sparse,
a set
of
b
a
si
s
Ψ
N
×
K
sh
ould
be fo
un
d to
make the
sig
nal’s rep
r
e
s
e
n
tation und
er
su
ch ba
si
s is
spa
r
se. The
Equation (2) i
s
written as:
.
.
.
min
arg
ˆ
0
y
s
t
s
s
s
(3)
s
x
(4)
The co
mpre
ssive
sen
s
in
g recon
s
tru
c
t
i
on algo
rithm
s
to solve
Equation (3) includ
e
variou
s type
s of L1-no
rm
convex o
p
tim
i
zation, g
r
e
e
d
y
sea
r
ch alg
o
rithm
s
, Bayesia
n
e
s
timat
i
on
algorith
m
s a
n
d
so on [5
-7]. And the spa
r
se ba
si
s
Ψ
can be DCT b
a
si
s, wavelet
basi
s
o
r
vario
u
s
types of redu
ndant di
ction
a
ry [8].
3. Effec
t
of the Numbe
r
of DM
D Mirror
s
to Image Recons
truc
tio
n
The num
be
r of DMD mi
rro
r
s i
s
equ
al to the
numb
e
r o
f
reco
nstructe
d image’
s pix
e
ls, and
it actually rep
r
esents the i
m
age resolution. The
larg
e
r
numb
e
r of DMD mi
rrors corre
s
p
ond
es to
highe
r resol
u
tion re
con
s
tructed im
age,
however,
th
ere a
r
e la
rg
e
r
num
ber
of unkno
wn
s in
the
equatio
n and
hence it costs much m
o
re time and memory to reco
nstruct im
age. In orde
r to
enha
nce co
mputational
efficien
cy, on
e com
p
romise is to
comb
ine some mi
rrors into
a la
rge
block, whe
r
e
the mirro
rs in
the same blo
ck pe
rfo
r
m
the same
statu
e
s, e.g., “on”
or “off”. Figu
re
2 sho
w
s an e
x
ample to co
mbine 3
×
3 mi
rro
rs.
(a)
(b)
Figure 2. (a)
A random p
a
ttern of a 6×6 DMD a
r
e
a
,
the gray gri
d
re
pre
s
ent
s 0 an
d the white grid
rep
r
e
s
ent
s 1 (b)
Combi
n
in
g 3×3 mi
rro
rs into a large p
i
xel, mirrors i
n
a large pixe
l are on the
same st
at
u
s
A
ssu
ming
t
h
e D
M
D
blo
c
k
si
ze
is
p
×
q
,
the ne
w
im
age pixel size
is
u
×
v
,
u=m/p
and
v=
n/
p
. Equation (1
) ca
n be
rewritten as:
.
~
)
(
11
1
11
)
1
(1
)
1
(
u
k
u
k
v
l
klt
kl
v
l
kp
p
k
i
lq
q
l
j
ijt
ij
t
x
pq
x
y
(5)
Whe
r
e
kl
x
~
is th
e mean valu
e of each
p
×
q
area an
d in the area th
e mirro
rs a
r
e
on the sam
e
status so
the measurement
element
of the area
can b
e
written a
s
klt
. Rewrite Eq
uati
on (5
) as:
.
~
11
u
k
v
l
klt
kl
t
x
y
(6)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Efficient Im
aging Strategy for Sin
g
le
Pixel Cam
e
ra in Earth Ob
servatio
n (Ch
uanrong Li
)
4797
.
pq
y
y
t
t
(7)
Equation (6)
has the
same
form as (1), and
kl
x
~
can be solved from it.
In orde
r to de
mostrate the
effect of the
numbe
r of DM
D mirrors to i
m
age recon
s
tructio
n
,
the thre
e-lin
e
bar pattern i
s
em
ployed
as th
e te
st target. T
he th
ree
-
line
ba
r
pattern ta
rg
et is
widely u
s
e
d
to estim
a
te th
e sp
atial reso
lution of opti
c
al image
s. In
the sim
u
latio
n
expe
riment
s,
the si
ze
of th
e imag
e
con
s
isting
of thre
e
-
line ta
rg
et is
128
×12
8
pixe
ls, a
s
sho
w
n
as i
n
Fig
u
re
3
.
