tai lieu wavelet

8/7/2019 tai lieu wavelet

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Lun vn cao hc TVT 2004 2006

Ngc Anh

B GIO DC V O TO

TRNG I HC BCH KHOA H NI

----------------

LUN VN THC S KHOA HC

NN NH SDNG BIN I WAVELET V

NG DNG TRONG CC DCH V DLIU A

PHNG TIN DI NG

NGHNH: IN TVIN THNG

NGC ANH

Ngi hng dn khoa hc: PGS.TS. Nguyn c Thun

H NI 2006


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MC LC

CC HNH V, BNG BIU TRONG LUN VN ..............................5

THUT NGTING ANH ......................................................................7

LI GII THIU .......................................................................................8CHNG 1: MU..............................................................................9

1.1. Csnghin cu v mc ch ca lun vn ...................................9

1.2. T chc lun vn............................................................................10

CHNG 2:TNG QUAN CC K THUT NN TRONG M HO

NH..........................................................................................................11

2.1. Gii thiu chung v nn nh s .....................................................11

2.2. Phn loi cc k thut nn .............................................................13

2.2.1. Nn tn hao v khng tn hao................................................13

2.2.2. M ho don v m ho da trn php bin i................13

2.2.3. M ho bng con.....................................................................14

2.3. Tiu chun nh gi cht lng m ho nh .................................14

2.4.Cc k thut nn c tn hao............................................................15

2.4.1. K thut m ho bng con ......................................................15

2.4.2. K thut m ho da trn php bin i.................................19

2.4.2.1. K thut m ho da trn php bin i DCT.................19

2.4.2.2. K thut m ho da trn php bin i DWT ...............25

CHNG 3:C S L THUYT BIN I WAVELET...................30

3.1. Cston hc ...............................................................................30

3.1.1. Bin i Waveletlin tc........................................................30

3.1.2. Bin i Waveletri rc .........................................................323.2. Tnh cht ca bin i Wavelet......................................................33

3.3. Gii thiu mt s hWavelet........................................................37

3.3.1. Bin i WaveletHaar............................................................37

3.3.2. Bin i WaveletMeyer .........................................................38


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3.3.3. Bin i WaveletDaubechies.................................................38

3.4. Mt sng dng ni bt ca Wavelet...........................................39

3.4.1. Nn tn hiu.............................................................................39

3.4.2. Kh nhiu ...............................................................................40

3.4.3. M ho ngun v m ho knh...............................................40

CHNG 4:CHUN NN NH TNH DA TRN BIN I

WAVELET JPEG2000..........................................................................41

4.1. Lch s ra i v pht trin chun JPEG2000...............................41

4.2. Cc tnh nng ca JPEG2000 ........................................................41

4.3. Cc bc thc hin nn nh theo chun JPEG2000 .....................42

4.3.1. X l trc bin i................................................................42 4.3.2. Bin i lin thnh phn.........................................................42

4.3.3. Bin i ring thnh phn (bin i Wavelet)........................43

4.3.4.Lng t ho - Gii lng t ho............................................44

4.3.5. M ho v kt hp dng d liu sau m ho ..........................45

4.3.6. Phng php m ho SPIHT..................................................45

4.3.7. Phng php m ho EZW.....................................................47

4.4. So snh chun JPEG2000 vi JPEG v cc chun nn nh tnh

khc.......................................................................................................49

CHNG 5:NG DNG WAVELET TRONG CC DCH V D

LIU A PHNG TIN TRONG THNG TIN DI NG...............54

5.1. Nn nh bng Wavelet...................................................................54

5.2.1. S khi tng qut...............................................................54

5.1.2. Bin i Wavelet.....................................................................55

5.1.3. Tnh ton nng lng tiu hao................................................56

5.2. Thut ton nn nh bng Wavelethiu nng - EEW.....................58

5.2.1. Hiu nng ca cc k thut loi b .........................................60

5.3.2. Cc kt qu thc nghim ........................................................62

5.3.2.1. nh hng n nng lng tnh ton v cht lng nh62


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5.3.2.2. nh hng n nng lng truyn thng v cht lng

nh.................................................................................................62

5.4. Cc tham s nn nh bng Wavelet...............................................62

5.4.1. Thay i mc bin i Wavelet..............................................62

5.4.2. Thay i cc mc lng t .....................................................62

5.5. Truyn nh trn mng...................................................................62

5.5.1. Phng php la chn tham sng......................................62

5.5.2. Kt qu thc nghim...............................................................62

KT LUN...............................................................................................63

Kt qut c v ng dng ca lun vn.........................................63

Hng pht trin nghin cu ................................................................63PH LC..................................................................................................65

TI LIU THAM KHO ........................................................................66


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CC HNH V, BNG BIU TRONG LUN VN

Hnh 2.1 S b khi qut h thng nn nh.........................................12

Hnh 2.2. S minh ho k thut m ho bng con M bng con .......16

Hnh 2.3 Minh ho qu trnh phn ly bng con cy bt phn...................17Hnh 2.4. Phn ly hai nh mu thnh bn bng con .................................18

Hnh 2.5. S b m ho theo chun JPEG ..........................................23

Hnh 2.6. Sp xp Zigzag cc h s DCT b m ho............................23

Hnh 2.7. S khi b gii m theo chun JPEG ..................................23

Hnh 2.8. Bank lc khi phc l thuyt s dng DWT 1D ......................28

Hnh 2.9. Minh hoDWThai chiu cho nh ............................................28

Hnh 2.10(a). Minh hoDWTkiu dyadic mc 3 nn nh..................28

Hnh 2.10(b). Minh hoDWTkiu dyadic mc 3 nn nh..................29

Hnh 3.1. Minh ho li nh t dyadic vi cc gi tr ca m v n ............33

Hnh 3.2. Phn tch a phn gii p dng cho biu din tn hiu.............36

Hnh 3.3. Hm ( )t ca bin i Haar ....................................................38

Hnh 3.4: Hm ( )t ca bin i Meyer..................................................38

Hnh 3.5. Hm ( )t ca h bin i Daubechies n vi n=2, 3, 7, 8........39Hnh 4.1: Trnh t m ho (a) v gii m JPEG2000 (b).........................42

