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Trang 1IMAGE AND VIDEO COMPRESSION FOR WIRELESS NETWORKS
Ho Anh Tuy
H anoi University o f Technology
N gu yen V inh An
Hanoi Open University
A b s tr a ct The demands for transmission of image, video and multimedia over wireless networks are increasing very rapidly The inherently characteristics of wireless medium as bandwidth narrowing, interferences and fading are big challenges The traditional compression techniques can not adapt to this changes In this paper, we will discuss of issues of using wavelet compression for image and video over wireless networks This paper also introduces some change of wavelet parameters in order to improve quality of transmission image and video over wireless network conditions
1 I n t r o d u c t io n
The t r a d i t i o n a l mobile netw ork s are use d for low - r a t e audio
co mmu nica tions New ge ner ati on of mobile comm uni cat io ns is e m e r g in g to t r a n s f e r
d a t a trafic a t m u ch h ig h er bit rate The d e m a n d s for m u lt im e di a, im a g e a n d video over wireless n e tw o r k s a re rapidly increasing F u t u r e I n t e r n e t will allow u s e r s access from mobile applian ces (PDAs, s m a r t phone, Web pads, h a n d PCs ) a nd high b a n d w i d t h app licatio ns (m-commerces, m u lt i m e d i a E-mail, video tel ephone, wireless LANs, PANs)
T r a n s m i s s i o n of Image a n d Video over Wireless N e tw o rk s a r e c h a l le n g i n g because of th e highly varia ble n a t u r e of the wireless link Radio is a n i n h e r e n t l y unreli abl e t r a n s m i s s i o n medi um when compared to a wired link d ue to i n tef ere nc e
a nd fading c r e a t e h i g h e r bit errors Typical wireless c h a n n e ls a re noisy a n d of
n a rr o w b a n d w i d t h For example, a customer using a code-division mu lti ple -ac ces s (CDMA) h a s only a 9.6 kbps ba n dw id th Even if t h e b a n d w i d t h i n c r e a s e s up to 2 Mbps for t h e 3G wireless, it is still not comparable to th e b a n d w i d t h of b r o a d b a n d optical c o m m u n i c a ti o n sy ste m s (ATM could allocate dozens of Mbps to end users)
T im e-v ar yi ng c h a r a c t e r i s t i c s of wireless c han ne l a n d limited b a t t e r y r es ou rce in
h a n d h e l d devices is a n o t h e r issue for scalable video s t r e a m i n g over w ir ele ss link with Q u a lit y of Service (QoS) Meanwhile, the capacity of a wirele ss c h a n n e l is
f lu ctu ate d d u e to t h e c h an gi ng distance between t h e t r a n s m i t t e r a n d t h e receiver
So it is i m p o r t a n t to e s t i m a t e the available wireless ne tw ork condition dy na mi ca lly and it is n e c e s s a r y to apply a p p ro p r i a te d video compression s t r a t e g y to h a n d l e the
va riability of w ir ele ss networks
33
Trang 22 Im a g e c o m p r e s s io n t e c h n i q u e s
T her e are four common m eth od s for compression, Discreate Cosine T r a n s f o r m (DCT), Vector q u a n ti z a t io n (VQ), Fra ct a l Compression and Di sc ret e Wave let
Tr ans fo rm (DWT)
DCT is a lossy compression alg or ith m t h a t s a m pl e s an i m a g e a t r e g u l a r intervals, analyzes the frequency components p r e s e n t in t h e sample, d is c ar d s those frequencies which do not affect the image as the h u m a n eye perceives it
Vector q u a n ti z a t io n (VQ) is a lossy compression t h a t looks a t a n a r r a y of da ta , not an individual value It compresses r e d u n d a n t d a t a while a t t h e s a m e time
r e ta in in g th e desired object or d a t a s t r e a m ’s original in te nt
Fractal compression is a form of VQ and is also a lossy compression The self similar sections of image is located and then using fractal algorithm to h an dle them DWT an alyzes signals into wavelets-functions t h a t ha ve bo th tim e and frequency domains The process is perform on the e n ti r e image, which differs from DCT t h a t works on sm a ll er block (8 x 8 picxels)
2.1 D iscrete C osine T r a n s fo r m (DCT)
Cu rrently, DCT is quite po pu la r in m an y compression p ro du cts such a s J P E G Image compression using DCT is i l l u s t r a te d in figure 1.