There are horizontal a
nd vert
ical
strip
e
s of 8, 4, 2, 1
pixels wi
de. Set the DMD
b
l
ock si
ze to 8,
4,
2, 1 respe
c
tively and then re
con
s
tru
c
t
the im
age. The othe
r importa
nt parameters in t
h
e
simulatio
n
ex
perim
ent a
r
e:
0-1
Bernoulli
ran
dom
matrix as
DM
D p
a
ttern, DCT
matrix a
s
spa
r
se
rep
r
e
s
entatio
n, SL0 algorit
hm as spa
r
e reco
nstrct
ion
algorith
m
[9].
The sa
mplin
g
rate is 0.6. The
recon
s
tru
c
tio
n
imag
es
are
sho
w
n
in Fi
gure
4. And
the re
co
nstru
c
tion time fo
r each ima
g
e
is
sho
w
n a
s
in
Table 1.
Figure 3. The
Three
-
line B
a
r Pattern Ta
rget
(a)
(b)
(c
)
(d)
Figure 4. Re
constructe
d Image
s und
er th
e Bl
ock Si
ze
of 8, 4, 2, 1 R
e
sp
ectively
Table 1. The
Re
con
s
tru
c
tio
n
Time of the Thre
e-lin
e Ta
rget
Block
size
8 4 2
1
Time (s)
0.99
1.76
50.2
4795
Figure 4 sho
w
s that the
resol
u
tion
of the re
co
nstru
c
ted ima
ge is
x
pixels fo
r the DM
D
bloc
k size
x
(
x
=8,4,2,1), which ve
rifies t
he above
pre
s
ente
d
theo
ry. Combine
d
with Tabl
e 1
,
it
can
be
con
c
l
ued that the
reco
nstructio
n
time increa
ses d
r
am
aticly
while th
e re
solution b
e
co
mes
highe
r. The
r
e
f
ore, it must
comp
romi
se t
he imag
e re
solution an
d reco
nstructio
n
time in the
EO
appli
c
ation of
single pixel
camera.
4. Efficient I
m
aging Strateg
y
for Imag
ing the Targ
et of Interes
t
In some ea
rth obse
r
vation
applicatio
n, the va
luable i
n
formatio
n exists only in small part
of the scen
e. It is more eff
i
cient to ima
g
e
just
that pa
rt of the scen
e. While
cha
nging th
e opti
c
al
para
m
eter
su
ch a
s
the
cal
i
ber a
nd fo
ca
l length of th
e imagin
g
le
ns i
s
mo
re
complicated a
nd
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801
4798
unsta
ble than
controlling th
e DMD mi
rrors, so t
he lo
ca
l imaging st
ra
tegy base
d
o
n
the operation
of DM
D i
s
a
better
choi
ce.
In Equatio
n
(1), th
e
size
of the
DMD i
s
m
×
n
and
th
e lo
cal im
agi
ng
area
is [
m
1
,
m
2
] ×
[
n
1
,
n
2
], the metho
d
i
s
to
sho
w
the
ran
dom p
a
ttern
of just thi
s
a
r
ea
and
al
ways
clo
s
e the oth
e
r, that would
be 0 in other
parts. And Eq
uation (1
) can
be rewriiten
as:
2
1
2
1
.
m
m
i
n
n
j
ijt
ij
t
x
y
(8)
By solving th
e Equatio
n (8) the
si
ze
of re
con
s
tru
c
te
d imag
e is (
m
2
-
m
1
+1) ×
(
n
2
-
n
1
+1)
,
whi
c
h is p
a
rt of the whole
sen
c
e.
The challe
ng
e of the lo
cal
imaging
mod
e
is h
o
w to fi
nd the inte
re
sted imagin
g
a
r
ea a
nd
locate
in
the
whol
e
DMD
plane
with
out
kn
owi
n
g
the
pri
o
r informa
t
ion of th
e e
a
r
th o
b
servati
o
n
scene. In this paper, a
n
efficient imagi
n
g
stra
te
gy employing the
combi
n
ing th
e DM
D blo
c
k and
local ima
g
ing
are pro
p
o
s
e
d
. The comb
ination
of the DMD blo
c
k has the adva
n
tage for fast
recon
s
tru
c
tin
g
taget ima
g
e
,
though th
e resol
u
tion of t
he ima
ge i
s
l
o
w b
u
t is
help
f
ul for findin
g
the
imaging a
r
ea
of interest.
The flow
cha
r
t of efficient imaging
strate
gy is sho
w
in
Figure 5.