Hnh 4.2: Minh honh vi RGB v YCrCb...........................................43

Hnh 4.3: Phng php Lifting 1D dng tnh ton bin i Wavelet.......44

Hnh 4.4: Minh ho cy t phn (a) v s phn mc (b)..........................47

Hnh 4.5: Hai cch sp xp th t cc h s bin i...............................48

Hnh 4.6: So snh JPEG v JPEG2000....................................................50

Bng 4.1: So snh JPEG v JPEG2000 ...................................................51

Hnh 4.7: Minh ho tnh nng ROI...........................................................52

Bng 4.2: So snh tnh nng ca JPEG2000 vi cc chun nn nh tnh

khc...........................................................................................................53

Hnh 5.1. S khi qu trnh nn nh bng Wavelet.............................54


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Hnh 5.2. (a) Bin i Wavelet 2D mc 3 v (b) Minh ho bng nh

CASTLE ................................................................................................56

Hnh 5.3. Phn b s hc cc h s thng cao sau php bin i Wavelet

mc 2.........................................................................................................59

Hnh 5.4: D liu sau php bin i Waveletvi hai k thut loi b HH

v H*.........................................................................................................61


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THUT NGTING ANH

CWT Bin i Wavelet lin tc (Continuous Wavelet Transform)

DCT Bin i Cosine ri rc (Discrete Cosine Transform)DFT Bin i Fourier ri rc (Discrete Fourier Transform)

DPCM iu xung m vi sai (Differized Pulse Code Modulation)

DWT Bin i Wavelet ri rc (Discrete Wavelet Transform)

EZW Wavelet cy zero (Embedded Zerotree Wavelet)

HVS H thng cm nhn hnh nh ca mt ngi

(Human Visual System)

IDWT Bin i Wavelet ri rc ngc

JPEG Chun nn nh ca y ban JPEG quc t(Joint Photographic Experts Group)

JPEG2000 Chun nn nh JPEG2000

Lossless Compression K thut nn nh khng tn hao (khng mt d liu)

Lossy Compression K thut nn nh c tn hao (c mt d liu)

MRA Phn tch a phn gii (Multi Resolution Analysis)

MSE Sai s bnh phng trung bnh (Mean Square Error)

PCM iu xung m (Pulse Code Modulation)

PSNR T s tn hiu nh trn nhiu (Peak Signal to Noise Ratio)

QMF Lc gng cu t phng (Quardrature Mirror Filters)

RLC M ho lot di (Run Length Coding)

ROI K thut m ha nh theo vng (Region Of Interest) Mt

tnh nng mi ni bt ca JPEG2000

SPIHT Phng php m ho phn cp theo vng

(Set partitioning in hierarchical trees)

STFT Bin i Fourier thi gian ngn (Short Time Fourier

Transform)

Wavelet Bin i bng con Wavelet

Wavelet Decomposition

Tree

Cy phn gii Wavelet


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LI GII THIU

Trong nhng nm gn y, nhu cu cc dch v d liu trn mng

di ng, nht l d liu a phng tin l rt ln. Cng vi nhu cu ,

vn t ra l lm th no tm c mt k thut m ho d liu then

cht (chun), c hiu qu truyn cc d liu ny trn mng di ng.

Mc ch ca lun vn l trnh by mt k thut nn nh s dng

bin i Waveletcho nh tnh v c bit l nh tnh trong cc dch v d

liu a phng tin trong mng di ng. So vi cc k thut nn s dng

php bin i trc y nh bin i Fourier(FT), bin i cosine ri rc

(DCT), bin i xp chng (LT),.., bin i Wavelet(DWT) c nhiu u

im khng ch trong x l nh m cn nhiu ng dng khc. Bng

chng l s ra i ca chun nn JPEG2000 (da trn DWT) c tnh nng

vt tri so vi JPEG(DCT). Tuy nhin chun JPEG, MPEG hay ngay

c JPEG2000 cng ch tp trung vo hiu qu nn (t s nn) v cht

lng nh m khng ch n nng lng tiu hao trong qu trnh x lv truyn trn mng. Trong lun vn trnh by mt k thut nn nh

trong mng di ng s dng bin i Wavelethiu nng khng chem

li hiu qu nn, cht lng hnh nh m cn tit kim nng lng x l

ca h thng. iu ny ha hn c th xy dng mt b m ho nh tit

kim nng lng x l, thi gian truyn m vn ph hp vi iu kin

bng thng thp, rng buc v cht lng d liu trong cc mng thng

tin di ng.


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CHNG 1: MU

1.1. Csnghin cu v mc ch ca lun vn c th s dng cc dch v Internet khng dy cng nh nhiu

dch v d liu khc trn nn cc ng dng di ng cn c mt k thut

then cht c th h trtruyn thng nhiu dng d liu trong thng tin

di ng t bo nh: thoi, vn bn, hnh nh v video. Tuy nhin vn

truyn thng ni dung a phng tin trong thng tin di ng gp mt s

kh khn: bngthng ca mng di ng tbo, nhiu knh, gii hn ca

pin cho cc ng dng, tnh tng thch dliu gia cc thu bao. Trong

khi vic ci thin bng thng di ng cn mt cng ngh mi ca tng

lai cn vic ci thin gii hn ca pin khng p ng c s pht trin

ca cc dch v tng lai, th phng php gim kch thc d liu bng

cc k thut nn l mt cch tip cn hiu qu gii quyt cc kh khn

trn.

Mc d cho n nay c rt nhiu k thut nn d liu a phng

tin nh: chun JPEG (da trn bin i DCT), chun JPEG2000 (da

trn bin i Wavelet) v chun MPEG, tuy nhin nhng k thut ny ch

tp trung vo hiu qu nn v c gng nh mt cht lng nh t v th

chng b qua vn tiu hao nng lngtrong qu trnh nn v truyn

RF (trong thng tin ng). Lun vn ny trnh by mt k thut hiu qu

khc phc nhng kh khn trn cho loi d liu a phng tin in

hnh trong thng tin di ng l nh tnh. l k thut nn nh s dngbin i Wavelet thch nghi v hiu nng cho d liu a phng tin

trong thng tin di ng.


