Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 3
,
Ju
n
e
201
6, p
p
. 1
140
~ 11
51
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
3.9
031
1
140
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Design of Multiplier for Medi
cal Image Compression Using
Urdhava Tiryakb
h
yam Su
tra
Suma
1
, V. Sridhar
2
1
Vid
y
a
Vikas
In
stitute
of
Engin
e
ering
&
Techno
l
o
g
y
, M
y
sor
e
,
In
dia
2
PES Colleg
e
of
Enginner
i
ng, Mand
y
a
, Ind
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 12, 2015
Rev
i
sed
Jan
5, 2
016
Accepte
d
Ja
n 20, 2016
Com
p
res
s
i
ng the m
e
dical im
ages
is
one of the challenging ar
eas
in
healthc
a
re
industr
y
which calls for an effectiv
e design of the compression algorithms.
The conven
tion
a
l compression algorithms used on medical images doesn’
t
offer enhan
ced
com
putation
a
l c
a
pabi
liti
es with respect to f
a
ster
processing
speed and
is more dep
e
ndent on
hard
ware
res
o
u
r
ces
.
The pr
es
en
t paper
has
identif
ied th
e potenti
al us
age of
Vedic m
a
them
at
ics
in the form
of Urdhava
Tir
y
akbh
yam
sutra, which c
a
n be used for designing an effic
i
ent
m
u
ltiplie
r
that
can b
e
us
ed
for enhan
c
ing
t
h
e cap
abi
lit
ies
o
f
the
exis
ting p
r
oces
s
o
r to
generate
enhan
ce compression
expe
rience. The design of the proposed
s
y
ste
m
is disc
usse
d with re
spe
c
t
to
5 significan
t algorithms and the outcome
of the proposed
stud
y
was testif
ied w
ith h
e
terog
e
neous samples
of medical
image to f
i
nd
that proposed
sy
stem
offers approximately
5
7
% of th
e
reduction in
size without an
y
s
i
g
n
ificant
loss of d
a
ta.
Keyword:
Bit lo
ad
ing
algo
rith
m
Power allo
catio
n
algo
rith
m
Reso
urce allo
catio
n
W
i
reless n
e
two
r
k
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Sum
a
,
Vid
y
a
Vik
a
s Institu
te o
f
Eng
i
n
eeri
n
g and
Tech
no
log
y
,
M
y
sore, I
ndi
a
Em
a
il: su
m
aal
d
u
r@g
m
ail.co
m
1.
INTRODUCTION
W
i
t
h
the a
d
va
ncem
ent of the
m
odernized
techniqu
e for diagnosis
of
the
disease
s
, the healthcare
sy
st
em
has u
n
d
er
g
one
a
rev
o
l
u
t
i
o
nary
c
h
a
nge
by
ad
o
p
t
i
n
g
m
e
di
cal
im
age
pr
ocessi
ng
. Al
t
h
o
u
g
h
m
e
di
cal
im
age processi
ng is a
pa
rt of digital im
age proces
sing
,
but it could be
said as
an advance a
p
plications
of
d
i
g
ital i
m
ag
e
p
r
o
c
essing
as th
e co
m
p
le
x
ities an
d
charecteristics asso
ciated
with
m
e
d
i
cal
i
m
a
g
es are
com
p
letely differe
nt fr
om
natural im
ages [1]
.
Us
ua
lly,
medical im
ages
are captured
using various e
x
isting
im
age capturing
devices
e.g.
X-ray, CT
-sca
n, MR
I etc. Such m
e
di
cal images posses
valua
b
le information
wh
ich
is u
s
ed
fo
r m
a
in
ly th
ree p
u
rpo
s
es e.g. i) d
i
agno
si
ng the diseases of the subject
, ii) st
o
r
i
n
g
th
e im
ag
es in
th
e d
a
tab
a
se
for furth
e
r clin
ical stu
d
i
es for
med
i
cal st
u
d
e
nts, an
d
iii) research
an
d
d
e
v
e
lo
p
m
en
t o
f
novel id
eas
to m
i
tigate the diagnosed
dise
ase.
Un
fortuna
t
ely, the m
e
dic
a
l im
ages (e.g
.
CT scan im
ages, MRI im
ages etc.)
gi
ves i
n
f
o
rm
at
ion em
bed
d
ed i
n
m
a
xim
u
m
resol
u
t
i
o
n
per sl
i
ces of t
h
e data
capture and thereby inc
r
easing the
si
ze of i
m
age f
r
om
gi
gaby
t
e
s
t
o
t
e
raby
t
e
s f
o
r j
u
st
one m
e
di
cal
repo
rt
.
Ho
weve
r,
wi
t
h
t
h
e dat
a
st
o
r
age
bei
n
g
cheapl
y
a
v
ai
l
a
bl
e i
n
fo
rm
s of di
st
ri
but
e
d
se
rve
r
s a
n
d
cl
o
u
d
e
nvi
r
o
nm
ent
,
st
ora
g
e i
s
ne
v
e
r a
pr
o
b
l
e
m
f
o
r t
h
e
m
e
di
cal
im
ages. The
ent
i
r
e
pr
o
b
l
e
m
shoot
s u
p
w
h
e
n
t
h
e
ci
rcum
st
ances cal
l
s
for
t
r
a
n
sm
i
t
t
i
ng t
h
e m
e
di
cal
im
ages. Such circum
stance is whe
n
th
e h
ealth
care i
n
du
stry
u
s
es
te
l
e
m
e
di
ci
ne [2]
.
T
h
e c
onc
ept
o
f
t
e
l
e
m
e
di
ci
ne al
l
o
ws t
h
e
pat
i
e
nt
an
d p
h
y
s
i
c
i
a
n t
o
i
n
t
e
ract
wi
t
h
eac
h ot
he
r usi
ng t
h
e
net
w
o
r
k
res
o
urce
s w
h
i
c
h
al
way
s
has l
i
m
i
t
a
t
i
ons o
f
b
a
nd
wi
dt
h. S
u
c
h
ap
pl
i
cat
i
ons
of t
e
l
e
m
e
di
ci
ne wo
r
k
s i
n
di
f
f
ere
n
t
p
r
i
n
ci
pl
e e.g.
i
)
doct
o
r
woul
d
like to access
the m
e
dical image using
do
wnlink tra
n
s
m
ission, or ii) doct
o
r c
o
uld
like to
per
f
o
r
m
som
e
pr
ocessi
ng
o
n
m
e
di
cal
im
ages t
h
at
resi
des
o
n
di
ffe
re
nt
m
a
chi
n
es al
o
ng
wi
t
h
ot
her
si
m
u
l
t
a
neo
u
s
d
a
ta tran
sfer.
Hen
c
e, su
ch
ap
p
licab
ility o
f
tele
m
e
d
i
cin
e
a
s
well as u
p
c
omin
g
robo
tic su
rg
ery calls for h
i
gh
ly
robu
st co
m
p
ressio
n
algorithm with
b
e
tter respo
n
se rate. Here th
e term resp
on
se will
mean
h
o
w fast the
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Design
o
f
Mu
ltip
lier fo
r Med
i
ca
l Ima
g
e
Comp
ression
Usi
n
g Urd
h
a
v
a
Tirya
k
bh
ya
m Su
tra (S
uma
)
1
141
al
go
ri
t
h
m
can per
f
o
r
m
encod
i
ng
of t
h
e st
re
am
s of m
e
di
cal
dat
a
an
d ge
n
e
rat
e
rec
onst
r
u
c
t
e
d i
m
age wi
t
h
o
u
t
lo
sing
sig
n
i
fican
t in
fo
rm
atio
n
o
f
clin
ical v
a
lu
e. Fr
om
past deca
de, there are
vari
ous al
gorithms and
t
echni
q
u
es i
n
t
r
od
uce
d
by
vari
ous
resea
r
che
r
s fo
r car
ry
i
ng
out
m
e
di
cal
image com
p
ressi
on
, w
h
ere m
a
jori
t
y
o
f
t
h
e st
u
d
i
e
s
hav
e
t
h
ei
r
ow
n a
d
vant
a
g
es a
n
d d
i
sadva
nt
ages
.
