TELKOM
NIKA
, Vol.12, No
.4, Dece
mbe
r
2014, pp. 89
7~9
0
4
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i4.296
897
Re
cei
v
ed Au
gust 26, 20
14
; Revi
sed
No
vem
ber 1
2
, 2014; Accepte
d
No
vem
ber
24, 2014
Sparsity Properties of Compressive Video Sampling
Generated by Coefficient Thresholding
Ida Wahida
h
*
1,2
, Tati Latifah R. Mengk
o
2
, Andriy
an
B. Suksmon
o
2
, Hendra
w
an
2
1
School of Ele
c
trical Eng
i
ne
e
r
ing, T
e
lkom Universit
y
Jl.
T
e
lekomu
ni
kasi No. 1, Ban
dun
g, Indon
esi
a
2
School of Ele
c
trical Eng
i
ne
e
r
ing a
nd In
form
atics, Institut
T
e
kno
l
og
i Ban
d
ung
Jl. Ganesa No.
10, Band
ung, Indo
nesi
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:
w
a
hi
dah
7@s
t
udents.itb.ac.i
d
A
b
st
r
a
ct
W
e
study th
e c
o
mpressiv
e
s
a
mp
lin
g (C
S) a
n
d
its
app
licati
o
n i
n
a
vid
e
o
en
codi
ng fra
m
ew
ork. T
h
e
vide
o i
n
p
u
t is
firstly transfor
m
e
d
into
a s
u
itabl
e d
o
m
ai
n in order
to ac
hiev
e
sp
arser
config
uratio
n of
coefficie
n
ts. T
hen, w
e
ap
pl
y coefficie
n
t thresh
old
i
n
g
to
classify w
h
ic
h frames are
to be sa
mp
l
ed
compressiv
e
ly
or conv
enti
ona
lly. F
o
r fra
m
es
chose
n
to
un
derg
o
co
mpre
ssive sa
mpli
ng
, the coeffici
e
n
t
vectors w
ill b
e
proj
ected i
n
to
sma
ller v
e
ctor
s usin
g
a ra
nd
om
meas
ure
m
ent matrix. As
CS req
u
ires t
w
o
ma
in co
nditi
on
s, i.e. sparsity and
ma
trix i
n
c
oher
ence, this
researc
h
is
focused o
n
the e
n
hanc
e
m
ent of the
sparsity pr
oper
ty of the inp
u
t sign
al. It w
a
s empiri
c
a
lly
pr
oven th
at the
sparsity e
nha
n
c
ement co
uld
b
e
reach
ed by a
p
p
lyin
g motio
n
compe
n
satio
n
a
nd thresh
ol
d
i
n
g
to the non-si
gnific
ant coeffi
cient cou
n
t. At
the
deco
der sid
e
, the reco
nstructi
on al
gorith
m
c
an e
m
p
l
oy b
a
si
s pursuit or L1
mi
ni
mi
z
a
t
i
o
n
al
gorith
m
.
Ke
y
w
ords
: c
o
mpressiv
e
s
a
mpli
ng, v
i
de
o co
din
g
, sp
arse re
pres
en
tation, si
gna
l
sparsity,
mo
tio
n
co
mp
en
sa
ti
on
1. Introduc
tion
Since ma
ny signal
s in natu
r
e have an in
ternal st
ru
ctu
r
e that ca
n b
e
exploited greatly, it
is not un
co
mmon that
we a
r
e a
b
le
to comp
re
ss
tho
s
e
sign
als to
some
extent so th
at the
recovery still acquires acceptabl
e accuracy. In line with that,
the c
o
mpressive sensi
ng/sampli
ng
is a
relatively
new pa
radi
g
m
in si
gnal
proce
s
sing,
wh
ere th
e sampl
i
ng fre
quen
cy
might be l
o
wer
than that of the Nyqui
st theorem
requirement [1],[2]. The acquisit
i
on phase is
very simple and
integrate
d
with
the com
p
re
ssi
on pha
se, as
th
e
n
a
me implies. Furth
e
rmo
r
e, com
p
re
ssive
vide
o
sampli
ng i
s
o
ne of the p
r
o
m
ising
appli
c
ations
of CS
due to its d
e
m
and o
n
the
low compl
e
xity
encodin
g
p
r
o
c
e
ss. A
s
a
co
nse
que
nce of
the
simpl
e
a
c
qui
sition, th
e
re
co
nstructio
n
ph
ase i
s
qu
ite
compli
cate
d yet computatio
nally feasible.