F ig u r e 1 J P E G compression.
The general forward a n d inverse DCT t r a n s f o r m for a 2D (N by M image) is
defined by the following e q ua tio n
DCT:
EY \ _ 2 r v w \ v l ' v l /Y \ ( 2x + X)vn { 2 y + \ ) n n
F(w,v) = f - C ( t < ) C ( v ) X s f ( y , x ) c o s -—^ -COS - — - (1)
IDCT:
t < : i \ _ 2 V ' V n t \ n t \ E V \ ( 2x + \ ) U 7 T (2y + \ ) v n /o x / ơ ỹ ) = f r Z ỵ C(u)C(v)F(u,v)co s - — -- -COS - — ; - ( 2 )
The main d i s a d v a n t a g e s of DCT is t h a t when the coded bit r a t e is lower t h a n
a cert ain value (0.25 bits/pixel), t h e r e are blocking effects in the decoded image, due
to t h e 8 x 8 block two d i m e n s i o n a l DCT In a n o t h e r i ss ue, for t h e w i r e l e s s n e t w o r k s ,
the ch an ne ls are noisy, th e blocks are lost because H u f f m an coding is a variable length code The noisier th e c h an ne l is, the more blocks a r e lost
Trang 32.2 D isc r e te W avelet T r a n s fo r m (DWT).
2.2.1 The wa vel et decomposition h a s been proved to be a good tool for image compression recently It performs b e tt e r t h a n DCT in te r m of compression ratio and quality of p i c t u r e which is reproduced The new J P E G 2000 s t a n d a r d s adopt
w av el et s u b b a n d coding, w h e r e t h e enc od er tiles t h e i m a g e in to blocks of N X N
pixels (N being a power of 2), calculates a 2-D Discrete Wav ele t T r an sf o r m (DWT),
q u a n t i z e s t h e t r a n s f o r m coefficients a n d encodes t h e m u s i n g a r i t h m e t i c coding Th e
discrete-time w a v el e ts have general form:
1
- 1/2 ¥
a
t - b
The v a ri a b l e a is used to scale the wavelet V ụ(t) by powers of two an d variable
b is used to t r a n s l a t e the wavelet in integer a m ou n t s To a n a l y se d a t a a t different
resolution, a fu nction W(t) is used in conjunction with the m o th e r wavelet Here
W ( 0 = ! ( - ! ) * C y F ( 2 / + *)
Ck are the w a v e le t coefficients which satisfy (5)
N- \
I C , = 2 and ỵ c kc „ = ĩ ổ h0
(4)
(5)
In t h i s case 5 is the delta function a nd b is the location index.
In fo rw a rd DWT, image is se pe ra te d into low-pass sa mples, r e p r e s e n ti n g a low-resolution vers ion of the original image a nd hi g h- p as s sa mples, r e p r e s e n ti n g a details which a r e needed for the perfect rec onstruction of the original image
A H Piapm òct
ị
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V e rtic a l Hl|fc QgriMotRl
Pngm nrtw
W a v e le t
T m pm àm
FmqMKlei
P m tn u k t
S c a lin g
F u n c tio n
U w V W e*
Frwpwnci*
S c a lin g
V b t ú a l
Wsvxlet
Law H odm tal Fraqittttfcf
Vertical
Scaling
Function
HH HL
LH
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ỸTỆQmcbỆ
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F ig u r e 2 The level 1 of wavelet decomposition process
Trang 4The en tir e process is carried o u t by excuting a 1-D s u b b a n d decomposition twice, first in horizontal t h e n in the veritcal (orthogonal) For example, the low pass sub b an d (Ll) r e s u l ti n g from the horizontal is f u r t h e r decomposed in th e veritcal, leading to L L1 a n d L H1 sub band Similarly, the high pa ss s u b b a n d H I is f u r t h e r
decomposed into HL1 a n d H H l An exam ple of the proccess of one level wa velet decomposition is depicted in figure 3 a n d the d e m o n s tr a ti o n of picture is shown in figure 4
F i g u r e 3 T h e proccess of one level wa velet decomposition.