Ho
we
ver
,
i
t
i
s
fo
u
nd t
h
at
exi
s
t
i
ng st
u
d
i
e
s a
r
e
m
u
ch
fo
cu
sed
on
size redu
ction
and
less fo
cu
s on co
m
p
u
t
atio
n
a
l
cap
ab
ilities e.g
.
p
r
o
cesso
r speed
,
h
i
gh
reso
l
u
tio
n,
sl
i
c
i
ng t
h
e
c
o
m
ponent
s
o
f
i
m
age et
c.
H
e
nce,
i
n
t
h
i
s
r
e
gar
d
s,
we ca
m
e
across
t
h
e
ev
ol
ut
i
o
n
o
f
Vedi
c
math
e
m
atics a
n
d its po
ten
tial app
licatio
n
t
h
at can
b
e
read
ily app
licab
le in
si
g
n
al processin
g
[3
],[4
]
.
Th
e
pri
n
ci
pl
e o
f
V
e
di
c m
a
t
h
em
ati
c
s i
s
based
on
t
h
e 1
6
p
r
i
n
ci
p
l
e that are ori
g
inally ter
m
ed
as Sutra
[5].
In orde
r
to
u
n
d
e
rstand th
e ap
p
licab
i
lity
o
f
Ved
i
c
m
a
th
e
m
at
ics, we will n
eed
to
un
d
e
rstan
d
th
at co
nv
en
tio
n
a
l
com
p
ressi
o
n
t
echni
que
s d
o
n
’t
foc
u
s
o
n
en
ha
nci
n
g t
h
e
p
r
oc
essor
spee
d
o
w
i
ng t
o
l
ack
of
val
u
a
b
l
e
co
nce
p
t
s
o
f
m
u
l
tip
lier. We fou
n
d
th
at Ved
i
c m
a
th
e
m
atics o
ffers
a sp
ecific su
t
r
a for m
u
ltip
l
i
er called
as
Urd
hva
Tiryak
bh
yam
s
u
tra,
wh
ich
can
b
e
h
i
gh
ly u
s
efu
l
fo
r
d
e
si
g
n
in
g
a
n
e
w m
u
ltip
lier. Th
is
Ved
i
c m
u
lt
ip
lier will b
e
assi
st
i
ng i
s
p
e
rf
orm
i
ng co
m
p
ressi
on wi
t
h
fast
er
spee
d as com
p
are
d
wi
t
h
t
h
e c
o
n
v
e
n
t
i
onal
s
c
hem
e
s.
Th
erefo
r
e,
we
m
a
k
e
u
s
e of th
is
m
u
ltip
lie
r in
d
e
si
g
n
i
n
g
a p
r
ocessor friend
ly an
d
co
st effectiv
e
med
i
cal
com
p
ressi
o
n
al
go
ri
t
h
m
.
The
pri
m
e purp
o
se
of t
h
e p
r
op
ose
d
sy
st
em
i
s
t
o
ens
u
re re
duct
i
on
of com
put
a
t
i
onal
ti
m
e
as well as retain
i
n
g h
i
gh
er con
t
en
ts of th
e im
age
conte
n
ts. Section 2 discus
ses about
t
h
e
re
se
arch
m
e
t
hod
ol
o
g
y
a
nd
resea
r
ch
an
d di
sc
ussi
on
h
a
s bee
n
di
sc
us
ses i
n
Sect
i
o
n
3.
An
d
fi
nal
l
y
Sect
i
on
4 m
a
kes som
e
concl
udi
ng
re
m
a
rks.
1.
1.
Back
ground
In t
h
e rece
nt
t
e
chn
o
l
o
gi
es, t
h
e
si
ze of
ha
rd
di
sks
of c
o
m
put
e
r
an
d
net
w
or
k
sy
st
em
s has i
n
creased
,
but
the use of m
e
dical image continues to
g
r
ow ex
pon
en
tially
at th
e sa
m
e
ti
me require a better im
age an
d better
v
i
su
al qu
ality
o
f
im
ag
e. Th
ese
m
o
tiv
ate th
e
n
eed
o
f
co
m
p
ressio
n
m
e
th
o
d
s. In
th
ese
p
r
o
f
essio
n
a
l techno
log
i
es,
suc
h
as m
e
dical im
ages, large
am
ounts
of da
ta’s are
re
quire
d
each and e
v
e
r
y day. S
o
im
age com
p
ressi
on ha
s
becom
e
s a nec
e
ssary to ens
u
re that th
eir storage
of data as
well as tra
n
sfe
r
i
n
i
n
secu
re m
e
di
um
net
w
o
r
ks
.
The work of Urba
niak
et
al.
[6]
basically focused on t
h
e
im
provem
ent
of t
h
e
di
ag
n
o
st
i
c
im
port
a
nt
im
ages for
diagnostic purpose and to ge
t better co
m
p
ressio
n
. He
re
the auth
or
investigated the image
com
p
ressi
o
n
o
f
art
i
f
act
s res
u
l
t
i
ng fr
om
JPEG 2
0
00 a
n
d
JPEG. T
h
e
perform
a
nce parameters selected for t
h
e
stu
d
y
are PSNR, qu
ality o
f
i
m
ag
e, Stru
ctural Si
m
ilarit
y
Qu
ality Measu
r
e (SSIM), an
d co
m
p
ression
rat
i
o
.
Th
is
resu
lt ind
i
cates th
at th
e co
m
p
ression
ratio
based
on
ROC
g
i
v
e
s
b
e
tter v
i
su
al qu
ality as
well as SSIM
g
i
v
e
s
bet
t
e
r pe
rf
orm
a
nces. Sai
n
i
et
al
. [7]
have
perf
o
r
m
e
d an expe
ri
m
e
nt
and
gi
ves a co
m
p
ari
s
on i
n
i
m
age
co
m
p
ression
lik
e HAAR
wav
e
let, Bi-orthog
on
al
W
a
v
e
lets, Dau
b
e
ch
ies
W
a
v
e
lets and Co
iflets wavelets.
These
algorithm
s
are performed and te
sting
has
done for differe
n
t m
e
dical im
ages to
reduce
the
im
a
g
e size
and l
e
ss
st
o
r
ag
e req
u
i
r
em
ent
s
and
i
t
i
s
rel
e
v
a
nt
t
o
di
ag
nost
i
cal
l
y
im
port
a
nt
regi
o
n
s.
The
out
c
o
m
e
of t
h
e
st
udy
was
foun
d wit
h
b
e
tter im
ag
e q
u
a
lity with an effective co
mp
ressi
on
ratio.
Nassi
ri
et
al
.
[
8
]
,
d
o
n
e a
n
e
x
peri
m
e
nt
on m
e
di
cal
im
age com
p
ression for dia
g
nostically im
portant
regi
ons
usi
n
g
Di
scret
e
Wave
l
e
t
Trans
f
o
r
m
s
. To
m
i
ni
mize th
e to
tal d
e
grad
atio
n and
g
e
t
a b
e
tter co
m
p
ression
rat
i
o
of
i
m
ages, t
h
e
D
W
T
c
o
m
p
ressi
o
n
i
n
cl
udes
ha
r
d
a
n
d s
o
ft
t
h
re
sh
ol
di
n
g
dec
o
m
posi
t
i
on m
e
t
hods
. T
h
e
stu
d
y
w
a
s tested
w
ith
g
r
ay
scale th
o
r
acic cag
e im
ag
e
o
f
size 512x
512
. Th
e st
u
d
y
o
f
a
v
o
l
u
m
etr
i
c
di
ag
no
st
i
cal
l
y
im
port
a
nt
regi
on
o
f
m
e
di
cal im
ages usi
n
g
3-
D l
i
s
t
l
e
ss
em
bed
bl
oc
k
al
go
ri
t
h
m
has bee
n
p
r
esen
ted
b
y
th
e au
thor Sudh
a et al. [9
]. Here th
e au
tho
r
m
o
d
i
fied
this alg
o
r
ith
m
u
s
in
g
Set Partitio
n
e
d
Em
bedded B
l
o
c
k C
o
de
r (
SPE
C
K
) m
e
t
hods
t
o
get
hi
g
h
i
n
t
e
r ba
n
d
c
o
r
r
el
at
i
on.