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1.2. T chc lun vn

Lun vn c trnh by thnh 5 chng v 1 ph lc. Chng 1,

tc gi trnh by tm tt csnghin cu v mc ch cng nh t chc

ca lun vn.

Chng 2 trnh by khi qut cc k thut nn nh, phn loi cc

nguyn l nn v nh ngha mt s thut ngc s dng rng ri nh

MSE, PSNR v SNR. Chng ny cng trnh by cs l thuyt ca cc

nguyn l nn c tn hao in hnh nh: m ho bng con; m ho da

trn bin i cosine ri rc (DCT), bin i xp chng (LT), bin i

Waveletri rc (DWT).

Chng 3 trnh by cston hc, tnh cht ca bin i Wavelet.Ni dung ca chng ny l l thut nn tng cho cc ng dng Wavelet.

Chng ny cng a ra mt s hWaveletph bin v gii thiu mt s

ng dng ni bt ca Waveletngoi ng dng nn nh.

Chng 4 gii thiu tng quan v chun nn JPEG2000 da trn

bin i Wavelet. Mc ch khng ch l gii thiu mt chun nn vt

tri so vi chun JPEG da trn bin i DCTm cn a ra mt la

chn gii quyt bi ton t ra trong lun vn. JPEG2000ang tng bc

c t chc ISO cng nhn nn chc chn s tr thnh mt chun nn

ph bin trong cc ng dng di ng tng lai. Cng trong chng ny,

tc gi trnh by tm tt cc bc thc hin nn nh theo JPEG200 v so

snh n vi chun JPEG v cc chun nn nh tnh khc.

Chng 5 cng l chng quan trng nht. Da trn k thut nn

nh bng Wavelet, lun vn a ra mt thut ton bin i nh bng

Wavelet hiu nng lm gim ng k nng lng tnh ton v truyn

thng cn thit cho nh m vn m bo c cht lng bc nh (v

nh vy gim c gi thnh dch v).


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CHNG 2:TNG QUAN CC K THUT NN

TRONG M HO NH

2.1. Gii thiu chung v nn nh s

Nn nh s l mt ti nghin cu rt ph bin trong lnh vc x

l d liu a phng tin. Mc ch l lm th no lu tr bc nh

di dng c kch thc nh hn hay di dng biu din m ch yu cu

s bt m ho t hn so vi bc nh gc. Nn nh thc hin c l do

mt thc t: thng tin trong bc nh khng phi l ngu nhin m c trt

t, c t chc. V th nu bc tch c tnh trt t, cu trc th s bit

c phn thng tin no quan trng nht trong bc nh biu din v

truyn i vi s lng bt t hn so vi nh gc m vn m bo tnh y

thng tin. pha thu, qu trnh gii m s t chc, sp xp li c

bc nh xp x gn chnh xc so vi nh gc nhng vn tho mn cht

lng yu cu, m bo thng tin cn thit.

Tm li, tn hiu nh, video hay audio u c th nn li bi chng

c nhng tnh cht nh sau: C s tng quan (d tha) thng tin v khng gian: Trong phm

vi mt bc nh hay mt khung video tn ti s tng quan ng k

(d tha) gia cc im nh ln cn.

C s tng quan (d tha) thng tin v ph: Cc d liu thu c

t cc b cm bin ca thit b thu nhn nh tn ti s tng quan

ng k gia cc mu thu, y chnh l s tng quan v ph.

C s tng quan (d tha) thng tin v thi gian: Trong mtchui nh video, tn ti s tng quan gia cc im nh ca cc

khung video (frame).


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S ca mt h thng nn d liu tng qut nh sau:

Hnh 2.1 S b khi qut h thng nn nhTrong hnh 2.1, b m ho d liu thc hin qu trnh nn bng

cch gim kch thc d liu nh gc n mt mc ph hp vi vic lu

tr v truyn dn trn knh. Tc bt u ra ca b m ho c tnh l

s bt cho mt mu (im nh). B m ho knh thc hin vic chuyn

i lung bt c nn thnh dng tn hiu ph hp c cho vic lu tr

v truyn dn, thng b m ho knh s dng cc k thut: m ho c

di thay i RLC (Run Length Coding)[4], m ho Huffman[4], m

ho shc [4]. B gii m thc hin qu trnh ngc li so vi b m

ho.

Trong cc h thng nn, t s nn chnh l tham s quan trng nh

gi kh nng nn ca h thng, cng thc c tnh nh sau:

Tsnn = Kch thc dliu gc / Kch thc dliu nn

i vi nh tnh, kch thc chnh l s bt biu din ton b bc nh.

i vi nh video, kch thc chnh l s bt biu din mt khung

hnh video (video frame).


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2.2. Phn loi cc k thut nn

Cc k thut nn ch yu c phn loi nh sau:

2.2.1. Nn tn hao v khng tn hao

Trong cc k thut nn khng tn hao (losses compression), nh khi

phc ging hon ton so vi nh gc. Tuy nhin, nn khng tn hao ch

t c hiu qu nn rt nh. Tri li, cc k thut nn c tn hao (lossy

compression) c tht c hiu qu nn cao hn rt nhiu m iu

kin cm nhn hnh nh thng thng s mt mt thng tin khng cm

nhn c v v th vn m bo cht lng nh. Mt s k thut nn c

tn hao gm: iu xung m vi sai DPCM,iu xung m PCM, lng

t ho vctVQ, m ho bin i v bng con. nh khi phc trong hthng nn c tn hao lun c s suy gim thng tin so vi nh gc bi v:

phng php nn ny loi b nhng thng tin d tha khng cn thit.