The second level of decomposition can be r e p e a t e d for existing LL1 sub band This ite ra ti ve process r e s u l t s in m u lt i p le ”t r a n s fo r m levels” If an imag e is decomposition into K levels t h e n the total n u m b e r of s u b b a n d s is 3 K + 1 The process of decomposition of a n image in t h r e e level as shown in figure 3 N u m b e r of requ ir ed su b b a n d s a f t e r t h r e e level decomposion of 2D ima ge is depicted in figure 5
LL HL
HL
HL
LH HH
LH H H
Figu re 4 T h re e level of 2-D Discrete Wavelet Decomposition
Trang 52.2.3 Q u a n t iz a t i o n is the process by which th e coefficients a r e reduced in
presision The q u a n ti z a t io n can be lossy or lossless
Each s u b b a n d of the wavelet decomposition is divided into r e c t a n g u l a r blocks (Code blocks), which a re coded in d ep e n d en t l y u s i n g a r i t h m e t i c coding These code blocks are coded a t a bit-plane a t a time, s t a r t i n g with the most significant bit- plane with a non-zero e le m e n t to the lea st sign ific ant bit-plane
2.2.4 Wavelet h a s some m ai n a d v a n t a g e s over DCT, includes:
• Im proved scalability: This is because t h e w a v el e t t r a n s f o r m process can be
r e p e a t e d for as m a n y time as needed T he decoder can stop an y time if needed, as full resolution of th e imag e m a y n ot required
• H ig h e r efficiency a t low bit rates
• It provide h i g h e r compression ratio a n d b e t t e r qu a lit y of reprod uced image
• T he d isa dva nc e of it is using w a v e l e t r e q u i r e more calculations when
c om pa rin g with DCT This leads to m or e complexing in th e h a r d w a r e and software i m p l e m e nt a tio n s
2.3 T he J P E G ( J o i n t P h o to g r a p h ic E x p e r ts G roup)
J P E G is well-known image compression m et ho d b a se d on DCT algorithm
J P E G compression can be done a t different u s e r defined compression levels, which
d e te r m i n e how much a n image is to be co mpressed The compression level is directly r el a te d to the ima ge quality Besides t h e compression level, th e image scene itself also h a s a n im p a c t on th e re s u l ti n g c om pr es si on ratio T h e sa m e compression level applied on simple scene may produce a s m a l l e r file (higher compression ratio)
t h a n on a very complex a n d p a t t e r n e d scene (lower compression ratio)
2.4 J P E G 2000 s ta n d a r d s
The J P E G s t a n d a r d s usi ng DCT a nd J P E G 2000 us in g DWT The difference in quali ty of imag e w he n compressed using J P E G a n d J P E G 2000 can be seen in the íìgureõ
J P E G 2000 s t a n d a r d provides a set of f e a t u r e s t h a t a re of vital imp o rt an c e to
m a n y em er gi n g applications Some of the f e a t u r e s t h a t t h i s s t a n d a r d possesses are:
S u p e rio r low bit-rate p e rfo rm a n c e : This offers b e t t e r p erf or m anc e t h a n c u rr e n t
s t a n d a r d s a t the low bit-rate
• Lossless a n d lossy compression
• Progressive tra n sm issio n by pixel accuracy a n d reso lu tio n : Progressive
t r a n s m i s s i o n allows pict ures to be r e c o n s t r u c t e d with in cr e as in g pixel accuracy or sp a t ia l resolution This n e ed s for m a n y ap plications an d for different t a r g e t devices
• Region o f In terest Coding: This f e a t u r e allows u s e r defined Regions-Of-
I n t e r e s t (p ar t s of a image t h a t are more i m p o r t a n t t h a n o t h e r p a r t s of it) in
t h e image to be compressed with b e t t e r qu a lit y t h a n t h e r e s t of the image
Trang 6• R o b u stn ess'to bit-errors: It is de sirable to consider ro b u s t n e s s to b it- e rr or s
while design ing the codestream This fe a t u r e is very i m p o r t a n t for wireless
co mmu nica tion applications
40:1 Com pressed J P E G 2000
F i g u r e 5 Co m p ar e the qu ality of image usin g J P E G a n d J P E G 2000.