He
re t
h
e
M
R
I im
ages ar
e use
d
fo
r t
e
st
i
ng t
h
e
pu
r
poses
. T
h
i
s
al
go
ri
t
h
m
im
pr
ove
s t
h
e c
o
m
p
ressi
o
n
rat
i
o
a
nd a
s
wel
l
as t
h
e i
m
prove t
h
e
vi
sual
p
e
rcep
tion
o
f
i
m
ag
es qu
ality. Joh
n
et al. [10
]
h
a
v
e
p
r
esented
a
h
i
gh
secu
rity, h
i
g
h
tran
sm
issio
n
syste
m
fo
r
tran
sm
it
tin
g
med
i
cally, d
i
agno
stically i
m
p
o
r
tan
t
repo
rts
fo
r
m
i
li
t
a
ry
and v
e
ry
hi
g
h
sec
u
r
e
envi
ro
nm
ent
dat
a
’s
usi
n
g
har
d
war
e
i
m
pl
em
ent
a
t
i
ons
m
e
t
hods.
The a
u
t
h
o
r
s
h
a
ve ca
rri
e
d
ou
t
encry
p
t
i
o
n
of
an
i
m
age on
FPG
A
[Vi
r
t
e
x 5
XC
5V
LX
11
0T]
a
nd
ha
ve al
so
im
pl
em
ent
e
d a 16
-st
a
ge
pi
pel
i
n
e m
o
d
u
l
e for
achi
e
vi
ng a
n
en
cry
p
tio
n
s
rate o
f
35
.5
Gbit/s with
2
1
40 co
nfigu
r
ab
le lo
g
i
c b
l
o
c
k
s
. Tiwari et al. [11
]
h
a
v
e
p
r
esen
ted
m
u
l
tip
le ap
proach
es so
lv
e a
prob
lem
s
o
f
storin
g
o
r
tran
sm
it
tin
g
larg
e
nu
mb
er
of m
e
d
i
cal d
a
ta or im
ag
es u
s
ing
di
ffe
re
nt
al
go
r
i
t
h
m
s
l
i
k
e DC
T, D
W
T a
n
d C
o
m
p
ressi
v
e
Sensi
ng t
e
c
hni
que
s. I
n
t
h
i
s
pape
r t
h
e
aut
h
o
r
per
f
o
r
m
e
d a com
p
ressi
ng an
d reco
nst
r
uct
i
o
n t
echni
q
u
e f
o
r
MRI im
age, CT im
age and Ultrasound im
age and
t
h
e aut
h
or
gi
v
e
n com
p
ari
s
o
n
s
of al
l
t
h
e t
h
r
ee di
ffe
rent
m
e
di
cal
im
ages by
usi
n
g di
ffe
r
e
nt
al
go
ri
t
h
m
s
. Here,
th
e p
e
rform
a
n
ce p
a
ram
e
ters tak
e
n
are
PSNR, MSE, co
m
p
ression
ratio
, qu
ality o
f
im
ag
e alo
n
g
with sto
r
ag
e
capaci
t
y
. The
wo
rk
by
G
u
pt
a et
al
. [12]
ha
ve p
r
ese
n
t
s
a m
e
t
hod
of l
o
ss
l
e
ss im
age com
p
ressi
on f
o
r
m
e
di
cal
im
ages using
pre
d
ictive coding techniques
as well as
i
n
t
e
ger
wavel
e
t
t
r
a
n
sf
orm
based
on m
i
nim
u
m
ent
r
opy
techniques
. T
h
is pa
per
prese
n
ts a
hybrid image com
p
re
s
s
ion a technique that
com
b
ines a
n
i
n
tege
r wa
velet
and
p
r
edi
c
t
i
v
e
al
go
ri
t
h
m
s
t
o
enha
nce t
h
e
per
f
o
r
m
a
n
ce of lossless c
o
m
p
ression. T
h
e evaluation
of this
technique
was
done
ove
r
greyscale
m
e
d
i
cal i
m
ag
e essen
tially u
s
in
g tran
sfo
r
m
a
tio
n
tech
n
i
qu
e along
with
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
11
4
0
– 11
51
1
142
pre
d
i
c
t
i
v
e-
base
d ap
p
r
oac
h
.
T
h
e p
r
op
ose
d
m
e
di
cal
im
age com
p
ressi
o
n
t
echni
q
u
es
o
f
f
e
r a hi
ghe
r l
e
vel
o
f
co
m
p
ression
ratio
and
m
i
n
i
m
u
m
en
tro
p
y
wh
en
it is ap
p
lied to
m
a
n
y
sev
e
ral
lev
e
ls
o
f
test i
m
ag
es.
The pa
pe
r p
r
e
s
ent
e
d
by
K
u
nchi
gi
et
al
. [13]
ha
ve
pres
ent
e
d a st
u
d
y
of a
Vedi
c
m
a
t
h
em
at
i
c
s
app
r
oach a
p
pl
y
i
ng f
o
r t
h
e d
e
si
gn
of
2-
D
DC
T ap
pl
i
cat
i
ons i
n
m
e
di
cal im
age pr
oces
si
ng
. He
re, t
h
e
aut
h
o
r
u
s
es an
Urd
hva Tiryagb
h
y
am
Ved
i
c su
tra
for th
e m
u
ltip
licatio
n
techn
i
qu
es in DCT. Th
is p
a
p
e
r also
stu
d
i
ed
di
ffe
re
nt
Vedi
c
sut
r
as use
d
f
o
r m
u
l
t
i
p
l
i
cat
i
o
n t
echni
que
s l
i
k
e, Ni
khi
l
a
m
sut
r
a,
Ur
dh
va
-T
i
r
y
a
gb
hy
a sut
r
a. The
resul
t
s
obt
ai
ne
d i
n
3
di
f
f
ere
n
t
cases, l
i
k
e si
n
g
l
e
di
gi
t
Vedi
c
sut
r
a
,
t
w
o
di
gi
t
Vedi
c s
u
t
r
a a
n
d
fi
nal
l
y
t
h
r
e
e di
gi
t
Vedi
c
sut
r
a
.
A
t
fi
nal
l
y
, t
h
e t
h
ree
di
gi
t
Ve
d
i
c sut
r
a
gi
ve
s
best
a
n
d
bet
t
e
r
res
u
l
t
am
ong
t
h
e t
h
ree. i
.
e
.,
hi
g
h
er
i
m
ag
e qu
ality as well as b
e
tt
er im
ag
e co
m
p
ression
ratio
. Sarala et al.
[14] h
a
v
e
presen
ted
a p
a
p
e
r on
i
m
ag
e
co
m
p
ression
u
s
ing
m
u
lti-le
v
e
l 2-D
DWT as well as Ved
i
c m
a
th
ematic
meth
o
d
s. A trad
itio
nal 2
-
D
com
p
ression al
gorithm
cons
umes
m
o
re power as
well as
m
o
re
m
e
m
o
ry
fo
r im
age com
p
ression
. B
u
t by
usin
g
the Ve
dic m
a
them
atics algorith
m
used
for im
age co
m
p
r
e
ssi
on
an
d re
con
s
t
r
uct
i
o
n g
i
ves
a bet
t
e
r
i
m
age
com
p
ression ratio as well as better vis
u
al quality of im
age. T
h
is m
e
thod is ve
ry use
f
ul for m
e
dical im
ages
.
Ved
i
c m
u
ltip
li
er u
s
es h
a
lf ad
d
e
r and
fu
ll ad
d
e
r. Th
is
meth
od
o
f
4
-
level 2
D
DWT tech
n
i
q
u
e
s attem
p
ts
to
i
n
crease t
h
e i
m
age res
o
l
u
t
i
o
n.
The sim
u
l
a
t
i
ons are d
one
usi
ng M
a
t
l
a
b 2
0
0
8
a ver
s
i
o
n as wel
l
as M
odel
S
im
6.3
versi
on a
n
d i
t
i
s
im
pl
em
ent
e
d usi
n
g
Xi
l
i
nx a
nd
FP
GA
Spa
r
t
a
n 3
ki
t
.
Least
but
not
l
a
st
, a
not
her a
p
pr
oac
h
by
So
wja
n
y
a
et
a
l
. [1
5]
, i
m
pl
em
ent
e
d an a
p
pr
oac
h
o
f
2-
D
DC
T ar
chi
t
e
c
t
ure
usi
n
g R
e
versi
b
l
e
Ve
di
c
Ad
de
r
approach. It is
use
d
to
re
duce the size
of the im
ag
e as well as in
both 1-D and
2-D im
age proc
essing
appl
i
cat
i
o
ns.