2.2.2. M ho don v m ho da trn php bin i

i vi m ho don (predictive coding) cc gi tr mang thng tin

c gi hay ang sn c sc s dng don cc gi tr khc, v

ch m ho s sai lch gia chng. Phng php ny n gin v rt ph

hp vi vic khai thc cc c tnh cc b ca bc nh. K thut DPCM

chnh l mt v din hnh ca phng php ny. Trong khi , m ho

da trn php bin i (transform based coding) th li thc hin nh sau:

trc tin thc hin php bin i vi nh chuyn s biu din nh t

min khng gian sang mt min biu din khc. Cc php bin i

thng dng l: DCT- bin i Cosine ri rc, DWT - bin i Wavelet

ri rc, LT - bin i trng (lapped) , tip thc hin m ho i vi cc

h s bin i. Phng php ny c hiu sut nn cao hn rt nhiu so

vi phng php nn don bi v chnh cc php bin i (s dng

cc thuc tnh nn nng lng ca mnh) gi gn ton b nng lng

bc nh ch bng mt s t cc h s, s ln cc h s cn li t c ngha

hn s b loi b sau khi lng t ho v nh vy lng d liu phi


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truyn nh i rt nhiu. Trong phng php m ho don, sai lch

gia nh gc v nh don vn c ngha (cn s dng bc tip

theo) sau khi lng t ho, chnh iu ny lm cho phng php m ho

don c nhiu d liu c truyn i hn so vi phng php m ho

bin i.

2.2.3. M ho bng con

Bn cht ca k thut m ho bng con (subband coding) l chia bng tn

ca tn hiu (nh) thnh nhiu bng con (subband). m ho cho mi

bng con, chng ta s dng mt b m ho v mt tc bt tng ng

vi tnh cht thng k ca bng con.

2.3. Tiu chun nh gi cht lng m ho nhnh gi cht lng ca bc nh (hay khung nh video) u

ra ca b m ho, ngi ta thng s dng hai tham s: Sai s bnh

phng trung bnh MSE (mean square error) v t s tn hiu trn

nhiu nh PSNR(peak to signal to noise ratio). MSEthng c gi

l phng sai lng t - 2q (quantization error variance). MSEgia nh

gc v nh khi phc c tnh nh sau:

( )22

,

1[ , ] - [ , ]q

j k

MSE f j k g j k N

= = (2.1)

Trong tng ly theo j, ktnh cho tng tt c cc im nh trong nh v

Nl sim nh trong nh. Cn PSNR gia hai nh (b bt cho mi im

nh, RMSEl cn bc 2 ca MSE) c tnh theo cng thc dB nh sau:

12log20 10

=

b

RMSEPSNR (2.2)

Thng thng, nu PSNR 40dB th h thng mt ngi gn nh khng

phn bit c gia nh gc v nh khi phc.

Mt tham s khc hay s dng trong cc h thng vin thng l t s

tn hiu trn nhiu - SNR , tuy vy SNR s dng cho mt h thng n nh

cng c cng thc dB nh sau:


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1010log Encoder input energy

SNRNoise energy

= (2.3)

2.4.Cc k thut nn c tn hao

Trong phn ny, tc gi la chn trnh by hai k thut nn tn hao

cho nn nh tnh v nh ng l: m ho bng con (subband coding)

v m ho s dng php bin i (transform coding). y l hai k thut

nn in hnh v cho hiu qu nn cng nh cht lng nh cao.

2.4.1. K thut m ho bng con

T tng chnh ca k thut m ho bng con l: cc nh c ly

mu u vo c phn ly thnh cc bng tn khc nhau (gi l cc tn

hiu bng con). Yu cu ca k thut ny l lm th no cc bng con

khng b chng cho ln nhau. c th phn ly tn hiu b m ho

(encoder) thnh cc bng con, nh c cho qua mt bank lc (filter

bank) gi l bank lc phn tch v mi u ra ca bank lc bng con c

ly mu xung h s 2. Cc u ra bng con tn sc ly mu xung

s ln lt c: lng tho c lp bng cc b lc v hng khc

nhau, m ho entropy, lu trv truyn i. pha b gii m (decoder),qu trnh c thc hin ngc li: gii lng t bng con tn s, ly

mu ln vi h s 2, cho i qua bank lc bng con tng hp ri cng tt

c cc u ra ca b lc khi phc li nh.

Cc b lc bng con thng c thit k xp x tho mn tiu

chun ca cc p ng tn s khng chng cho. Mc ch l gii

tng quan cc h s tn s kt qu. y chnh l tnh cht quan trng m

qu trnh lc bng con c gng t c. Cc b lc bng con c thitk l cc xp x vi cc b lc chn tn s l tng, trong p ng

tng hp t tt c cc b lc bao trm tt c bng tn ca nh. Tuy nhin

trong thc t, s tng quan tng khng bao git c do nhng b

lc ny ch xp x vi cc b lc l tng.


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Hnh 2.2 di y l s tng qut gii thch k thut m ho bng con.

Hnh 2.2. S minh ho k thut m ho bng con M bng con

Cc b lc s dng trong m ho bng con l cc b lc gng t

phng QMF (quardrature mirror filters), do vy chng ta ch cn

thit k cc b lc thng thp c p ng H() cn p ng ca cc b

lc thng cao l H(+)ch l s dch pha 180o so vi b lc thng thp.

S chnh xc ca b lc ph thuc vo s cc h s ca b lc.

Mt trong cc phng php m ho bng con l p dng s phn ly

cy bt phn phn ly d liu nh thnh cc bng tn khc nhau. tng ca phng php ny l: trc tin lc v lc bnh phn ly

nh thnh cc bng con tn s cao v thp, sau tip tc phn ly nhng

ch p dng cho bng con tn s thp to thnh cc bng con tn s

cao v thp tip tc lc b. K thut ny rt ph bin v cng c


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p dng trong cc b m s dng bin i Wavelet. u ra ca cc bng

con sau khi gin lc sc lng t ho v m ho c lp. Mi

bng con s s dng b lng t ho ring v mi b lng t ho ny c

tc ly mu ring (bt/mu).

Nh vy r rng m ho bng con khng t c s nn, m n

ch thc hin vic gii tng quan dnh gc v tp trung nng lng

ca nh vo mt s bng con. Nn cht c l do s lc b nh

(decimation) v do s lng t ho (quantization).

Hnh 2.3 Minh ho qu trnh phn ly bng con cy bt phn

Trong cc h thng m ho bng con hai chiu thc t, ngi ta chia mintn s - khng gian hai chiu ca nh gc thnh cc bng khc nhau bt

k mc no.