3 V i d e o c o m p r e s s i o n T e c h n o l o g y
3.1 Video compression is performed w h e n a n i n p u t video s t r e a m is -analyzed and r e d u n d a n t info rma tio n is discarded Each e ve n t is t h e n assigned a code- commonly occurring e ven ts are as signed few bits an d r a r e ev ent s will have more bits This is called va ria b le length encoding respectively (VLC) One of the best-
known video s t r e a m i n g tec h ni q ue s is the s t a n d a r d called M P EG {Motion Picture
Experts Group) The basic principle of MP EG is to compare two compressed images
to be t r a n s m i t t e d over the ne tw ork and u s i n g the first compressed image as a
Trang 7reference fra m e (called an I-frame), only se nding the p a r t s of the following images (B-frame a n d P-frame) t h a t differ from the reference image
3.2 Th er e are five M P EG s t a n d a r d s being used Each s t a n d a r d was designed
for a specific application an d bit r a t e M P E G-1 was designed for up to 1.5 Mbps,
st a n d ad i ze d for compression of moving pict ures a n d audio MPEG-2 was designed for betw een 1.5 a nd 15 Mbps It is based on M P E G -1, b u t for t h e compression and
t ra n s m i ss io n of digital b r o ad c as t television The most significant e n h a n c e m e n t from
M P E G-1 is its ability to efficiently compress in te rla c ed video
The Motion P ic tu re E xp er ts Group (MPEG4) s t a n d a r d s for m u lti m e d ia a nd Web compression MPEG-4 is based on object-based compression In di vi d u al objects
wi th in a scene a re t r ac ke d se pe r a tly a nd compresses t o g e t h e r to c re at e a n M P E G-4
file t h a t is very scalable, from low bit r a t e s to very high
MPEG-4 is a new ge n er at io n of I n t e r n e t- b a s e d video ap plications a n d Video Coding Exp ert s Group H.264 s t a n d a r d s for video compression is now widely used in videoconferencing systems MP EG 4 and H 263 prom ises to significant outperform, providing b e t t e r compression of video t o get her with a r an g e of f e a t u r e s supp or ting high-quality, low b i t- ra te s t r e a m i n g video
3.3 The H.261 a n d H.263 st a n d a r d s H.261 is a n ITU s t a n d a r d designed for
two way comm uni catio n over ISDN lines (Videoconferencing) a n d sup po rt s d a ta
r a t e s of m ult ip les of 64Kbps The algorithm is b a se d on DCT a n d can be used in
i n tr a - f r a m e a n d i n te r- f ra m e mode H.261 s u p p o r t s CIF a n d QCIF resolutions
H.263 is bas ed on H.261 with e n h a n c e m e n t s t h a t improve video quality over modems It s u pp o rt s CIF, QCIF, SQCIF, 4CIF a n d 16 CIF resolutions
The H 264 s t a n d a r d does not explicitly define a CODEC, r a t h e r th e s t a n d a r d defines the sy n t a x of a n encoded video b i t s t r e a m t o g e t h e r with th e met ho d of decoding this b i ts tr e a m The basic functional e le m e n t s (prediction, tr ansform,
qu an tiz a tio n , en tro p y encoding) a re little different from M P E G l , MPEG2, MPEG-4,
H.261, H.263
3.4 The M P E G l , M P E G2, MPEG4, H.261, H.263 use 8x 8 DCT transform
The “Ba se lin e ” profile H.264 uses th r ee tr an s fo r m de p en di ng on t h e type of res idual