The CS meth
od ca
n bre
a
k
the Nyqui
st Shann
on limit by taking fewer mea
s
u
r
em
ents for
exact recove
ry [1], as l
o
n
g
a
s
the
sig
nal i
s
ad
equ
ately sp
arse
and th
e rand
om matri
c
e
s
are
inco
herent to each oth
e
r
. Variou
s al
gorithm
s hav
e been prop
ose
d
to reconstruct hig
h
l
y
incom
p
lete
sign
als. The
s
e algo
rithm
s
are
ca
tegorized into
three c
l
asse
s, i.e. convex
optimizatio
n, gree
dy
alg
o
ri
thm,
and
iterative thre
shol
ding. In th
i
s
rese
arch, we
use
the co
nvex
optimizatio
n rep
r
e
s
ente
d
by
basi
s
p
u
r
suit (
BP) [
3
]. Theoretically, basi
s
pursuit shou
ld
outperfo
rm m
a
tchin
g
pu
rsu
i
t (MP) in te
rms of
a
c
cu
ra
cy. On the
other
hand, M
P
might be l
e
ss
compl
e
x and have faster p
r
ocessin
g
time. In gener
al,
the basis p
u
rsuit meth
od will re
con
s
tru
c
t
the optimum
sign
al by means of line
a
r
prog
ra
m
m
ing
.
The receive
d
sign
al will
be de
comp
osed
into smalle
r
parts fro
m
a
n
ove
r
-compl
ete di
ct
iona
ry. The
de
cisi
o
n
on
which e
l
ement m
u
st
b
e
sele
cted i
s
re
sulted fro
m
the cal
c
ulatio
n of L1 norm.
The pap
er by
[4] investigates the ch
an
ce
of compressive sam
p
ling
to be implemented in
a video co
di
ng frame
w
o
r
k. Ho
weve
r, it did not con
s
id
er mot
i
on co
mpen
sation to red
u
ce
temporal red
unda
ncy by exploiting inter-f
rame co
rrelation. Other works relate
d to compressive
video sam
p
li
ng incl
ude [
5
] and [6].
The form
er
method focu
sed o
n
vide
o pro
c
e
ssi
ng
and
recon
s
tuctio
n
of multiple f
r
ame
s
simult
aneo
usly
rather tha
n
forming smalle
r blocks, whil
e the
latter stu
d
ied
distri
buted vi
deo
codi
ng, i
n
whi
c
h th
e coder co
ndu
ct
ed conventio
nal samplin
g
for
referen
c
e o
r
key fra
m
e
s
a
nd
comp
re
ssi
ve sam
p
ling
for n
on
refe
re
nce
fram
es.
The a
ppli
c
ati
on of
comp
re
ssive
video sam
p
ling
in multi
m
edia co
mm
uni
cation su
ch as
wi
rele
ss
visu
al se
nso
r
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 897
– 904
898
netwo
rks (WVSN) i
s
stu
d
ied
by [7],[10], whil
e
si
ngle
pixel
camera a
ppli
c
ation fo
r e
a
rth
observation
can be foun
d in [18].
2. Compressi
v
e
Samplin
g
Con
s
id
erin
g the ra
w video seq
uen
ce wit
h
very large
digital data, with a traditio
nal video
codi
ng meth
o
d
, the video i
nput is first transfo
rm
e
d
, q
uantized, and
then entropy
cod
ed. In the
comp
re
ssive sampli
ng me
thod, the video se
que
nc
e
or the tran
sformed
seq
u
ence is si
mp
ly
multiplied
by
a ra
ndom
me
asu
r
em
ent/projectio
n ma
t
r
ix, such a
s
G
a
ussian,
Had
a
m
ard, Be
rn
ou
lli,
etc. There are two matri
c
es utilized i
n
th
is scheme, i.e. the
sparsifying
matrix
and the
proje
c
tion m
a
trix
. Th
e
dimen
s
ion
o
f
the proje
c
ti
on matrix i
s
M
N
, where
M
<
N
, im
plies
a
smalle
r n
u
mb
er of
rows th
an column
s. I
t
is expe
cted
that one
can
recover th
e video
seq
uen
ce
with a slo
w
e
r
mea
s
ureme
n
t rate denot
ed by
M
. Among the p
r
opertie
s
fost
ering the g
o
a
l of
comp
re
ssive sampli
ng are
the sp
arsity level
of
the
i
nput
sign
al a
nd the
in
coh
e
ren
c
e
me
asure
betwe
en those two matrices [8]. With compressiv
e sampling, it was proven that we can ap
pl
y
sampli
ng fre
quen
cy le
ss
than Nyq
u
ist
boun
d to s
parse
sign
als. However, the re
co
nst
r
u
c
ted
sign
al/video q
uality remain
s sati
sfacto
ry in terms of P
S
NR.
Each input entity
x
, e.g.
pixel block or frame in
N
-length ve
cto
r
form, is proce
s
sed
according to
a comp
re
ssive samplin
g
princi
ple,
where the in
p
u
t is multiplied by a ran
dom
proje
c
tion
ma
trix
of
size
M
N
. T
he b
a
s
ic fo
rmul
atio
n to obtai
n th
e output
sig
n
a
l
y
of
length
M
is
as
follows
.
y
=
x
(1)
Thus, the me
asu
r
em
ent ra
te of this sam
p
ling me
cha
n
i
sm is
R
=
M
/
N
. Dep
endin
g
on the
sele
ction of p
r
ocessin
g
level, the numb
e
r of sa
mple
s
N
may rep
r
e
s
ent G
O
P (group of pictu
r
es)
length, frame
size, o
r
ev
en blo
ck
si
ze in ca
se
s
whe
r
e the in
put is split into seve
ral
non-
overlap
ped bl
ocks.