Hnh 2.4 di y minh ho vic phn ly 2 nh mu thnh 4 bng con LL,

HL, LH v HHmc u tin.


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Hnh 2.4. Phn ly hai nh mu thnh bn bng con

Nhc im ca k thut m ho bng con:

Mt trong nhng vn ch yu ca k thut m ho bng con

l gii quyt bi ton cp pht bt (l s bt cp cho mi bng con) t

c hiu sut cao nht. Mt trong nhng cch thc hin l s dng

tng cp pht bt ti u cho mi u ra bng con c lng t ho.

Tuy nhin cch ny ch yu thch hp cho trng hp tc cao

(1bt/mu).

Trc khi i vo nghin cu k thut m ho da trn php bin

i, chng ta s tng kt mt s nhc im ca k thut m ho bng

con nh sau:

K thut m ho bng con khng xc nh c h thng m ho ti u

cho cc ng dng tc bt thp.

Vic cp pht bt ti u s thay i khi tc bt tng thay i,

iu ny lm qu trnh m ho phi lp li hon ton cho mi tc bt

xc nh.


19/67


Ngc Anh

Khng hon ton gii tng quan cho tt c cc bng tn, y l do

cc b lc khng phi l l tng v c s chng cho nh gia cc bng

tn lin k. Do vy lun lun tn ti mt s tng quan nh gia cc

bng tn k nhau v d liu s khng c nn hon ton.

K thut m ho bng con khng hiu qu khi thc hin b chuyn ng

trong video v rt kh thc hin nh gi chuyn ng cc bng con

(sai s don l rt ln).

2.4.2. K thut m ho da trn php bin i

Mt php bin i l mt hm ton hc c s dng bin i

mt tp cc gi tr ny thnh mt tp gi tr khc v to ra mt cch biudin mi cho cng mt ngun tin. Tt c cc php bin i m chng ta

nh trnh by di y u l khng tn hao (lossless); vi s chnh xc

ca cc php ton s hc th cc php bin i vn bo tn c chnh

xc bt k mc no. Nhng hu ht cc k thut m ho u c tn

hao bc lng t ho do c s lm trn gi tr cho cc h s php bin

i.

Phn ny chng ta s trnh by cc k thut m ho da trn php bin

i c s dng trong nn nh.

(a) K thut m ho da trn php bin i cosine ri rc DCT

(b) K thut m ho da trn php bin i chng LT

(c) K thut m ho da trn php bin i DWT

2.4.2.1. K thut m ho da trn php bin i DCT

Php bin i cosine ri rc DCT (Discrete Cosine Transform)

bin i thng tin nh t min khng gian sang min tn s c th biu

din di dng gn hn. Tnh cht ca n tng t nh bin i Fourier,

coi nh u vo (tn hiu audio hoc video) l cc tn hiu n nh bt


20/67


Ngc Anh

bin theo thi gian. hiu r k thut ny trc ht ta cn tm hiu bin

i Fourier.

Bin i FourierFT

Bin i Fourier FT (Fourier Transform) l mt php bin i

thun nghch, n cho php s chuyn i thun nghch gia thng tin

gc (min khng gian hoc thi gian) v tn hiu c x l (c bin

i). Tuy nhin mt thi im bt k ch tn ti mt min thng tin

c th hin. Ngha l tn hiu trong min khng gian khng c s xut

hin thng tin v tn s v tn hiu sau bin i Fourierkhng c s xut

hin thng tin v thi gian.

FTcho bit thng tin tn s ca tn hiu, cho bit nhng tn s noc trong tn hiu, tuy nhin n khng cho bit tn s xut hin khi no

trong tn hiu. Nu nh tn hiu l n nh (stationary c cc thnh

phn tn s khng thay i theo thi gian) th vic xc nh cc thnh

phn tn s xut hin khi no trong tn hiu l khng cn thit.

Php bin i FTthun v nghch c nh ngha nh sau:

X(f) =

dtetx ftj2)( (2.4)

x(t) =

dfefX ftj2)( (2.5)

Php bin i FTcng c thc p dng cho tn hiu khng n nh

(non-stationary) nu nh chng ta ch quan tm n thnh phn ph no

c trong tn hiu m khng quan tm n n xut hin khi no trong tn

hiu. Tuy nhin, nu thng tin v thi gian xut hin ca ph trong tn

hiu l cn thit, th php bin i FTkhng c kh nng p ng c

yu cu ny, y cng l hn ch ca php bin i ny.

c bin i Fourierri rc DFT(Discrete Fourier Transform) th

php tch phn trong biu thc ton hc ca bin i FT, ta thay bng

php tng v tnh ton n vi cc mu hu hn.


21/67


Ngc Anh

H s php bin i DFT thkca mt chui gm Nmu {x(n)}c

nh ngha:

X(k) =

=

1

0

)(N

n

kn

NWnx , k=0,., N-1 (2.6)

Trong WN= e Nj /2 = cos (2/N) j sin (2/N), cn chui {x(n)} c th

khi phc bng DFTngc nh sau:

x(n) =N

1

=

1

0

)(N

k

kn

NWkX , n=0,., N-1 (2.7)

nh ngha v cc tnh cht ca bin i DCT

Bin i DCT thun v ngc mt chiu gm Nmu c nh ngha

nh sau:

DCT= X(k) =N

2ck

=

+1

0 2

)12(cos)(

N

n N

knnx

, k= 0,1,,N-1 (2.8)

IDCT = x(n) =N

2

=

+1

0 2

)12(cos)(

N

k

kN

knkXc

, n= 0,1,,N-1 (2.9)

Trong ck=

=

0,1

0,2/1

k

k

CDCTv IDCTu l bin i trc giao, tch bit v thc. Tnh cht

phn tch (separable)y ngha l bin i nhiu chiu ca n c th

phn tch thnh cc bin i mt chiu. Tnh cht trc giao y ngha

l nu cc ma trn ca DCTv IDCTl khng bt thng (non-singular)

v thc th bin i ngc ca chng c tht c bng cch p dng

ton t hon v. Cng nh bin i FT, DCT cng coi d liu u vo l

tn hiu n nh (bt bin).