d a t a t h a t is to be coded: a t r a n s fo r m for 4 X 4 a r r a y of l u m a DC coefficients in i n t r a macroblocks, a t r a n s f o r m for 2 x 2 a r r a y of c h ro m a DC coefficients in any mocroblock a n d a t r a n s f o r m for all ot her 4 x 4 blocks in th e r es id u al data H.264 uses sc al a r qu a nt iz e r
4 V id e o o v e r W ir e le s s N e tw o r k
4.1, Su p p o r t i n g video over Wireless Net wor ks is a h a r d problem because of
t h r e e factors:
• Scarcity of ba nd wi d th
• Tim e-v ar yi ng e rr o r c h arac ter is ti cs of th e t r a n s m i s s i o n channel
• Power l im i ta t io n s of the wireless devices
Trang 8Th e eme rg ing of 3G wireless n e tw o rk s such as GP RS (General P a c k e t Radio Service), CDMA (Code Division Multiple Access), CDMA2000, W-CDMA boosts
e n o rm o u s dev elop men t of wireless video a nd services They a re desig ned w i t h the capa bility of providing high speed d a t a services, r ang in g, from more t h a n 100Kbps
to se veral Mbps However, t r a n s m i s s i o n of video a n d m u li t m e d i a s t r e a m s over wirele ss n e tw or k s still faces several challenges Firstly, t r a n s m i s s i o n of video over wireless c ha nn e l is highly prone to erro rs due to m u lt i - p a t h effects, s h a d o w i n g a nd inter feren ce Secondly, the b a n d w i d t h of wireless c h a n n e l can v a r y significnatly over time The rea so n is t h e a m o u n t of b a n d w i d t h t h a t is a ssi gn ed to a u s e r can be
a function of th e signal s t r e n g t h (low signal s t r e n g t h , more processing gain a t the
r eceiver a n d different b a n d w i d t h may be dynamically a ssi g ne d to t h e user ) a nd
in te r fe r e n ce level (high i n ter fer en ce condition, h e av i er c h a n n e l coding) Thirdly,
m u lt i - u s e r s h a r i n g th e wireless c h a n n e l with he te ro ge no us d a t a types c an also lead
to significant b a n d w i d t h v a ri a ti o n which can f u r t h e r lead to overflow of n e tw o rk buffer an d hence p a c k e t loss Finally, d a t a t ra n s m i s s i o n can be i n t e r r u p t e d completely de p en di n g on wireless i m p l e m e n ta t io n (handoff process, cell reselection)
4.2 Quality of Service (QoS) control in wireless n e tw o rk s c an help alleviate
t h e b a n d w i d t h v a ri a ti o n a n d p a c k e t delay/loss problem b u t it is often costly For example, to m a i n t a i n a re a so na b le d a t a r a t e for a u s e r n e a r the cell b o u n d a ry , a large proportion of power of base st a ti o n (BS) needs to be a ssi gn ed which limiting
th e capacity of the BS to serve o th er users Video s t a n d a r d s MPEG -4 h a s a set of tools providing improved compression efficiency a nd e rr o r r e s i l i e n c e In addition,
MP EG -4 provides scalability for both sp a t ia l a n d t e m p o r a l resolution
e n h a n c e m e n t s E r ro r control a n d power control are two very effective ap p ro a ch e s for su p p o r t i n g quali ty of service E r r o r control is perform ed from i n d iv i d u a l use r
po in t of view by i nt ro d u c in g r e d u n d a n c y to combat t h e t r a n s m i s s i o n errors One of
t h e p o p u l ar e rro r coding tec h ni q ue s is Reed-Solomon coding, which can deal with
b u r s t error If the original mes sage length is M, we will add p a r i t y d a ta , so the codeword is of len g th N > M which can recover e rr o rs of len gt h up to (N-M)/2.By