The inp
u
t sig
nal
x
can
be
treated in ei
ther its o
r
igin
al
form o
r
tra
n
sformed int
o
anothe
r ba
si
s
function. After the transfo
rmation pro
c
e
ss, it
is expected that the si
gnal coefficient
s becom
e
spa
r
ser. The
relation
shi
p
can be written as
x
=
z
(2)
whe
r
e
z
i
s
the rep
r
e
s
entati
on of
x
in the
domai
n. Neverthele
s
s, for a video se
quen
ce
with low
spatial a
nd te
mporal red
u
n
dan
cy, which has fa
st
motion scen
es, th
e spa
r
sity level of transfo
rm
coeffici
ents
could still re
m
a
in low. Hen
c
e, in addition
to the spa
r
sif
y
ing transfo
rm, we also a
pply
several sp
arsity enhancem
ent met
hod
s as di
scusse
d in Section
3. Doin
g so, bet
ter accu
ra
cy
coul
d be a
c
hi
eved [9].
3. Rese
arch
Metho
d
This sectio
n
briefly di
scusse
s the
sign
al sp
a
r
sity o
r
sp
arse
ne
ss
and it
s dyn
a
m
ics,
a
s
well a
s
the en
han
ceme
nt method. Gen
e
rally, one ca
n have a sparser data by
me
rely ch
oo
sing
a
suitabl
e ba
si
s fun
c
tion fo
r the input
si
gnal, be
ca
use mo
st of the tran
sform
coeffici
ents
h
a
ve
negligibl
e
val
ue. Thi
s
i
s
i
n
a
c
cordan
ce with
Parse
v
al theo
rem.
Ho
weve
r, th
e recon
s
tru
c
tion
stage of
co
m
p
re
ssive sa
m
p
ling comm
o
n
ly
sea
r
che
s
fo
r a
spa
r
sest
solutio
n
. The
r
efore, the effort
to re
pre
s
e
n
t t
he
sign
al a
s
sparse
a
s
p
o
ssible
can
alle
viate re
co
nstruction
e
rro
r. I
n
ad
dition to
t
he
spa
r
sifying transfo
rm, we
also a
pply two enha
nc
em
ent method
s. Firstly, motion com
pen
sa
tion
and e
s
timatio
n
su
ppo
rted
by a sim
p
le
b
l
ock mat
c
hin
g
algo
rithm i
s
expecte
d to
result in
spa
r
se
motion vecto
r
s. Secon
d
ly, thre
shol
ding t
o
the
amount
and the absolute value of non-signifi
ca
nt
coeffici
ents i
s
sup
p
o
s
ed
to
sep
a
rate the
spa
r
se a
nd
non-sp
arse f
r
ames,
su
ch t
hat only
spa
r
se
frame
s
ca
n g
o
throug
h co
mpre
ssive sa
mpling.
3.1. Sparsit
y
Enhanceme
n
t b
y
Motion Compens
a
ti
on
Motion-com
p
ensated fra
m
es g
ene
ration
is u
s
ually correspon
ding to
a motion e
s
ti
mation
algorith
m
. Motion estimati
on is the det
ermin
a
tion
of motion vectors that de
scribe the temp
oral
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sparsity Pro
p
e
rties of
Com
p
re
ssi
ve Vid
e
o
Sam
p
ling Generated b
y
Coeffici
ent …
.
(Ida Wahi
da
h)
899
cha
nge from one imag
e to anothe
r. The
vectors ar
e typically ba
se
d on adja
c
e
n
t frames, forwa
r
d
or ba
ckwa
rd
directio
n, in a video seq
uen
ce
. This i
s
an ill-condi
tioned proble
m
beca
u
se the
motion is in 3
D
but the ima
ges a
r
e on a
2D pla
ne. Th
e motion vect
ors
refer to th
e whol
e imag
e
frame or
spe
c
ific pa
rts, su
ch as
squ
a
re
s, recta
ngul
ar blocks, or on
a per pixel basi
s
. We stud
ie
d
how the hig
h
-redu
ndant
video se
que
nce
s
yield
b
e
tter CS improvem
ent o
v
er conve
n
tional
comp
re
ssion
comp
ared
with that of
low r
edu
nda
nt videos. O
u
r comp
re
ssi
ve video sy
stem
modifies the
video pro
c
e
s
sing pl
atform
[4] by in
tegrating the acq
u
isition p
h
a
s
e, texture, and
motion co
din
g
. Figure 1
sh
ows the gen
e
r
al blo
ck di
ag
ram of the sy
stem.