Trong cc chun nn nh tnh vo video, ngi ta thng s dng DCT

v IDCTc kch thc 8 mu. Bc nh hoc khung nh video kch thc

NxNc chia thnh cc khi khng chng cho nhau hai chiu gi l

cc nh con kch thc 8x8 ri p dng bin i DCT hai chiu b m

ho v p dng bin i IDCTb gii m.

Bin i DCTv IDCT8 mu to thnh cc ma trn 8x8 theo cng thc:


22/67


Ngc Anh

2-D DCT = Xk,l=4

)()( lckc

= =

+

+7

0

7

0, 16

)12(cos

16

)12(cos

m n

nm

lnkmx

(2.10)

Trong k,l = 0,1,..,7

2-D IDCT= xm,n =

= =

+

+7

0

7

0 lk,

16

1)l(2ncos

16

1)k(2mcosX

4

)()(

k l

lckc (2.11)

Trong m,n = 0,1,..,7

v c(k),c(l)=

+

=

0,1

0&,2/122 lk

lk

Thut ton tnh 2-D DCTv IDCTl: thc hin php bin i 1-D ln

lt cho hng ri n ct ca ma trn.

So snh DCTv KLT

Hiu qu ca bin i DCT trong vic gii tng quan tn hiu nh tng

ng vi bin i Karhunen-Loeve (KLT). KLT l php bin i theo

khi ti u nht cho nn d liu kha cnh thng k bi: n c th gii

tng quan mt cch ti u tn hiu nh trong min php bin i (bng

cch tp trung hu ht thng tin nh vo mt s h s ca php bin i)

v so vi cc php bin i khc n c th ti thiu ho MSEgia nh

khi phc v nh gc.Nn v gii nn nh da theo php bin i DCT trong JPEG

JPEG l chun nn s quc tu tin cho cc nh tnh c tng

mu lin tc gm c nh n sc v nh mu. Trong k thut ny cc

khi nh kch thc 8x8 c p dng thc hin DCT, sau lng t

ho cc h s ri m ho entropy sau lng t.

i vi nhng nh mu RGB, p dng k thut nn ny, trc

ht phi chuyn sang ch mu YUV(Yl thnh phn chi, Uv Vl 2thnh phn mu). Thnh phn chi l nh n sc xm. Hai thnh

phn mu cn li cha thng tin v mu. Vic m ho v gii m nh

trong JPEGc thc hin cho thnh phn chi ri mu.

S khi b m ho v gii m ca JPEG nh sau:


23/67


Ngc Anh

Hnh 2.5. S b m ho theo chun JPEG

Hnh 2.6. Sp xp Zigzag cc h s DCT b m ho

Hnh 2.7. S khi b gii m theo chun JPEG

Qu trnh x l thnh phn chi pha m ho c gii thch nh

sau:

(a) nh gc c chia thnh cc khi nh (block) nh kch thc 8x8

khng chng cho ln nhau. Tip theo, gi tr ca mi im nh


24/67


Ngc Anh

mi khi khi nh sc tri 128. L do l do gi tr cc im

nh c gi tr t 0 n 255 (c m ho bi 8 bt khng du), p

dng bin i DCT s to ra cc h s AC c di gi tr t -1023 n

+1023 (c thc m ho bi 11 bt c du). Nhng h s DC li c

gii gi tr t 0 n 2040 (c m ho bi 11 bt khng du) v cn

cch x l khc phn cng hoc phn mm so vi cc h s AC.

Chnh v th vic tr gi tr mi im nh i 128 l sau khi bin

i DCT c cc h s DC v AC c cng di gi tr thun li cho vic

x l v biu din.

(b) mi khi nh hai chiu kch thc 8x8, p dng bin i DCT

to ra mng hai chiu cc h s bin i. H s c tng ng vi tns khng gian thp nht nhng li c gi tr ln nht c gi l h s

DC (mt chiu), n t l vi chi trung bnh ca c khi nh 8x8.

Cc h s cn li gi l cc h s AC (xoay chiu). Theo l thuyt,

bin i DCT khng em li s mt mt thng tin nh, m n gin

n ch chuyn thng tin nh sang min khng gian mi thut li hn

cho m ho bc tip theo.

(c) Mng hai chiu cc h s bin i c lng t ho s dng b

lng t ha t lng nht. Ngha l cc h s sc lng t ho

ring l v c lp. Qu trnh lng t ho l da trn sinh l ca h

thng mt ngi: cm nhn hnh nh c nhy km hn cc h s

tn s cao v c nhy tt hn cc h s c tn s thp. V th cc

h sc chn sao cho thc hin lng t ho th i vi cc h s

tn s cao v lng t ho tinh i vi cc h s c tn s thp. Bng

lng t ho c ly t l to ra cc mc nn thay i tu theo

tc bt v cht lng nh. Vic lng t ho s to ra rt nhiu gi

tr 0, c bit l tn s cao. Qu trnh lm trn trong khi lng t

ho chnh l nguyn nhn chnh gy ra s tn hao nhng li l nhn

t chnh em li hiu sut nn.


25/67


Ngc Anh

(d) tn dng u im ca cc h s c lng t c gi tr gn

bng 0, mng hai chiu cc h s c lng t sc sp xp

theo hnh Zigzag to thnh mng mt chiu. Cch sp xp ny cho

php gim thiu nng lng tn hao trung bnh v to ra dy cc gi

tr bng 0 lin tip. Cng theo cch sp xp ny, cc h s DC c

tch khi cc h s AC v s dng k thut m ho iu xung m vi

sai DPCM.

(e) Bc cui cng ca b m ho l s dng m ho entropy chng hn

m ho Huffman cho cc AC v DC (sau khi m ho DPCM)

tng thm hiu qu nn cng nh gim thiu li.

pha gii m, lung bt m ho c gii m entropy, sau mng haichiu cc h s DCT c lng t ho c gii sp xp Zigzag v

gii lng t. Mng hai chiu cc h s DCT kt qu sc bin i

IDCT ri cng mi gi tr vi 128 xp x to thnh cc khi nh con

kch thc 8x8. Ch l bng lng t ho v m ho entropy c pha

m ho v gii m l ng nht.