a d d i n g extr a p a r i t y d a t a of len g th R bytes, a t l ea st p a r t of erro rs c an be recovered
by t h e receiver T h e l a r g e r the value of R, more th e e rro rs will be corrected Choosing of R should be considered carefully be cau se p a ri t y d a t a in tr o d u c e s more trafic to th e limited n e tw o rk b a n d w i d th a n d m ay cause p a c k e t loss due to congestion
4 3 The P e a k Signal-to-Noise Ratio (PSNR) m e a s u r e s t h e size of e rro r
r e la tiv e to p eak va lu e of t h e signal Xpeak In o t h e r word, it is use d to m e a s u r e the fidelity of a compressed image with its original High PS NR m e a n s t h a t the compressed image is very sim ila r to the original The f or m ul a r to calcu lat e PS N R is
2
where X peak is the peak value of the signal and Ơ2 * d is the Mean S qua re E rro r MSE
(6)
Trang 9Me an s q u a r e e rr o r (MSE) m ea su re s the difference b e tw ee n the original a n d
r ec ons tr uct ed im a g e is calculated by
Here, X n, Y n N a re the i n p u t d a t a sequence, t h e r e c on st r u ct e d d a t a a n d the
length of d a t a sequen ce
The W a v e le t t r a n s fo r m with the a d v an t ag e of m u lt ir es o lu ti on is good solution for im pro vi ng PS NR We will compare PSNRs for different resolutions w i t h sa m e compression r a t i o in table 1
T a b l e 1 C o m p a r i s o n of P S N R ’s Lena colored image of size 512 X 512 for diff eren t
r e s o l u ti o n s
Compression
Original (bits)
No of resolutions
(K)
After compression (bits)
PSNR (dB) Ratio
19.314852
20.806499
27.138719
28.922634
29.289699
29.162789
4.4 P o w e r control is performed by controlling th e t r a n s m i s s i o n power a n d
t ra n s m i s s i o n r a t e for a group of users So e r r o r control a n d power control
te c hn iq ue s a r e n e c e s s a r y to e n su r e high-quality video delivery from appli cat ion level a n d t r a n s m i s s i o n level
It is n e c e s s a r y to u n d e r s t a n d overall wireless sy st em perform anc e (such as capacity) w h e n m ul t i p le types of traffic, each wi th d ist in c t c h a ra c t e r i s t i c a r e
p r e s e n t in t h e s a m e sector
5 N e w t r e n d s in im a g e a n d v id e o c o m p r e s s io n
5 1 C u r r e n t l y , video communications are c ar ri ed out u s i n g source coders a n d
c h a n n e l coders desig ned i n d e p e n d e n t of each o t h e r b a se d on t h e t he or e tic al
f oun dat io n of S h a n n o n ’s “separation p rin cip le ” , which s t a t e s t h a t this s e p a r a t i o n is
op tim al [4]
However, w h e n considering wireless video co mmu nica tions , t h e r e a r e some
r e a s o n s not to a d h e r e to the s e pa r a t io n principle For example, S h a n n o n ’s work
Trang 10m a k e no a s s u m p t i o n a b o u t the e rro r c ha ra c te ri st ic s of t h e c h a n n e l on which data would t r a v e r s e It also do esn’t t ak e into account th e op tim iza tio n possible in
c h a n n e l u t i l i z a t i o n t h r o u g h static al multiplexing This is tr u e for all p o p u l a r video
s t a n d a r d s , i n c l u d i n g MPEG-1, MPEG-2, H.261 an d H.263 Coders are designed with little r e g a r d to t h e e rro r c ha ra c te ri st ic s of the channel
5.2 A l t h o u g h ex isting compression tec hn iqu es h e l p fit video s t r e a m s into the
b a n d w i d t h a v ai la b l e in wireless ch annels, t h e r e are a n u m b e r of i ss u e s which affect