Figure 1. Our propo
se
d co
mpre
ssive video sam
p
ling
3.2. Sparsit
y
Enhanceme
n
t b
y
Coeffic
i
ent Thre
s
ho
lding
We tail
or th
e
video
sequ
en
ce
by pre-p
r
o
c
e
ssi
ng
and
dividing it int
o
refe
re
nce a
nd n
on-
referen
c
e fra
m
es. T
hen,
coefficient th
re
shol
d
T
c
an
d c
o
mp
r
e
ss
ive th
r
e
s
h
o
l
d
,
i.e. the ratio
of
non-sig
n
ifica
n
t co
efficient
co
unt to
the
total nu
mbe
r
of t
r
an
sform coefficie
n
ts, a
r
e
determine
d
empiri
cally. T
he
T
c
value i
s
ba
sed
on the re
no
wned
Parseval th
eore
m
, while
derivation is
based on th
e Can
d
e
s
eq
uation. According to t
he classical theorem, the total energy of 2
D
disc
rete
s
p
ace is
as
follows
.
∑∑
|
,
|
∞
∞
∞
∞
|
Ω
,
Ψ
|
Ω
Ψ
(3)
After discrete
co
sine tra
n
sf
orm (DCT),
we have th
e (
p,q
)
th
order
DCT
c
o
effic
i
ent for an
N
N
image h
a
ving intensit
y f(x,y) denoted by
C
pq
and supp
orte
d by the cosin
e
kern
el functi
on of
the ba
sis
D
n
(t
) a
nd a
no
rmali
z
ation f
a
ctor
ρ
(n
) [11], where
0
p,q,
x,y
N
-1. The
DCT
coeffici
ents di
stributio
n
re
semble
s L
apla
c
ian
in
so
m
e
experim
ental
results after t
e
sting
with
th
e
Kolmogo
rov-Smirnov method [12]. In
most of our
e
x
perime
n
ts, the popul
ar JPEG block si
ze of
8
8 pixel
s
is
use
d
. Hen
c
e,
the following
type-II DCT coefficient valu
e is co
nsi
dered.
,
∑∑
,
cos
cos
(4)
The conditio
nal proba
bility of transfo
rm coeffici
ent
value
p(I
m,
n
|
2
) is
app
rox
i
mately a
zero-m
ean G
aussia
n
distri
bution. Mean
while, t
he e
m
piri
cal data
of image block varian
ce
is
con
s
i
s
tent
wi
th half-Gau
s
sian
di
stribut
ion a
ppr
oxim
ations. Co
nsiderin
g
thi
s
ca
se of
blo
c
k
var
i
anc
e
2
, the fit proba
bility of
transfo
rm coeffici
ent
s
is then a m
u
ltiplication
of the conditio
n
al
prob
ability an
d its vari
an
ce
pro
bability. T
he expe
ct
ed
value of the t
r
an
sform
coe
fficients
can
be
use
d
to rep
r
e
s
ent the coefficient thre
sh
o
l
d of our interest.
∞
∞
(5)
By using the maximum po
ssi
ble DC co
efficient
I
0,0
= 2040 a
nd the
followin
g
relat
i
onship from t
he
integral tabl
e in [13].
(6)
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4: 897
– 904
900
we
coul
d
co
mpute the
ex
pecte
d value
of tran
sfo
r
m
co
efficient fo
r thresholdin
g
, as
well
a
s
the
expecte
d value of energy.
∞
√
2
.
0
8
1
0
2040
2040
(7)
This la
st e
quation p
r
e
s
ent
s the relation
ship
betwe
en av
erag
e ene
rg
y after
transfo
rmatio
n an
d the
blo
c
k varia
n
ce v
a
lue. G
r
eate
r
varian
ce
me
ans faste
r
o
b
j
ect motio
n
a
nd
detailed
spati
a
l texture of the imag
e. Th
e maximu
m value of coefficient vari
an
ce is propo
rtio
nal
to I
0,0
2
/4 or approximatel
y 1.04e+0
6
. The de
rivatio
n
of threshol
d value
T
c
from the ene
rgy
expecta
nce is sho
w
n in Ta
ble 1.
Table 1. The
derivation of
coeffici
ent thresh
old value
T
c
s E[I
2
]
E[I
2
]
90%
T
c
0,1 0,05
0,045
0
1 0.5
0,45
0
10 5
4,5
0
100 50
45
3
10
3
500 450
23
10
4
5000
4500
45
10
5
4,97
10
4
4,47
10
4
246
In order to
de
rive the
comp
ressive
thre
shold val
ue
(
N
s
/N
>
), the
t
enets pu
blish
ed in
a
pape
r by [8] stated that ran
dom mea
s
u
r
e
m
ents
can b
e
used fo
r sig
n
a
ls
s
-spa
rse in any basi
s
a
s
long a
s
ob
eys the following co
ndition
ln
.
ln
2
.