Hai thnh phn mu cng c m ho tng t nh thnh phn chi

ngoi tr khc bit l chng c ly mu xung h s 2 hoc 4 c

chiu ngang v dc trc khi bin i DCT. pha gii m , thnh phn

mu sc ni suy thnh kch thc gc.

2.4.2.2. K thut m ho da trn php bin i DWT

Mi quan h gia bin i Waveletv Fourier

Khng ging nh bin i Fourierch thch hp khi phn tch nhng tn

hiu n nh (stationary),Waveletl php bin i c s dng phn

tch cc tn hiu khng n nh (non-stationary) l nhng tn hiu c

p ng tn s thay i theo thi gian.

khc phc nhng hn ch ca bin i FT, php bin i Fourierthi

gian ngn STFTc xut. Ch c mt s khc bit nh gia STFT

v FT: Trong bin i STFT, tn hiu c chia thnh cc khong nh v


26/67


Ngc Anh

trong khong tn hiu c ginh l tn hiu n nh. thc hin

k thut ny cn chn mt hm ca sw sao cho di ca ca sng

bng cc khong tn hiu phn chia. Vi php bin i STFT, chng ta c

th thu c p ng tn s - thi gian ca tn hiu ng thi m vi

php bin i FTta khng thc hin c.

Bin i STFTi vi tn hiu lin tc thc c nh ngha nh sau:

X(f,t) =

dtetwtx ftj 2* ])()([ (2.12)

Trong di thi gian ca ca s l (t-), chng ta c th dch chuyn

v tr ca ca s bng cch thay i gi trtv thu c cc p ng

tn s khc nhau ca on tn hiu ta thay i gi tr .Gii thch bin i STFTbng nguyn l bt nh Heissenber, nguyn l

ny pht biu l: Khng thbitc chnh xc c biu din thi gian

- tn sca mt tn hiu (hay khng thbit cc thnh phn phca tn

hiu mt thi im nht nh). Ci m ta c th bit l trong mt

khong thi gian nht nh tn hiu c nhng bng tn no. y c gi

l bi ton phn gii. Vn ny lin quan n rng ca hm ca s

m chng ta s dng. Nu hm ca s cng hp th phn gii cng tthn v ginh tn hiu l n nh cng c chnh xc nhng phn

gii tn s li km i. Ta c cc h qu sau:

Ca shp -> phn gii thi gian tt, phn gii tn skm

Ca srng -> phn gii tn stt, phn gii thi gian km

Trn cscch tip cn bin i STFT, bin i Waveletc pht trin

gii quyt vn v phn gii tn hiu (min thi gian hoc tn s)

m STFTvn cn hn ch. Bin i Waveletc thc hin theo cch:

tn hiu c nhn vi hm Wavelet(tng t nh nhn vi hm ca s

trong bin i STFT), ri thc hin bin i ring r cho cc khong tn

hiu khc nhau trong min thi gian ti cc tn s khc nhau. Cch tip


27/67


Ngc Anh

cn nh vy cn c gi l: phn tch a phn gii MRA (Multi

Resolution Analysis): phn tch tn hiu cc tn s khc nhau v cho

cc phn gii khc nhau.

MRA khi phn tch tn hiu cho php: phn gii thi gian tt v phn gii

tn skm cc tn scao; phn gii tn s tt v phn gii thi gian

km cc tn sthp. Nh vy k thut ny rt thch hp vi nhng tn

hiu: c cc thnh phn tn s cao xut hin trong khong thi gian ngn,

cc thnh phn tn s thp xut hin trong khong thi gian di chng

hn nhnh v khung nh video.

C s ton hc cng nh cc tnh cht ca bin i Waveletlin tc s

c trnh by chi tit trong chng 3.Bin i Waveletri rc DWT

Bc ny c th hiu php bin i DWTnh l p dng mt tp cc b

lc: thng cao v thng thp. Thit k cc b lc ny tng ng nh k

thut m ho bng con (subband coding) ngha l: ch cn thit k cc b

lc thng thp, cn cc b lc thng cao chnh l cc b lc thng thp

dch pha i mt gc 180o. Tuy nhin khc vi m ho bng con, cc b

lc trong DWTc thit k phi c p ng phphng, trn v trc

giao.

Hnh 2.11 di y minh ho dng tng qut ca bin i DWT mt

chiu. Theo tn hiu c cho i qua cc b lc thng cao v thng

thp Hv G ri c ly mu xung (down sampling) h s 2 to thnh

bin i DWTmc 1. Bin i ngc th thc hin ngc li: ly mu ln

(up sampling) h s 2 ri s dng cc b lc khi phc H, G(l tng

l Hv Gchnh l H, G).


28/67


Ngc Anh

Hnh 2.8. Bank lc khi phc l thuyt sdng DWT 1D

T bin i DWTmt chiu c th mrng nh ngha bin i DWThai

chiu theo cch: S dng cc b lc ring bit, thc hin bin i DWT

mt chiu d liu vo (nh) theo hng ri thc hin theo ct. Theo cch

ny nu thc hin bin i DWTmc 1, s to ra 4 nhm h s bini. Qu trnh bin i DWThai chiu c th minh ho nh hnh 2.12

di y, trong 4 nhm h s l: LL, HL, LH, HH (ch ci u tin

tng ng thc hin lc theo hng, ch ci th hai tng ng thc

hin lc theo ct).

Hnh 2.9. Minh hoDWThai chiu cho nh

Hnh 2.10(a). Minh hoDWTkiu dyadic mc 3 nn nh


29/67


Ngc Anh

Hnh 2.10(b). Minh hoDWTkiu dyadic mc 3 nn nh

Hai thut ton nn sdng DWTin hnh

So vi bin php bin i DCTs dng trong chun nn JPEG ra

i 1992, nn nh da trn bin i DWT c nhng ci tin ng k.

Tuy nhin ci tin mang tnh t ph s dng DWT nn nh bt u l

k thut m ho EZW(embedded zero-tree wavelet).