It
can al
so
be
use
d
t
o
cal
cul
a
t
e
t
h
e 1-
D a
n
d 2
-
D
DC
T
us
i
ng m
i
nim
u
m
num
ber
of
har
d
wa
re
com
pone
nts.
Here
, the aut
h
or
designe
d
a novel m
e
thod
by using
Xilinx IS
E 12.3i,
Verilog
HDL tools. It
con
s
um
es l
e
ss
po
we
r co
nsum
pt
i
on as
wel
l
as l
e
ss
m
e
m
o
ry
due t
o
repl
ace
m
e
nt
of ad
der
wi
t
h
re
versi
b
l
e
Vedi
c
math
e
m
atics
ap
pro
ach
es. Th
is no
v
e
l algo
rith
m
i
m
proves the overa
ll syste
m
perform
ance in im
age
processi
ng. He
nce, although there
are vari
ous categories
of
com
p
ression a
l
gorithm
s
witnessed m
o
st recently
in
m
e
d
i
cal i
m
ag
es, bu
t v
e
ry few of th
em
are foun
d
to
ad
dress th
e com
p
u
t
atio
n
a
l co
m
p
lex
ities. Th
erefo
r
e,
t
h
ere i
s
a
ne
ed
of
a st
u
d
y
t
h
at
coul
d
pot
en
tially ad
dress su
ch co
m
p
u
t
atio
n
a
l
issu
es.
1.
2.
The Problem
Usually, t
h
e si
ze of t
h
e m
e
dical im
ages is too la
r
g
e t
o
st
ore.
Owi
ng
t
o
t
h
e a
dva
nce
m
ent
i
n
t
h
e
medical studie
s
, the
r
e a
r
e increasing
de
pendencies
ass
o
ci
ated wit
h
a
n
e
fficient st
ora
g
e and c
o
st e
f
fective
transm
ission of the m
e
dical images.
A m
e
dical im
age from Sky Scan
x-ray
de
vi
ce [
1
6
]
gene
rat
e
s i
m
ages
o
f
si
ze 80
0
0
x
8
0
00
pi
xel
s
, w
h
i
c
h i
n
n
u
t
s
hel
l
l
eads t
o
ge
nerat
i
on
o
f
6
4
M
B
o
f
i
m
age dat
a
ju
st
fo
r o
n
e sl
i
ce
of t
h
e
CT scan im
ag
e. T
h
ere
f
ore,
other s
o
phistica
t
ed m
e
dical
im
agi
n
g
devi
ces
l
i
k
e M
R
I ca
n
gene
rat
e
ar
o
u
n
d
1.
19
GB of im
ag
e d
a
ta,
wh
ich
are no
t on
ly d
i
fficu
lt to
st
ore
but
hi
g
h
l
y
cha
l
l
e
ngi
n
g
t
o
pe
rf
orm
t
r
ansm
i
s
si
o
n
.
Hence
,
suc
h
p
r
o
b
l
e
m
call
s
for
per
f
o
r
m
i
ng com
p
ressi
o
n
t
echni
que
. At
pr
esent
,
va
ri
o
u
s
com
put
i
ng t
o
o
l
s e.g.
C
U
D
A
[1
7]
, Qt
-T
hrea
de
d
[
18]
, O
p
enC
L
[1
9]
et
c
are
i
n
use in the
proces
sing s
u
ch m
a
ssive size of t
h
e
medical im
ag
es. To s
o
m
e
extent, the
discussion
of t
h
e problem
a
ssociated
with the m
e
dical
im
age
com
p
ressi
o
n
was d
o
n
e i
n
o
u
r
pri
o
r
wo
rk
[2
0]
. The
p
r
o
b
l
e
m
s
t
h
at
have bee
n
i
d
e
n
t
i
f
i
e
d f
o
r t
h
e p
r
op
os
e
d
syste
m
are as follows:
Less Fo
cus on Co
mputatio
na
l Capability
:
The e
x
i
s
t
i
ng t
ech
ni
q
u
e
m
a
i
n
l
y
focuse
s on pe
rf
o
r
m
i
ng
co
m
p
r
e
ssion
by r
e
du
cing
t
h
e
sizes of
m
e
di
cal
im
ages o
f
u
n
i
f
orm
di
m
e
nsi
ons
.
We
strongly feel that focus
o
n
m
e
d
i
cal i
m
ag
e co
m
p
ressi
o
n
sh
ou
ld
b
e
also
ex
tend
ed
toward
s en
suring th
e co
m
p
u
t
ati
o
n
a
l cap
ab
ility o
f
the syste
m
from the hardwa
re viewpoi
nt. Hence, the
r
e is
a
need
of the sy
ste
m
that
can provide a
n
efficient
an
d h
a
rd
w
a
r
e
fr
iend
ly stan
dard
s t
o
p
e
rform
c
o
m
p
ression of medical
im
ages.
Less Empha
s
i
s
o
n
Multipliers
: Mu
ltip
liers p
l
ays a critical ro
le i
n
d
i
gital i
m
ag
e processin
g
esp
ecially
whi
l
e
pe
rf
orm
i
ng com
p
ressi
on
. Ef
fi
ci
ent
desi
g
n
o
f
m
u
lt
i
p
l
i
e
r whi
l
e
p
e
rf
orm
i
ng co
m
p
ressi
on al
w
a
y
s
increases the s
p
eed
of
proces
sor,
wh
ich
is ex
trem
ely
i
m
p
o
rtan
t in
tele
med
i
cin
e
.
Howev
e
r, th
ere is less
work
fo
cu
sed
u
s
ing
conv
en
tio
n
a
l techn
i
qu
e for adop
tio
n
o
f
m
u
ltip
liers in
m
e
d
i
cal
i
m
ag
e co
m
p
ressi
o
n
.
Ev
en
th
e
u
s
ag
es o
f
m
u
ltip
liers
b
y
u
s
i
n
g Ved
i
c m
a
th
e
m
atics
were
on
ly tested
on
VLSI
o
r
FPGA
p
l
atform
s
with
narrowe
d
expe
rim
e
ntal studies. He
nce,
there is a
need
of
an
ef
fect
i
v
e
desi
g
n
of
m
u
l
t
i
pl
i
e
r
usi
n
g c
o
s
t
effect
i
v
e c
o
m
put
at
i
o
nal
ap
p
r
oac
h
t
o
e
n
s
u
re p
r
oce
sso
r
per
f
o
r
m
a
nce whi
l
e
ha
n
d
l
i
n
g com
p
ressi
on
o
f
sophisticated medical
im
ages
f
o
r
car
ry
ing
o
u
t com
p
ressi
on
.
Less Emphasi
s on data red
und
ancies
: It is fo
und
th
at maj
o
rity o
f
the ex
istin
g
techn
i
qu
es on
m
e
d
i
cal
im
age com
p
ression ignores c
onsi
d
eri
n
g elimin
atio
n
of
red
und
an
t
d
a
ta.
Alth
oug
h m
a
j
o
rity o
f
t
h
e ex
isting
t
echni
q
u
es
us
es l
o
ssl
ess a
p
pr
oac
h
f
o
r
pe
rf
orm
i
ng com
p
ressi
o
n
,
but
i
t
seem
s t
o
i
g
n
o
re
t
h
e
dat
a
redun
d
a
n
c
ies t
h
at resu
lts in eith
er less PSNR
v
a
lu
es
o
r
no
n-su
ppo
rtab
ility i
n
co
lored im
ag
e co
m
p
ression
.
The above problem
s
are the
prim
e
id
en
tificatio
n
factors of th
e p
r
obl
em
s fou
n
d
aft
e
r re
vi
ewi
n
g t
h
e
ex
istin
g
system
.
Hen
ce, the p
r
ob
lem
sta
t
e
m
en
t
of the propose
d study can be stated as – “
It is a
com
p
ut
at
i
o
nal
l
y
ch
al
l
e
ngi
ng
t
a
sk t
o
desi
gn
a t
e
c
hni
que
t
hat
e
n
s
u
res
p
r
ocess
o
r f
r
i
e
n
d
l
y
as
w
e
l
l
as
cos
t
ef
f
ect
i
ve compr
e
ssi
on
sc
heme
on
al
l
s
o
rt
s
of
medi
c
a
l
i
m
age
s.
”.