(8)
The small co
nstant of 1.7
is ba
sed
on
previou
s
e
m
piri
cal resul
t
s to gua
rant
ee less
decodin
g
failure [14]. To
solve Equ
a
tio
n
(9
),
we u
s
e the Lam
be
rt W fun
c
tion
, represented
by
W(
z
) a
nd defi
ned as the in
verse of
f(z) =
z
e
z
sat
i
sf
y
i
ng
W(
z
)
e
W(z
)
= z
. The mathematical hist
ory
of
W(
z
)
begi
n
s
when
Lamb
e
rt solve
d
the
trinomial e
q
u
a
tion, that is
sub
s
e
que
ntly transfo
rme
d
by
Euler into the form [15]
x
-x
= (
-
)vx
+
. For
n
= 1 and
=
1
1
2
1
3
1
4
⋯
(9)
For
=
-1, we have
ln
ln
10
…
2
.
3
(10
)
This e
quatio
n solve
s
ou
r objective to
obtain the sparsity level
and event
ually the
comp
re
ssive threshold
. The la
st se
ries conve
r
ge
s for |
v|
< 1/
e
and define
s
a function
T(
v
)
calle
d the tre
e
functio
n
. Thus, the
La
mbert
W fun
c
tion h
a
s th
e
gene
ric
se
ri
es exp
a
n
s
ion
as
follows
.
∑
!
∞
(11
)
⋯
(12
)
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TELKOM
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Sparsity Pro
p
e
rties of
Com
p
re
ssi
ve Vid
e
o
Sam
p
ling Generated b
y
Coeffici
ent …
.
(Ida Wahi
da
h)
901
We u
s
e the n
egative bra
n
ch of the Lambert functio
n
W
-1
(x
), as it is de
sign
ated
to have
an inve
rsely
prop
ortio
nal
relation
ship
b
e
twee
n m
e
a
s
urem
ent
rate
and
comp
re
ssive
thresho
l
d
value. Accord
ing to [16], th
e ratio
nal fun
c
tion
W
-1
(x
)
p
r
ovide
s
a
rel
a
tive app
roximation e
r
ror f
o
r
W
-1
(x
) of less
than 10
-4
for
any
x
[-0.3
33, -0.033]
.
.
.
.
.
.
.
.
(13
)
4. Results a
nd Discu
ssi
on
We im
pleme
n
t com
p
re
ssi
v
e video
sa
mpling in
Ma
tlab with th
re
e main
scen
ario
s a
n
d
variou
s video
seq
uen
ce
s. In the first
sce
nario,
we
o
b
serve the influ
ence of blo
c
k or pat
ch
size
,
rangi
ng from
4
4 to 32
32
pixels, to the accura
cy re
pre
s
ente
d
by average PS
NR (pea
k si
g
nal
to noise rati
o). Larg
e
r bl
ock size co
u
l
d lose in
tra
b
l
ock pixel-correlation, while smalle
r blo
c
k
implies long
e
r
total p
r
o
c
e
s
sing tim
e
. In the second
scenari
o
, we
de
monst
r
ate h
o
w
vari
ou
s types
of video i
npu
t, i.e. low to
high
red
und
a
n
cy, affect th
e re
co
nst
r
u
c
ted vide
o’s PSNR. T
he l
o
w
redu
nda
ncy
seque
nce pe
rtains to fa
st m
o
ving obje
c
t
s
in a sce
ne o
r
high d
e
tails i
n
video texture,
and vice versa. In the last
scena
rio,
the comp
re
ssive coeffici
ent
thresh
old
and
its optimal val
u
e
in term
s of P
S
NR is inve
stigated.
T
he
hi
gher the
coefficient th
re
sho
l
d, the
gre
a
te
r the
chan
ce
for
the system to
sele
ct conve
n
tional sampl
i
ng, and ev
e
n
tually yieldin
g
better a
c
cu
racy yet high
er
compl
e
xity. The vide
o
seq
uen
ce
emplo
y
ed in
our ex
perim
ents ha
s a
resolutio
n
si
ze
of 8
0
64
pixels an
d a frame rate of 15 fps.
Figure 2. PSNR
comp
ari
s
on for Traffic seq
uen
ce in
a video pro
c
e
ssi
ng sch
e
me
for variou
s
block si
ze a
n
d
measureme
n
t rate
Our
simulatio
n
s in
clud
e the effect of comp
ressive sampling
with
the combi
n
ation of
measurement
rate (MR), block size (BS), and vari
ous
comp
re
ssive threshold
s
on
reco
nst
r
ucte
d
video
PSNR. These simul
a
tion
results are
then
comp
a
r
ed
with
the
theoretical
results, e
s
pe
ciall
y
the value
s
of coeffici
ent thresh
old
T
c
an
d com
p
ressiv
e thre
shol
d
.
In mos
t
s
i
mulations
,
we us
e
a block si
ze o
f
N
=
m
×
n
pixels
.