Figure 5. The
Flow Ch
art o
f
Efficient Ima
g
ing Strategy
A simulation
scene,
whi
c
h
con
s
i
s
ts
of a ship i
n
the ocean,
is empl
oye
d
as th
e
experim
ent scen
e. The im
age si
ze i
s
2
048
×20
48 pi
xels, whi
c
h e
qual
s to the
total numbe
r
of
DMD mirro
r
s.
As only
a small area
ne
ar the
shi
p
o
r
ju
st the flag
of the
ship i
s
of inte
re
st, it’s
better to reconstruct th
e i
m
age of ju
st
that are
a
. The lo
cation
o
f
target is
un
kno
w
n, a
nd l
o
w
resolution im
age of the whol
e scene
to help find such inform
ation. The st
eps to efficie
n
tly
recons
truc
t the target of
interes
t
are as
follows
:
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TELKOM
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An Efficient Im
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g
le
Pixel Cam
e
ra in Earth Ob
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n (Ch
uanrong Li
)
4799
Figure 6. The
Simulation Scen
e of a Ship in the Oce
a
n
Step 1
: Set the DM
D blo
c
k si
ze of 32 t
o
com
b
i
ne th
e mirrors and
use all the
mirro
rs of
DMD to ima
g
e
the
whole
scene i
n
lo
w
resolution. T
here
are 64
×64 pixel
s
in t
he recon
s
tru
c
ted
image. The
sampling
rate i
s
0.3.
Step 2
: L
o
ca
te the targ
et i
n
the lo
w resolution ima
g
e
and
cal
c
ulat
e the
corre
s
p
ondin
g
cordinate i
n
the DM
D pla
n
e
, and ju
st use 256
×25
6
m
i
rro
rs
aro
und
the target
sp
ot to image, the
unus
ed
mirrors
are always off. Set the DMD block
s
i
z
e
4 to image the ship in middle
res
o
lution.
There are al
so 64×64 pixel
s
in the re
con
s
tru
c
ted ima
g
e
. The sam
p
li
ng rate is 0.6.
Step 3
: Lo
cat
e
the
inte
sted
pa
rt of th
e
ship in
the
mid
d
le
re
solution
imag
e a
nd
calcul
ate
the corre
s
po
nding
co
rdi
n
ate in the
DMD pl
ane,
u
s
e 64
×64 mirrors aro
und
the
target sp
ot
to
image, set the DMD blo
ck size 1 to image the shi
p
in high resol
u
tion. There
are al
so 64
×64
pixels in th
e reco
nstructe
d
image. Th
e sampling
ra
te
is 0.6. Th
e ot
her im
porta
nt parameters i
s
the same a
s
i
n
3.1.
One
of the frames of the
DMD an
d the
re
co
n
s
tructe
d imag
e in
Step 1
to 3
are
sh
own
respe
c
tively as Figu
re 7, Fi
gure 8 a
nd Fi
gure 9.
(a)
(b)
Figure 7. (a)
One of the fra
m
es of the DMD
pattern in
Step 1; (b) The re
con
s
tructed low
resolution im
age of 64
×64
pixels
(a)
(b)
Figure 8. (a)
One of the fra
m
es of the DMD pa
ttern in
Step 2; (b) The re
con
s
tructed middle
resolution im
age of 64
×64
pixels
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TELKOM
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Vol. 12, No. 6, June 20
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801
4800
(a)
(b)
Figure 9. (a)
One of the fra
m
es of the DMD
pattern in
Step 3; (b) The re
con
s
tructed high
resolution im
age of 64
×64
pixels
It can b
e
see
n
that in the
reco
nstructe
d
low
re
solutio
n
imag
e, only
a bri
ght
spot
on the
bottom left can be recogn
ized; in the
reco
nstr
ucte
d
middle resolu
tion image, the sh
ape
of the
ship
can be
clearly re
cog
n
i
z
ed. The resolution of the image in Step 2 is 8 times higher tha
n
that
in Step 1. In the re
co
nstructed high resol
u
tion imag
e, the detaile
d in
formati
on, like the symbol
of
the ship,
can
be
re
cog
n
ized. As there i
s
n
o
mi
rro
r
combinatio
n in
Step 3, th
e i
m
age
re
sol
u
tion
achi
eved the
highe
st in this simulation ex
perim
en
t, whi
c
h is 4 time
s
highe
r than th
at in Step 2.
The reco
nst
r
ucted lo
w re
solutio
n
imag
es
can b
e
e
n
larg
ed to th
e origi
nal si
ze of the
imaging
scen
e and the i
n
tere
sted a
r
ea
in low
re
solu
t
i
on imag
e ca
n be repla
c
e
d
by that of the
high re
sol
u
tio
n
image, the result is
sho
w
n in Figure 10
.