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I
J
ECE
I
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8-8
7
0
8
Design
o
f
Mu
ltip
lier fo
r Med
i
ca
l Ima
g
e
Comp
ression
Usi
n
g Urd
h
a
v
a
Tirya
k
bh
ya
m Su
tra (S
uma
)
1
143
1.
3.
The Proposed So
lut
i
on
The p
r
i
m
e goal
of t
h
e
pr
op
ose
d
sy
st
em
i
s
t
o
e
nha
nce the
pe
rform
a
nce of
medical image com
p
ression
b
y
ap
p
l
ying
an effectiv
e m
u
lti
p
lier d
e
si
g
n
mo
tiv
ated
fro
m
Ved
i
c m
a
th
e
m
atics. Th
e d
e
si
g
n
o
f
th
e m
u
lti
p
lier is
done consideri
ng the algorit
h
m
ca
lled as
U
r
dha
va
Tirya
k
bh
ya
m
su
tra
t
h
at
i
s
respo
n
si
bl
e f
o
r pe
rf
orm
i
ng
v
e
rtical and
cro
s
swise m
u
ltip
licatio
n
.
Fi
gu
re
1.
Sc
he
m
a
of
Pr
op
ose
d
M
e
di
cal
Im
age C
o
m
p
ressi
o
n
Th
e
d
e
sign
of th
e
p
r
op
o
s
ed alg
o
rith
m
is b
a
sed
o
n
a fact th
at add
ition
o
f
im
ag
e el
e
m
en
ts b
y
co
n
c
urren
t
tech
n
i
q
u
e
s will lead
to
p
a
rtial p
r
o
d
u
c
ts an
d th
is cap
ab
ility can
b
e
furth
e
r streng
th
ened
by
in
corpo
r
ating
U
r
dha
va Tirya
k
bh
ya
m su
tra
to pro
m
o
t
e
p
a
rallelis
m
.
Th
e system allo
ws sim
u
l
t
an
eou
s
co
m
p
u
t
atio
n
of su
mm
a
tio
n
s
of th
e elem
en
ts
b
e
ing
g
e
n
e
rated
b
y
th
e
p
a
rtial
m
u
ltip
licatio
n
.
Hen
ce, su
ch
fo
rm
s
of m
u
ltiplier
do
not de
pe
nd on proce
ssor and its freque
ncy of cloc
k. In othe
r langua
ge, the
propos
e
d
ap
pro
ach
of Ved
i
c m
a
th
e
m
a
t
ics allo
ws th
e
syste
m
to
ex
ecu
te th
e
Ved
i
c
m
u
ltip
lier with
ou
t an
y si
g
n
i
ficant
d
e
p
e
nd
en
cy on
f
r
e
qu
en
cy of
clo
c
k
.
He
nce, the contribution
o
f
th
e
p
r
op
osed
system
can
be br
ief
e
d as,
To
read the m
e
dical im
age and is a
p
plicable
on both graysc
ale as well as
c
o
lored im
ages.
To
app
l
y m
u
lt
i
p
le b
l
o
c
k-w
i
se op
er
ation
f
o
r
th
e g
i
v
e
n im
ag
e.
W
e
test it usin
g b
l
o
c
k size of
8
x
8
,
16x16,
an
d 32x
32
.
To apply the
U
r
dha
va
Tiryakb
h
y
am
su
tra
on eac
h t
e
st
bl
ock
fo
r pe
rf
o
r
m
i
ng com
p
res
s
i
on
of t
h
e m
e
di
cal
im
ages.
To a
d
d
r
ess t
h
e
red
u
nda
ncy
p
r
o
b
l
e
m
s
whi
l
e
per
f
o
rm
i
ng l
a
rge m
e
di
cal
i
m
age com
p
res
s
i
on
by
usi
n
g
ru
n-
l
e
ngt
h
co
di
ng
.
To
g
e
n
e
rate the en
cod
e
d
im
a
g
e and
ch
eck
for its q
u
a
lity in
th
e resp
ectiv
e recon
s
tru
c
t
e
d
im
ag
e u
s
in
g
PSNR a
n
d MS
E.
To
ch
eck
th
e
co
nsisten
c
y of th
e p
r
op
osed tech
n
i
qu
e
o
n
m
u
ltip
le typ
e
o
f
m
e
d
i
cal i
m
ag
es o
n
stand
a
rd
d
a
tasets.
2.
R
E
SEARC
H M
ETHOD
The im
pl
em
entat
i
on of t
h
e pro
posed sy
st
em
is carri
ed out
us
i
ng M
a
t
l
a
b using n
o
rm
al
32 bi
t
m
achi
n
e.
The pr
op
osed
sy
st
em
consi
d
ers a
m
e
di
cal
im
age as an i
n
put
and
perf
or
m
s
co
m
p
ressi
o
n
based
on
Ur
dh
av
a
Ti
ryakbhya
m
a
ppr
oach,
w
h
i
c
h pe
rfo
rm
s vert
i
c
al
and cr
oss
over
m
u
lt
i
p
li
cat
i
on i
n
Ve
di
c m
a
t
h
em
ati
c
s. In o
r
der
t
o
cl
osel
y
observe t
h
e
pr
ocessi
ng t
i
m
e
of t
h
e com
p
ressi
on al
gori
t
h
m
s
bei
n
g ap
pl
i
e
d, we
choose
t
o
carr
y
ou
t
t
h
i
s
experim
e
n
t
on num
erous
m
achi
n
es with
m
u
l
t
i
p
l
e
processor of core
-
i
5, dual
core, AM
D et
c. In order t
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
11
4
0
– 11
51
1
144
ease off the c
o
m
puta
tional com
p
lexities ass
o
ciated with
the processing of larger
size
of m
e
dical images,
we
consider converting the input im
age (I
ori
g
) to grayscale. Our
Algorithm
-
1
will show the basic step for
perf
orm
i
ng t
h
i
s
con
v
ersi
on t
h
a
t
result in grayscale image (I
gra
y
).
Algorithm-1:
Reading Input Image
In
put
: Inp
u
t Ima
g
e (I
ori
g
)
Output
: Gray
s
c
ale Im
age (I
gr
a
y
)
Star
t
1. Read I
orig
2. Res
i
ze I
orig
256
x
256.
3. Convert the I
orig
to Gray
s
cale
(I
gra
y
).
End
After obtaining the grayscale im
age (I
gra
y
), t
h
e next
st
ep
i
s
t
o
perfo
rm
the com
p
ressi
on t
echni
que
usi
ng Ve
di
c com
p
ressi
on al
go
ri
t
h
m
t
h
at
i
s
highl
i
ght
ed i
n
A
l
gori
t
h
m
-
2. The al
gori
t
h
m
t
a
kes t
h
e i
nput
o
f
I
gra
y
and t
h
en
perf
o
r
m
s
t
h
e di
st
i
n
ct
bl
ock pr
ocess
i
ng of ei
t
h
er
of
t
h
e si
ze 8
x
8, 16
x
16
, and
32
x
32. T
h
e sizes of the
blocks are fed to the syste
m
u
s
ing the user interface
and hence are of string type
. According to the Algorith
m
-
2, t
h
e si
ze of
t
h
e consi
d
ered bl
ock i
s
i
n
creased t
o
dou
bl
e preci
si
on and st
ored i
n
m
a
t
r
ix R.
The syste
m
will
also
increase the precision of I
gra
y
t
o
do
ubl
e f
o
r
bet
t
e
r eval
uat
i
on. The
next
phase o
f
i
m
plem
ent
a
t
i
on wi
l
l
be t
o
execut
e
t
h
e o
p
e
rat
i
on of
Ve
di
c com
p
ressi
on
by
appl
y
i
ng
Ve
dic m
u
ltiplier. For t
h
is purpos
e, the size of the I
gra
y
i
s
eval
uat
e
d and i
s
m
a
pped i
n
a separat
e
m
a
t
r
i
x
of r
o
w and colum
n
ele
m
ents. Th
e algorith
m
also considers
certain extra
z
e
ro
ele
m
ents
to the I
gra
y
m
a
tri
x
and t
h
en i
t
perform
s co
m
p
ressi
on. In orde
r t
o
carry
out
a
com
p
ressi
on, the sy
st
em
designs a new
fu
n
c
t
i
on for Ve
di
c
m
u
lt
i
p
l
i
er (as show
n i
n
Li
ne-5
of Al
g
o
ri
t
h
m
-
2),
where
N
i
s
s
i
z
e
o
f
X
,
T
is tr
an
sp
o
s
itio
n
m
a
trix
,
p
is a
ma
trix
with
ele
m
en
t 1
-
(
N
-1
) an
d
q
is a
m
a
tri
x
with
ele
m
ent 0 to (
N
-1). Fi
nal
l
y
, the al
gori
t
h
m
appl
i
e
s t
h
e Vedi
c M
u
l
t
i
p
l
i
e
r on t
h
e squared bl
ocks o
f
t
h
e im
age for a
size R. Th
e o
u
t
co
me o
f
th
is alg
o
r
ith
m
is a co
m
p
ressed
v
e
rsio
n
o
f
an
i
m
ag
e u
s
in
g
Ved
i
c Mu
ltip
lier.