4x
4
4x
8
8x
8
8x
16
16x
16
16x
32
32x
32
10
15
20
25
30
35
40
45
50
P
e
r
bandi
ngan P
S
N
R
ber
ba
gai
l
a
j
u
penguk
ur
an dan uk
ur
an bl
ok
U
k
ur
an bl
ok
PS
N
R
(d
B)
M
R
=
20%
M
R
=
40%
M
R
=
60%
M
R
=
80%
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ISSN: 16
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TELKOM
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mb
er 201
4: 897
– 904
902
Figure 3. PSNR
comp
ari
s
on for several
video input o
r
de
red b
a
sed
on spatial a
n
d
temporal
redu
nda
ncy, GOP length
= 12 [17]
Figure 4. Re
constructe
d PSNR
of comp
ressive threshold
expe
ri
ment, with co
efficient thre
shold
T
c
= 35 and T
SS algorithm
E
n
do
s
c
o
py
Mo
t
h
e
r
Tr
a
f
f
i
c
Ne
ws
R
h
i
nos
MR
I
Mo
b
ile
20
25
30
35
40
45
V
i
d
e
o
S
e
que
nc
e
(
L
ow
t
o
H
i
gh R
e
d
u
n
dan
c
y
)
PS
N
R
(
d
B
)
M
R
20
%
bl
o
k
8
x
8
M
R
30
%
bl
o
k
8
x
8
M
R
40
%
bl
o
k
8
x
8
M
R
2
0
%
b
l
ok
32x
32
M
R
3
0
%
b
l
ok
32x
32
M
R
4
0
%
b
l
ok
32x
32
50
55
60
65
70
75
80
85
90
95
27
30
33
36
39
42
45
48
C
o
m
p
r
e
s
s
i
v
e
T
h
r
e
s
hold G
a
m
m
a
(
%
)
PSNR
(d
B)
P
S
N
R
C
o
m
p
a
r
is
on of
V
a
r
i
ous
G
a
m
m
a
V
a
lue,
T
c
=
35,
T
S
S
,
G
O
P
=
12,
B
S
=
8x
8
T
r
af
f
i
c
,
M
R
20%
T
r
af
f
i
c
,
M
R
30%
T
r
af
f
i
c
,
M
R
40%
M
obi
l
e
,
M
R
20%
M
obi
l
e
,
M
R
30%
M
obi
l
e
,
M
R
40%
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sparsity Pro
p
e
rties of
Com
p
re
ssi
ve Vid
e
o
Sam
p
ling Generated b
y
Coeffici
ent …
.
(Ida Wahi
da
h)
903
The effe
ct of
blo
c
k si
ze
variation to
the recon
s
tru
c
ted
sig
nal a
c
cura
cy o
r
P
S
NR
i
s
sho
w
n in Fig
u
re 2. Intere
stingly, despite
the cl
ear PS
NR d
e
crea
se
over larg
er b
l
ock si
ze for
MR
= 80%, the
contra
st tende
ncy is
ob
serv
ed for M
R
= 2
0
% to 60%. T
h
is
coul
d be
caused by the
ill-
con
d
ition
s
of the low rate e
n
vironm
ent, such t
hat the
smaller BS co
uld not outpe
rform the la
rg
er
BS. These re
sults lea
d
us
to
the selecti
on of block si
ze 8
8 and 3
2
32 pixel
s
in the sub
s
eq
uent
experim
ents.
Mean
while, t
he recon
s
tru
c
ted PSNR co
mpari
s
o
n
of variou
s in
put v
i
deo
seq
uen
ce
type is pre
s
e
n
ted in Figu
re 3. For the
next ex
perim
ent, we ch
oo
se the g
r
eyscale T
r
affic a
nd
Mobile sequ
e
n
ce a
s
hig
h
-
and lo
w-redu
ndant video resp
ectively.
Figure 4
sho
w
s the
influe
nce
of
com
p
ressive
samp
ling th
re
shol
d
to the P
S
NR of
recon
s
tru
c
ted
signal. It ca
n be seen th
at at some p
o
int of
, the PSNR ob
se
rvation re
sults in
pea
k value, i.
e. arou
nd 8
0
%
to 90%. As predi
cted,
th
e increa
se
of measurement
rate affe
cts t
he
recon
s
tru
c
tio
n
accu
ra
cy of high-redu
nd
ant video
gre
a
tly, repre
s
e
n
ted by Traffi
c se
que
nce. On
the other
han
d, mode
st improvem
ent is
resulted
fo
r low-re
dun
dant
video, i.e. Mobile sequ
en
ce.
This is in a
g
ree
m
ent wi
th the theoretical
analy
s
is in our p
r
evious work,
in which t
h
e
recomme
ndat
ion for
is 0
.
89. The
co
mpre
ssive th
reshold
of
85% is
suita
b
le for all
of
ou
r
experim
ental
scena
rio
s
.
Gene
rally, a
com
p
re
ssive video
sa
mpling m
e
th
od with
sp
a
r
sity
enha
ncement
and th
re
sho
l
ding
sup
port
coul
d b
e
im
plemente
d
wi
th promi
nent
re
sults in th
e
terms
of PSNR.