Figure 10. Th
e Integration
of Three
Re
constructe
d Image
s
From th
e int
egrate
d
ima
g
e
in Fig
u
re 1
0
, not only t
he po
sition
o
f
the obje
c
t i
s
clea
rly
sho
w
n, but al
so the detail
e
d informat
io
n of the ship ca
n be re
cog
n
ized.
The total
nu
mber of fram
es
of the
DM
D in
3
ste
p
s i
s
6
4
×64
×
0.3
+
64
×6
4×0.6+64×64
×0.6
=61
44, an
d
the memo
ry
co
st is
19.
2MB. If di
re
ctly re
con
s
truct the
whol
e scen
e in
high
resolution, 20
48×204
8×0.6
=
25
165
83
fra
m
es of
DM
D
and 9.3
8
TB
memeroy mu
st be
nee
ded
. If
the flippin
g
ra
te of DMD is
1000
times p
e
r
se
con
d
, th
e mea
s
u
r
em
e
n
t strategy in
this p
ape
r n
e
e
d
about 6 seco
nds
for ob
servation,
while
42
min
u
te
s o
b
se
rvation ti
me is ne
ede
d
witho
u
t ado
p
t
ing
su
ch strategy
. As to the recon
s
tru
c
tion t
i
me, the total
time con
s
um
ed in 3 step
s is 42.8 se
co
n
d
s
on an
Intel i
5
-24
30M
CP
U
@ 2.4
0
G
H
z laptop
compute
r
with
10GB m
e
m
o
ry in MAT
L
AB
environ
ment. The test of imaging the
whole sce
n
ce
whitho
ut ado
pting th is strategy is not d
one
sin
c
e there is no enou
gh m
e
mory to sto
r
e su
ch
hu
ge
data amou
nt of the measu
r
ement matrix.
5. Conclusio
n
In this pape
r,
to meet the appli
c
ation d
e
mand of e
a
rth obse
r
catio
n
imaging
，
a
n
efficient
strategy
of co
mbining different
numb
e
rs of
mi
rro
rs in
DMD to
adju
s
t image resol
u
tion an
d u
s
i
n
g
spe
c
ific
are
a
i
n
DM
D to reconstruct th
e a
r
ea of i
n
tere
st
is p
r
e
s
ente
d
for si
ngle pix
e
l cam
e
ra. Th
e
simulatio
n
ex
perim
ent i
s
carri
ed
out to
verify the
the
o
ry by im
agin
g
the th
re
e-li
ne ta
rget
and
for
the appli
c
atio
n mode to im
age a
ship in
the large
are
a
of oecan in
which thre
e
step
s to imag
e
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TELKOM
NIKA
ISSN:
2302-4
046
An Efficient Im
aging Strategy for Sin
g
le
Pixel Cam
e
ra in Earth Ob
servatio
n (Ch
uanrong Li
)
4801
the scen
e from lo
w to h
i
gh resol
u
tio
n
are ex
e
c
u
t
ed. The
re
sult sho
w
s th
at the detail
e
d
informatio
n of the intereste
d
object is re
cog
n
ized whil
e con
s
umi
ng much le
ss measure
m
ent a
n
d
cal
c
ulatio
n ti
me than
tra
d
itional im
ag
ing me
th
od,
and
it vali
dates the
effectivene
ss
and
pra
c
ticality of the propo
se
d strategy. F
u
ture
work will focus on t
he auotom
atic algo
rithm for
target re
go
co
nition and lo
cation in vario
u
s ea
rth ob
se
rvation appli
c
ation mode.
Ackn
o
w
l
e
dg
ements
This
work was finan
cially
supp
orted
by
the CAS/SAFEA International Pa
rtnership
Program fo
r Creative
Rese
arch
Tea
m
s a
nd t
h
e
Natio
nal
Hi
gh
Technol
og
y Re
sea
r
ch
and
Develo
pment
Progra
m
(No
.
2013AA121
304).
Referen
ces
[1]
Pittman T
B
, et al. Optical imagi
ng b
y
mea
n
s
of t
w
o-ph
oto
n
qua
ntum ent
ang
leme
nt.
Physical Rev
i
ew
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5): R342
9-R3
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[2]
Duarte MF
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agi
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mplin
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ensiv
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ne
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mber
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ao
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