Algorithm-2:
V
e
dic Compressi
on Algorithm (
VCA
)
In
put
: Gra
y
s
cal
e Im
age (I
gra
y
)
Output
: Co
mpre
ssed I
m
age using
Vedic approach
Star
t
1. Initiali
ze the
size of the
block (
8
x
8 ||
16
x
16 ||
32
x
32)
2.
R
Double th
e precision of block size.
3.
X
Double th
e precision of I
gr
a
y
.
4. Evaluate
the s
i
ze of X
5. Appl
y
functio
n of Vedic m
u
ltiplier
)
2
/
)).
1
.(
2
(
cos(
,
2
(
N
pi
q
p
N
V
T
mult
6. Apply
compression
T
comp
X
V
.
.
7. Perform block
wise Vedic Compression
]
,
[
,
)
(
R
R
X
block
V
comp
V
comp
End
The out
com
e
of t
h
e Al
gori
t
h
m
-
2
i
s
subject
ed t
o
t
h
e quan
t
i
z
at
i
on t
echnique. H
o
we
ver,
we prefer t
o
perf
orm
t
h
e quant
i
zati
on i
n
b
i
t
di
screte st
ag
e co
m
p
ared t
o
com
m
on st
yl
e of ap
pl
y
i
ng q
u
ant
i
zat
i
on i
n
im
age
processi
n
g
. Al
gori
t
h
m
-
3 hi
gh
l
i
ght
s t
h
e st
ep
s bei
ng used
f
o
r carry
i
ng o
u
t
quant
i
zat
i
on
over t
h
e com
p
ressed
im
age (from
Algorithm
-
2).
We consider a th
reshold
value
T
H
=5
fo
r an
alysis p
u
r
p
o
s
e. Th
e in
itial s
t
ep
o
f
th
is
alg
o
r
ith
m
ma
in
ly ev
alu
a
tes th
e size
of the c
o
m
p
ressed image i.e. V
comp
(b
lo
ck
) and
th
en
it
map
s
th
e size o
f
it to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Design
o
f
Mu
ltip
lier fo
r Med
i
ca
l Ima
g
e
Comp
ression
Usi
n
g Urd
h
a
v
a
Tirya
k
bh
ya
m Su
tra (S
uma
)
1
145
a
m
a
trix
with
P (row) and
Q(co
lu
m
n
). Fo
r all
th
e ele
m
en
ts
o
f
th
is
m
a
trix
co
n
s
id
erin
g
th
e
max
i
m
u
m
li
mi
ts o
f
P
an
d
Q ele
m
en
ts, th
e p
r
op
o
s
ed
syste
m
a
tte
m
p
ts to
co
m
p
are the absolute value of c
o
m
p
ressed ima
g
e i.e.
V
co
m
p
(b
lo
ck
) with
th
e
th
resh
o
l
d
T
H
. Under a
n
y circu
m
s
t
ances, if the abso
lute value of com
p
ressed
image i.e.
V
co
m
p
(b
lo
ck
) is fo
un
d
to
b
e
with
in
th
e li
mits o
f
th
resh
o
l
d
T
H
, than the syste
m
ass
i
gn zero value t
o
the
com
p
ressed im
age and i
n
creases i
t
s
count
k
t
o
read ot
her bl
oc
k el
em
ent
s
.
The syste
m
also initialize
the
quant
i
zat
i
on v
a
l
u
e t
o
be 8 and eval
uat
e
s m
i
nim
u
m
and
m
a
xim
u
m
argum
ent
s
of com
p
ressed for m
a
ki
ng i
t
appl
i
cabl
e
for e
quat
i
on s
h
o
w
n
i
n
Li
ne-15
of
Al
gori
t
h
m
-
3. The o
u
t
c
om
e of t
h
i
s
al
gori
t
h
m
is a qua
nt
i
zed i
m
age.
Algorithm-3: Q
u
anti
zatio
n
of Compresse
d Ima
g
e
In
put
: Thresh
old (T
H
), Quantizat
ion value (Q), V
com
p
(block)
Output
: Quantized Im
age of V
com
p
(block)
Star
t
1. Initiali
ze the
t
h
reshold to rem
o
ve sm
aller values (T
H
=5)
2. M
a
p the s
i
ze o
f
V
com
p
(block)
P(row), Q(col)
3.
FOR
i=1 to
P
4.
FOR
j=1 to
Q
5.
IF
V
com
p
(bloc
k
)<T
H
6.
V
com
p
(block)=0
7.
k
=
k
+1
8.
END
9.
END
10.
END
11.
l
=100.
k
/(P*Q)
12. Initializ
e the
quantized value
Q=8.
13.
α
1
= arg
min
[V
com
p
(block)
]
14.
α
2
=
arg
ma
x
[V
com
p
(block)
]
15. Apply
Quan
tization using
|
)
(
).
2
1
(
|
1
2
1
)
(
block
V
Q
comp
Q
block
V
comp
End
Th
e ou
tco
m
e o
f
Algo
rith
m
-
3
i.e.
qua
ntized image is now s
u
bjected
t
o
Hu
ffm
an C
odi
ng.
The
reason
behi
nd c
h
o
o
si
ng di
ct
i
onary
based enco
d
i
ng m
echani
s
m
e.g. Huffm
an codi
n
g
i
s
t
h
at
it
can
perf
or
m
com
p
ressi
on of
al
l
cat
egori
e
s of
dat
a
. The
H
u
ffm
an codi
n
g
can be
ter
m
ed as an e
n
tropy-based approac
h
that is
hi
ghl
y
depen
d
e
nt
on eval
uat
i
on
of t
h
e f
r
equ
e
nci
e
s of array
sym
bol
s. The pot
ent
i
a
l
of t
h
i
s
codi
ng sche
m
e
i
s
preci
se i
d
ent
i
f
i
cati
on of col
o
rs i
n
m
e
di
cal im
ages wit
hout
any
si
gni
fi
cant
l
o
ss of v
a
l
u
abl
e
i
n
form
at
i
on.
M
o
reove
r, at
present
,
t
h
e
m
e
di
cal
im
age processi
n
g
has
al
ready
adopt
ed such di
ct
i
onary
based en
codi
ng
schem
e
i
n
i
t
s
l
o
ssl
ess JPEG
com
p
ressi
on whi
c
h i
s
freq
u
e
nt
l
y
adopt
ed
i
n
m
e
dical
imagi
ng i
n
t
h
e f
o
rm
of
DICOM stan
dard
s.
Howev
e
r, we will ch
oo
se to
i
m
p
l
e
m
en
t th
e Hu
ffm
a
n
Co
d
i
n
g
i
n
a p
a
ttern
d
i
fferen
t
fro
m
conve
nt
i
onal
p
r
act
i
ces
as shown i
n
Al
g
o
ri
t
h
m
-
5. In t
h
i
s
case, we choose
t
o
i
n
i
t
i
a
li
ze
t
h
e quant
i
zat
i
on val
u
e
Q=8 and pe
rf
o
r
m
s
zi
gzag scanni
n
g
of t
h
e q
u
ant
i
zed im
age based on t
h
e concept
of
Ur
d
hava Ti
ryakb
h
y
am
in
Vedi
c m
a
t
h
em
at
i
c
s. The al
go
ri
t
h
m
chooses
t
o
per
f
orm
t
h
e zi
gzag scanni
n
g
f
o
r
al
l
t
h
e cases of
sq
uared
bl
ock
sizes
R
of
8
x
8 or 16
x
16 or
3
2
x
32.