th e memory, c o m p u t a t i o n a l capabilities a nd i n t e r n a l d a t a t r a n s f e r c h a n n e l s of wirele ss devices In addition, the wireless co mmu nica tion e n v i r o n m e n t is highly prone to i n t r o d u c e e rr o r s into digital bit s t r e a m s The video compression a lg or ith m s remove m u ch of t h e r e d u n d a n c y in video d a ta , a n d as a result, t h e effects of c han ne l
i n te r fe r e n c e r ip p le s t h r o u g h not j u s t the c u r r e n t image being display, b u t also successive i m a g e s T h e predictive tech niq ue s used in M P EG c a u s e e rro rs in a
r e c o n s t r u c t e d video f ram e to p ro p a g a t e t h r o u g h time into f u t u r e fr ames This can also c au se to lose sy nc hr oni zat io n in decoding process
5.3 T h e selection of a n image compression a lg o ri th m for video and
m u l t i m e d i a co m m u n i ca ti o n d ep end s not only on the t r a d i t i o n a l crit eri al of achi eva ble compre ssio n ratio a n d the qua lity of re c o n st r u c t e d images, it also
d e p e n d s on as so c ia te d energy con sum ption a nd ro b u s t n e s s to h i g h e r bit e r r o r ra te s Wav ele t a l g o r i t h m e nab les significant reduction in c o m p u t a t i o n as well as
c o m m u n i c a ti o n needed, with m in im al d e g ra d at i o n in image quality St u d y ha s shown t h a t the wa vel et step consu mes more t h a n 60% of th e CPU ti m e durin g image co m pr e ssi on process By us in g optimizing a lg o ri th m of th e t r a n s fo r m step,
pe rf o r m a n c e a n d energy r e q u i r e m e n t s of the e n ti r e image co mpression process can
be sig nific antl y improved
5.4 We know t h a t forward wavelet t r a n s fo r m uses a 1-D subba nd decomposition process w h e r e a 1-D set of sa m p les is converted into t h e low-pass
s u b b a n d (Li) a n d hi gh -p as s s u b b a n d (Hi) Dong-Gi Lee a n d Sujit Dey have
p r e s e n t e d a wavelet- ba sed t r a n s fo r m alg or ith m t h a t a i m s a t minimizing
c o m p u t a t i o n e n e r g y (by red u c in g t h e n u m b e r of a ri t h m e t ic o p e ra t io n s a n d memory accesses) a n d c o m m un ic a tio n energy (byreducing n u m b e r of t r a n s m i t t e d bits) in
“A da pt ive a n d E n er g y Efficient Wavelet Image Compression For Mobile Mult ime dia
D a t a Servi ces ” [7] T h e i r idea is exploits the n um er ic a l d ist r ib u t i o n of t h e high-pass coefficients to e l i m i n a t e a large n u m b e r of sa m p le s in the compre ssio n process The work shows t h a t on the [512x512] Lena image sample, the d i s t r ib u t i o n of high-pass coefficients a f t e r ap pl y in g a 2 level wavelet as following (see figure 6).
We observe t h a t ab out 80% of t h e high- pas s coefficients for level 1 are less
t h a n 5 In t h e q u a n t i z a t i o n step, all small va lued coefficients a r e set to be zeros, so
a lots of h i g h - p a s s coefficients do not ha ve to be computed This h as two
a d v a n t a g e s : firstly, th e a lg or ith m helps to reduce the co m p u t at i o n energy consumed
d u r i n g i ma ge compre ssio n process and secondly, because the enco de r and decoder
a re a w a r e of t h e e s t im a t i o n tec hnique, only small a m o u n t s of in fo r m a ti o n need to