Table 2. The
spa
r
sity ratio
on various
method
s and
video se
que
n
c
e types, T
c
=3 and
=80%
Video Frame
original
transform
MC
ME
th
reshold1
th
reshold2
Mother &
daughter
reference
97.50%
72.13%
51.84%
20%
non
ref
97.50%
36.76%
28.96%
26.97%
Traffic
reference
99.98%
69.94%
46.58%
20%
non
ref
99.96%
51.97%
81.33%
38.09%
Ne
w
s
reference
100%
75.37%
56.21%
20%
non ref
100%
51.97%
24.55%
21.48%
Rhinos
reference
100%
70.98%
46.80%
20%
non ref
100%
51.97%
63.28%
38.03%
Mobile
reference
99.92%
95.16%
84.92%
20%
non
ref
99.88%
51.97%
45.68%
42.01%
Table 2
presents t
he sp
arsity
ratio
a
s
the pe
rcenta
ge of si
gnificant co
efficien
t count
s
to the total sample
s after
each p
r
o
c
e
s
s involved in o
u
r
system. T
he g
r
eate
s
t d
e
crea
se in
, i.e.
yielding
spa
r
sest data, i
s
a
c
hieve
d
by sp
arsity
tra
n
sfo
r
m with the
averag
e of 3
6
.7
%. The secon
d
p
r
oc
es
s to
ma
k
e
g
o
d
o
wn is the
dete
r
mination of
coeffi
cient th
re
shol
d, den
ote
d
by thre
sh
ol
d1
in the table,
with the ave
r
age of 19.5
%
. With
a lo
wer
sp
arsity ratio, the re
q
u
ired
numb
e
r of
measurement
s in projection transf
orm
is obviously lower
as
we
ll. Due to the utilization of
threshold
T
c
=3 for the
refe
rence frame
s
i
n
this expe
ri
ment, the
re
sulted ratio
i
s
relatively hi
gh.
The hi
ghe
r t
h
re
shol
d val
ues i
n
lin
e
with the th
eo
retical
an
alysis, for i
n
sta
n
c
e
T
c
=42, would
prod
uce a very low spa
r
sity
ratio.
5. Conclusio
n
This pap
er provide
s
an
empiri
cal
e
v
i
dence of t
he p
r
omi
s
in
g implem
ent
ation of
comp
re
ssive video sam
p
li
ng. The ima
ge block o
r
patch
size is inversely proportio
nal to
the
PSNR of re
constructe
d video, esp
e
ci
al
ly for m
easurement rate g
r
eate
r
than 5
0
%. Moreove
r
,
despite the d
e
crea
se in
sp
atial and/o
r
t
e
mpo
r
al redu
ndan
cy, com
p
re
sive samp
ling with m
o
tio
n
comp
en
satio
n
su
ppo
rt is
quite reli
able
in most
of the test video
seq
uen
ce
s i
n
clu
d
ing m
e
d
i
cal
video. Ho
we
ver, for extre
m
ely low red
unda
nt video
s like Mobile
seq
uen
ce, the mea
s
u
r
e
m
ent
rate re
quirem
ent is high
er. As for ou
r last scen
a
rio, na
mely the coef
fici
ent thre
sh
olding
scena
rio,
the increa
se
of compressive thre
shol
d positiv
ely affects the a
c
cura
cy with
optimum value
arou
nd 8
0
%. If we set the l
a
rge
r
comp
re
ssive th
re
sho
l
d, then the a
c
cura
cy tend
s to deteri
o
ra
te
slightly. Having these re
sults,
together with the sim
p
licity of
the
encodin
g
pro
c
e
ss, we cou
l
d
recomme
nd t
he comp
re
ssi
ve video
sam
p
ling to
be i
m
pleme
n
ted i
n
seve
ral fut
u
re
appli
c
atio
ns,
su
ch a
s
wirel
e
ss visual
se
nso
r
networks (WVSN) a
n
d
video su
rve
illance.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 897
– 904
904
Referen
ces
[1]
Can
des EJ., Romber
g J.,
T
ao
T
.
Robust Unc
e
rtaint
y Princ
i
p
l
es: Exact Sign
al Rec
o
ver
y
fro
m
High
l
y
Incompl
e
te F
r
eque
nc
y
Inf
o
rmation.
IEEE Transactions on Inform
ation Theory
. 2006; 52: 4
89-5
09.
[2]
Don
oho D. Co
mpresse
d Sen
s
ing.
IEEE Transactions on Inform
ation Theory.
2006; 52: 1
289-
130
6.
[3]
Che
n
SS., Do
noh
o D
L
., Sau
nders
MA. Ato
m
ic Dec
o
mp
os
ition
b
y
B
a
sis
Pursuit.
SIAM Journ
a
l on
Scientific C
o
mputin
g
. 199
8; 43: 129-1
59.
[4]
Stankovic V., Stankovic L.,
Chen
g S.
Compressiv
e
Vi
deo S
a
mpl
i
ng
. 1
6
th
Eu
ro
pe
an
Si
g
nal
Processi
ng Co
nf. Lausa
nne,
S
w
itz
e
rla
nd. 2
008.