Fi
nal
l
y
, t
h
e scanned
rep
o
r
t
s
of t
h
e
bl
ock
s
are m
a
pped i
n
a m
a
t
r
i
x
(N
M
)
wi
t
h
a specific row (M
1
) and c
o
lum
n
size (M
2
). A ne
w m
a
trix (XZ
v
) is f
o
r
m
u
l
at
ed with reshaped
structure of
t
r
ansposi
t
i
on o
f
zi
gzag scanned im
age
el
ement
s
and NM
. The next
part
of t
h
e im
p
l
em
ent
a
ti
on of Al
g
o
r
i
t
h
m
-
5
will be
to perform
run length encoding m
e
chanism
that
takes the input of XZv. The m
echanis
m
to perfor
m
Ru
n
Leng
th
Co
d
i
ng
on
n
e
w
matr
ix
(XZv) is sh
own
in
Alg
o
r
ith
m
-
4
th
at g
e
n
e
rates a ma
trix
Xrle to
sto
r
e th
e
encode
d val
u
es
. Ho
wever
,
i
t
sho
u
l
d
be
not
ed
t
h
at
Al
gori
t
h
m
-
4 i
s
em
bedded wi
t
h
Al
go
ri
t
h
m
-
5 i
n
Li
ne-8.
Algor
ithm-4:
Algor
ithm for
Ru
n Le
ngt
h
Co
din
g
In
put
: Ne
w matr
ix (XZv) from St
ep-3-7 in Algorithm-5.
Output
: Encoded Values of run length (Xrle)
Star
t
1. L
size of m
a
trix XZv
2.
IF
i <
2.L
3. comp=1
4.
FOR
j=j
to L
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I
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08
IJEC
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o
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.
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No
. 3,
J
u
ne 2
0
1
6
:
11
4
0
– 11
51
1
146
5.
IF
j==L
6.
Break
()
7.
END
8.
IF
XZV(j) = = XZV(j+1)
9. comp=comp+
1
10.
ELSE
11.
Break
()
12.
END
13.
END
14. Assign co
mp
Xrle(k+1)
15. Assign
XZv(
j)
Xrle(k)
16.
IF
j==l
& X
Z
v(j-1)= = XZv(j)
17.
Break
()
18. i=i+1, j=j+1
,
k=k+2
19.
IF
j= =
L
20.
IF
|
L
, 2|
= = 0
21. Assign 1
Xrle(k+1)
22. Assign
XZv(
j)
Xrle(k)
23.
ELSE
24. Assign 1
Xrle(k+1)
25. Assign
XZv(
j)
Xrle(k)
26.
END
27.
Break
()
28.
END
29.
END
End
Hen
ce, th
e ex
ecu
tio
n
o
f
Alg
o
rith
m
-
4
resu
lts
i
n
g
e
n
e
ratio
n
o
f
a
matr
ix
(Xrle). Th
e
m
a
tr
ix
c
o
m
p
crea
tes
a
m
a
trix of element starting from
fi
rst el
e
m
en
t an
d
with
in
crem
en
t o
f
2
step
s til
l th
e v
a
lu
e th
at co
rresp
o
n
d
s
with
th
e size o
f
Xrle. Fin
a
lly, we calcu
late p
r
ob
ab
ility o
f
g
e
n
e
rated
m
a
tr
ix
fo
r ru
n
length
co
d
i
ng
to
red
u
c
e
com
puta
tional
com
p
lexities of space factor and form
ul
a
t
e
a Huffm
an dic
tionary ranging from
the value 0 to
m
a
xim
u
m
prob
abi
l
i
t
y
fact
or. The desi
gn
of
t
h
e Al
g
o
ri
t
h
m
-
5
i
s
as show
n be
l
o
w.
Algorithm-5: H
u
ffma
n Co
ding
for Quanti
z
e
d Image
In
put
: Quantizat
ion value (Q)
Output
: Encoded Image
Star
t
1.
Use Q=8
2. Apply
Block p
r
ocessing
3.
IF
R=8, XZv
=
zigzag (
)
(
block
V
comp
Q
, 8x8)
4.
ELSE IF
R=16
5. XZv=zigzag (
)
(
block
V
comp
Q
, 16x16)
6.
ELSEIF
R
=
32
7. XZv=zigzag (
)
(
block
V
comp
Q
, 32x32)
8. Apply
Run Length Coding
9. Apply
Huffman Dictionar
y
Co
ding
10. Write Code in a File
End
Th
e i
m
p
l
e
m
en
t
a
tio
n
o
f
th
e Alg
o
r
ith
m
-
5
will
g
e
n
e
rate co
d
e
wh
o
s
e leng
th
(L) is ev
alu
a
ted
an
d
m
a
trix
reposi
t
i
ng t
h
e code i
s
roun
d of
f t
o
L/
8 and i
s
assi
gned t
o
new
m
a
t
r
i
x
(Lcd)
.
If t
h
e
m
odul
us of (L/
8
) i
s
foun
d t
o
b
e
less
th
an
th
e size
4
,
th
e s
y
ste
m
recursively checks again of equivale
nce of the sa
me with zero value. A
p
o
s
itiv
e case i
n
th
is co
nd
itio
n
will in
crease th
e co
un
t o
f
t
h
e rou
n
d
o
ff
valu
es. Fin
a
lly,
th
e g
e
n
e
rated
co
d
e
is
sub
j
ect
ed t
o
wri
t
e
i
n
a new fi
l
e
for t
h
e
pur
pose
of
d
ecodi
ng
operat
i
on. The
out
c
o
m
e
of Al
gori
t
h
m
-
5 i
s
co
m
p
ressed
i
m
ag
e, wh
ich
will b
e
sav
e
d in
directo
r
y fo
r
furth
e
r ev
alu
a
tio
n o
f
recon
s
tru
c
ted
i
m
ag
e. Th
e step
s
of dec
onst
r
uct
i
on f
o
l
l
o
ws t
h
e
i
nverse pr
oce
ss of t
h
e al
l
t
h
e al
gori
t
h
m
s
,
where t
h
e o
u
t
c
om
es were anal
y
zed
usi
ng o
r
i
g
i
n
al
si
ze of im
age
(i
n bi
t
s
), com
p
ressed si
ze of im
age (in bits)
,
com
p
ression ratio, Mean Square
d
Erro
r, an
d PS
N
R
.
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I
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8-8
7
0
8
Design
o
f
Mu
ltip
lier fo
r Med
i
ca
l Ima
g
e
Comp
ression
Usi
n
g Urd
h
a
v
a
Tirya
k
bh
ya
m Su
tra (S
uma
)
1
147
3.
RESULTS
A
N
D
DI
SC
US
S
I
ON
Th
e o
u
t
co
m
e
o
f
th
e p
r
o
p
o
s
ed
syste
m
h
a
s b
een
tested
with
Co
rn
ell Un
iv
ersity d
a
tase
t [2
1
]
, wh
ere th
e
p
e
rfo
r
m
a
n
ce p
a
ra
m
e
ters are
main
l
y
i) Siz
e
o
f
Co
m
p
ressed
Imag
e, ii) Co
m
p
ress
io
n
Rati
o
,
iii) Mean
Sq
u
a
red
Erro
r, and i
v
)
Peak Si
gnal
-
t
o
-Noi
se rat
i
o
. The dat
a
se
t
consi
s
t
s
of around
10
00 M
R
I im
ages, where we
choose
to
ev
alu
a
te b
o
t
h
g
r
ayscale as
co
lo
red
m
e
d
i
ca
l i
m
ag
es. Ho
wev
e
r, th
is sect
i
o
n
o
f
th
e m
a
n
u
scrip
t
will h
i
g
h
lig
h
t
only the significant cases
of the sa
m
p
le data
set images
and their outco
m
e
s when they were subjected to the
di
scussed al
go
r
i
t
h
m
s
of t
h
i
s
paper.
Tabl
e 1 hi
ghl
i
ght
s t
h
e sam
p
le im
ages of t
h
e dat
a
set
s
t
h
at
has been consi
d
ered t
o
perf
or
m
eval
uat
i
on
o
f
th
e prop
o
s
ed
syste
m
. A cl
o
s
er lo
ok
in
to
th
e sa
m
p
le
will
show t
h
at
pr
op
osed
syste
m
has been anal
yzed
co
n
s
id
ering
mu
ltip
le t
y
p
e
s o
f
i
m
ag
es with
resp
ect to
co
lor, sizes, an
d
v
i
su
al p
e
rcep
tib
ilit
y facto
r
s. Tab
l
e 2
shows t
h
e st
eps bei
ng unde
rt
aken fo
r t
h
e fi
rst
sam
p
l
e
of
m
e
di
cal
im
ages from
t
h
e dataset
as exhi
bi
t
e
d i
n
Tabl
e
1. The vi
sual
out
com
e
show
s every
st
ep o
f
co
m
p
ressi
on
and decom
p
ressi
on i
nvol
ve
d i
n
generat
i
ng t
h
e
reconstructed i
m
ages. The Table 2 also
highl
ights the type of the algorith
m being im
ple
m
ented on each s
t
ep of
com
p
ressi
on and
decom
p
ressi
on
usi
n
g
Ve
di
c m
a
t
h
em
atics.
Whi
l
e
i
n
t
h
e pr
ocess o
f
gene
rat
i
on o
f
t
h
e
reconst
r
uct
e
d i
m
age, t
h
e sy
stem
spont
aneo
u
s
l
y
checks or
i
g
i
n
al
si
ze of an
im
age, si
ze of com
p
ressed i
m
age,
and com
p
ression rat
i
o
. The sy
st
em
t
h
en checks M
ean Square
d Erro
r and Peak Si
gna
l
-
t
o
-Noi
se rat
i
o. Th
e
vi
sual
out
com
e
sho
w
s t
h
at
for
every
bl
ock si
ze i
n
i
n
creasi
n
g o
r
de
r, t
h
e
vi
s
u
al
i
t
y
of t
h
e
re
const
r
uct
e
d i
m
age i
s
wel
l
bal
a
nced.
T
h
ere i
s
no
bl
urri
ness
or
a
n
y
fadi
n
g
effe
ct
even
if the block si
zes we
re increased for the
pur
pose
of c
o
m
p
ressi
on. Th
erefore, t
h
e pr
op
osed sy
st
em
can of
fer
bet
t
e
r reconst
r
uct
i
on
of t
h
e c
o
m
p
ressed
im
age wi
t
hout
m
u
ch l
o
ss o
f
si
gni
fi
cant
i
n
fo
rm
at
i
on whi
c
h i
s
of
hi
ghest
im
port
a
nce i
n
pat
hol
ogi
cal
in
v
e
stig
atio
n
.
Tab
l
e
1
.
Sam
p
l
e
s con
s
id
ered
fo
r th
e testing
Size: 192 KB
Di
m
e
nsion: 256 x
256
Size: 206 KB
Di
m
e
nsion: 1024 x
1024
Size: 77.
5
KB
Di
m
e
nsion: 1280 x
996
Size: 267 KB
Di
m
e
nsion: 1365 x
1365
Size: 91.
4
KB
Di
m
e
nsion: 375x375
Size: 146 KB
Di
m
e
nsion: 600x447
Size: 92.
6
KB
Di
m
e
nsion:500x468
Size: 69.
6
KB
Di
m
e
nsion: 502x474
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
11
4
0
– 11
51
1
148
Tabl
e 2 Vi
sual
Out
c
om
es
of
S
t
eps
i
n
cl
ude
d
i
n
Gene
rat
i
o
n o
f
R
eco
nst
r
uct
e
d Im
age
St
eps
8x8
16x16
32x32
COM
P
RE
SSI
ON
Vedic Co
m
p
r
e
ss
ion
[Algorith
m
-
2
]
Quantiz
ation
[Algorith
m
-
3
]
Huff
m
a
n Coding
[Algorith
m
-
4
]
[Algorith
m
-
5
]
DEC
O
MP
RES
S
I
O
N
Huff
m
a
n Decoding
I
nver
s
e of Algor
ith
m
-
4
I
nver
s
e of Algor
ith
m
-
5
Dequantiz
ation
I
nver
s
e of Algor
ith
m
-
3
Vedic Deco
m
p
r
e
ss
ion
I
nver
s
e of Algor
ith
m
-
2
Table 3. Num
e
rical
Outcom
es
Block
Size
Factor
s 8x8
16x1
6
32x3
2
CS 1596
08
1511
97
1004
44
CR 3.
2848
3.
4676
5.
2197
M
S
E 2.
3839
19.
989
9
18.
282
5
PSNR
44.
358
35.
122
7
35.
510
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
Design
o
f
Mu
ltip
lier fo
r Med
i
ca
l Ima
g
e
Comp
ression
Usi
n
g Urd
h
a
v
a
Tirya
k
bh
ya
m Su
tra (S
uma
)
1
149
Tabl
e 3 s
h
ow
s
t
h
e n
u
m
e
ri
cal out
c
o
m
e
of t
h
e pr
o
pose
d
sy
s
t
em
consi
d
eri
n
g t
h
e
fi
rst
t
e
st
im
age from
t
h
e sam
p
l
e
s sh
ow
n i
n
Ta
bl
e
1.
The
val
u
e s
h
o
w
s t
h
at
si
ze of com
p
resse
d
im
age
(CS)
keep
s
on
r
e
du
cin
g
w
ith
the increase of blocki
ng size. Moreover, the
r
e is a s
m
o
o
t
h
in
crem
en
t p
a
tt
ern
in
th
e Co
m
p
ressi
on
Ratio
(CR)
as well as Mean Squa
red E
r
ror (MSE
) with t
h
e incre
a
se
in
b
l
o
c
k
sizes,
wh
ile PSNR is fo
und
to
decline wh
en
t
h
e 1
6
x
1
6
bl
oc
ks as
com
p
are
d
t
o
8
x
8
bl
oc
k
si
ze. T
h
e
o
u
t
c
om
e sho
w
s
v
a
ri
abl
e
pat
t
e
rn
of
PS
NR
on
di
ffe
rent
bl
oc
k si
ze.
Fi
gu
re
2.
Sec
o
nd
Im
age o
f
Sa
m
p
l
e
Dat
a
set
from
Tabl
e 1
Table 4. Num
e
rical
Outcom
es
for Second Image
in
dataset
Block
Size
Factor
s 8x8
16x1
6
32x3
2
CS
1868
86
1624
72
1609
19
CR
2.
8054
3.
2269
3.
2581
M
S
E 5.
0103
12.
241
7
27.
128
2
PSNR
41.
132
1
37.
252
4
33.
796
6
The fi
rst
sam
p
le im
age hol
ds a si
ze of 19
2 K
B
and di
m
e
nsion
of
25
6x
25
6,
hence, we
hav
e
t
e
st
ed wi
t
h
t
h
e Hi
gh
Defi
n
i
t
i
on (HD) i
m
age of si
ze 1
0
2
4
x
1
0
2
4
of
si
ze 206
KB
, w
h
i
c
h i
s
sho
w
n i
n
Fi
g
u
re 2.
The
num
eri
cal
outcom
e
for this HD im
age s
hows that size of com
p
resse
d im
age drops
wi
t
h
t
h
e i
n
crease of bl
ocki
n
g
si
ze,
while co
m
p
ression ratio as w
e
ll as
m
ean squared error is
fo
un
d t
o
si
gni
fi
cant
l
y
i
n
crease
it
s dim
e
nsi
on wi
t
h
t
h
e
i
n
crease of
bl
o
c
k si
ze. The P
S
NR
val
u
es f
o
r 8
x8
bl
ock
i
s
fou
n
d
t
o
be
4
1
db,
w
h
i
c
h d
r
o
p
s t
o
37
db
an
d 3
3
db
for t
h
e
bl
oc
k
si
ze of 1
6
x
1
6
and
32
x3
2.
Howe
ver,
ret
a
i
n
i
ng t
h
e
PSN
R
val
u
es wi
t
h
i
n
t
h
i
s
range i
s
qui
t
e
acceptable with no loss of signifi
cant
inform
ation duri
ng the com
p
r
e
ssion operation executed
by the
al
gori
t
h
m
s
of t
h
e pr
op
osed sy
st
em
. Our next
set
of eval
uat
i
on was t
o
chec
k t
h
e sim
i
l
a
r consi
s
t
e
ncy
for
col
o
red
im
ages.
Fi
gu
re
3.
Si
xt
h
Im
age of
Sam
p
l
e
Dat
a
set
fr
o
m
Tabl
e 1
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