[5]
Marcia RF., Willett R.
Co
mpr
e
ssive C
o
d
ed
Aperture V
i
de
o
Reco
nstructio
n
. 16
th
Europ
e
an Si
gna
l
Processi
ng Co
nferenc
e. Laus
ann
e, S
w
itz
e
rl
and. 20
08.
[6]
Prades-
N
eb
ot J., Ma Y., Huang T
.
Distribute
d
Vide
o Cod
i
n
g
Using C
o
mpr
e
ssive Sa
mpli
n
g
. Picture
Codi
ng S
y
mp
o
s
ium. Chic
ago,
USA. 2009.
[7]
You
L., Han
Y., Li S., Su
X. So
urce a
n
d
T
r
ansmission
Co
ntro
l for W
i
re
less V
i
sual
Se
nsor
N
e
t
w
o
r
ks
w
i
t
h
C
o
mpress
ive Se
nsin
g a
n
d
Ener
g
y
H
a
rv
esting.
T
e
lk
o
m
nika J
ourn
a
l
of Electrica
l
En
gi
neer
ing
.
201
3; 11: 246
8
-
247
4
[8]
Can
des EJ., Romb
erg J., T
ao
T
.
Stable
Sign
al R
e
co
ver
y
from Inc
o
mpl
e
te an
d Inaccur
a
t
e
Measur
ements
.
Commu
n
ic
ati
ons on Pur
e
an
d Appl
ied M
a
th
ematics.
200
6; 59: 120
7-1
223.
[9]
F
o
w
l
er JE., M
un S., T
r
amel EW
. Block-Based
Compr
e
ssed Se
nsi
n
g
of Images
a
nd Vi
de
o.
F
ound
atio
ns a
nd T
r
ends i
n
Si
gna
l Processi
n
g
. 2012; 4: 29
7
-
416.
[10]
Kang LW
., Lu
CS.
Distributed Co
mpressi
ve Vide
o Sen
s
ing
. 34
th
IEEE International Conf. On
Acoustics, Spe
e
ch an
d Sig
nal
Processin
g
. T
a
ip
ei, T
a
i
w
a
n
. 200
9: 116
9-11
72.
[11]
Papak
ostas GA., Koulour
iotis
DE., Karakasi
s E
G. Efficient 2-D DCT
Co
mputatio
n from
an Imag
e
Repr
esentati
o
n
Point of Vie
w
. In: Chen Y.S.
Editor
. Image
Processi
ng. InT
e
ch; 2009: 21
-34.
[12]
Lam EY., Goo
d
man JW
. A M
a
thematic
al A
n
al
ysis
of the
D
C
T
Coefficient
Distributi
ons f
o
r Images.
IEEE Transactions on I
m
age
Processing.
20
00; 9: 166
1-16
66.
[13] Gradshte
y
n IS.
,
R
y
z
h
ik IM. T
abl
e
of Integr
al
s, Series, a
nd
Products. 5
th
e
d
. Ne
w
Y
o
rk:
Academ
ic.
199
4.
[14]
Kung
HT
., Lin
T
., Vlah D.
Id
e
n
tifying
Ba
d M
easur
e
m
ents
i
n
C
o
mpress
ive
Sens
ing
. 1
st
In
ternatio
nal
W
o
rkshop o
n
Securit
y
in C
o
mputers, Net
w
orkin
g
and C
o
mmunicati
ons.
Chin
a. 20
11.
[15]
Corless
RM., Gonnet GH., Hare DEG., Jeffrey
DJ., Knuth DE. On the Lam
bert W Function.
Advanc
es in C
o
mputati
o
n
a
l
Mathe
m
atics.
1
996; 5: 32
9-35
9.
[16]
Cha
pea
u-Bl
on
dea
u F
., Monir A. Numerical
Ev
alu
a
tion
of the Lam
bert W
F
unction a
nd
Appl
icatio
n
to Generatio
n
of Gener
al
ize
d
Gaussian N
o
i
s
e
w
i
t
h
E
x
po
n
ent ½.
IEEE
Transactions on Signal
Processi
ng
. 20
02; 50: 21
60-2
165.
[17] Wahidah
I.,
Hendra
w
a
n,
Suksmono A
B
., Mengko
T
L
R.
Correcting Temporal Artifacts in
Co
mpress
ive
Vide
o Sa
mpl
i
ng w
i
th Motion Estimatio
n
.
19th Asia-Pacific Co
nfe
r
ence o
n
Commun
i
cati
o
n
s. Bali, Indo
n
e
sia. 20
13.
[18]
Li C., Wang Q., Cao C., Ma L. An Efficient
Im
aging Strat
e
gy
for Single
Pixel Cam
e
ra in Earth
Observatio
n.
T
e
lko
m
nika Jo
ur
nal of Electric
al
Engin
eeri
ng.
2
014; 12: 4
794-
480
1.
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