Thut ton EZW da trn kh nng khai thc cc thuc tnh a

phn gii ca bin i Waveleta ra mt thut ton t phc tp trong

tnh ton m vn cho hiu qu nn cao. Nhng ci tin v nng cp ca

EZW v sau ra i mt s thut ton tng t nh: SPIHT (set

partitationing in hierarchical tree cy phn cp phn tp) v ZTE

(zero-tree entropy coding m ho entropy cy zero).

Gn y cn c thm mt thut ton na c xut l LS

(lifting scheme) s dng to cc bin i Wavelets nguyn. K thutny s dng cc b lc Wavelettrc giao em li hiu qu rt cao cho cc

ng dng nn nh c tn hao. Chng ta s trnh by 3 thut ton in

mnh ny chng 3.


30/67


Ngc Anh

CHNG 3:C S L THUYT BIN I

WAVELET

3.1. Cston hc

3.1.1. Bin i Waveletlin tc

Bin i Waveletlin tc (ContinuousWaveletTransform - CWT)

ca mt hm ( )f t c bt u t mt hm Wavelet m (mother

Wavelet) ( )t . Hm Waveletm ( )t c th l bt k mt hm s thc

hoc phc lin tc no tho mn cc tnh cht sau y:

Tch phn suy rng trn ton b trc tca hm ( )t l bng 0. Tc l:

( ) 0t dt

= (3.1)

Tch phn nng lng ca hm trn ton b trc t l mt s hu

hn, tc l:

( )2

t dt

< (3.2)

iu kin (3.2) c ngha l hm ( )t phi l mt hm bnh phng kh

tch ngha l hm ( )t thuc khng gian ( )2L R cc hm bnh phng kh

tch.

Sau khi hm Wavelet ( )t c la chn, bin i Waveletlin tc

ca mt hm bnh phng kh tch ( )f t c tnh theo cng thc:

( ) ( ) *1

,t b

W a b f t dt aa

=

(3.3)

Bin i ny l mt hm ca hai tham s thc a v b. Du * k hiu llin hip phc ca ( )t . Nu chng ta nh ngha mt hm ( ),a b t theo

biu thc:

( ),1

a b

t bt

aa

=

(3.4)


31/67


Ngc Anh

chng ta c th vit c:

( ) ( ) ( ),, a bW a b f t t dt

= (3.5)

Theo ton hc ta gi y l tch v hng ca hai hm ( )f t v ( ),a b t .

Gi tr 1a

l h s chun ho m bo rng tch phn nng lng ca

hm ( ),a b t sc lp vi a v b :

( ) ( )2 2

,a b t dt t dt

= (3.6)

Vi mi gi tr ca a th ( ),a b t l mt bn sao ca ( ),0a t c

dch i b n v trn trc thi gian. Do b c gi l tham s dch.t tham s dch 0b = ta thu c:

( ),01

a

tt

aa

=

(3.7)

iu cho thy rng a l tham s t l.

Khi 1a > th hm Wavelet sc tri rng cn khi 0 1a< < th

hm sc co li. Sau y chng ta snh ngha php bin i ngc

ca bin i Waveletlin tc. Gi ( ) l bin i Fourierca ( )t :

( ) ( ) j tt e dt

= (3.8)

Nu ( ),W a b l bin i CWT ca ( )f t bng hm Wavelet ( )t , th

bin i ngc ca bin i CWT sc tnh nh sau:

( ) ( ) ( ),21 1

, a bf t W a b t dadbC a

= (3.9)

vi gi tr ca Cc nh ngha l:

( )2

C d

= (3.10)

Bin i CWT ch tn ti nu C dng v hu hn. Do Cc

gi l iu kin tn ti ca bin i Wavelet. Cng vi hai iu kin


32/67


Ngc Anh

nu trn, y l iu kin th 3 m mt hm cn phi tho mn c

thc la chn lm hm Wavelet. Chng ta c th xem bin i CWT

nh l mt ma trn hai chiu cc kt qu ca php tnh tch v hng

gia hai hm ( )t v ( ),a b t . Cc hng ca ma trn tng ng vi cc gi

tr ca a v cc ct tng ng vi cc gi tr ca b do cch tnh bin i

Wavelettheo tch v hng trnh by trn:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )* , ,, , a b a bf t g t f t g t dt f t t f t t dt

= = (3.11)

3.1.2. Bin i Waveletri rc

Vic tnh ton cc h sWaveletti tt c cc t l l mt cng vic

ht sc phc tp. Nu tnh ton nh vy s to ra mt lng d liu

khng l. gim thiu cng vic tnh ton ngi ta ch chn ra mt tp

nh cc gi tr t l v cc v tr tin hnh tnh ton. Hn na nu vic

tnh ton c tin hnh ti cc t l v cc v tr trn cslu tha cs

2 th kt qu thu c s hiu qu v chnh xc hn rt nhiu. Qu trnh

chn cc t l v cc v tr tnh ton nh trn to thnh li nh t

(dyadic). Mt phn tch nh trn hon ton c th thc hin c nh

bin i Waveletri rc (DWT). Do , vic tnh ton bin i DWTthccht l s ri rc ho bin i Waveletlin tc (CWT); vic ri rc ho

c thc hin vi s la chn cc h s a v b nh sau:

2 ; 2 ; ,m ma b n m n Z = = (3.12)

Vic tnh ton h s ca bin i Waveletc th d dng thc hin

bng cc bng lc snhiu nhp a knh, mt l thuyt rt quen thuc

trong x l tn hiu.


33/67


Ngc Anh

Shift n

m = -2

m = -1

m = 0

m = 1

m = 2

Hnh 3.1. Minh ho li nh t dyadic vi cc gi tr ca m v n

3.2. Tnh cht ca bin i Wavelet

Tt c chng ta u bit rng bin i Fourierl mt bin i

v ang c p dng rng ri trong nhiu ngnh khoa hc v k thutkhc nhau. Bin i Fourierchuyn mt hm tn hiu t min thi gian

sang min tn s. S dng bin i Fourierta c th bit c trong tn

hiu ( )f t c cc thnh phn tn s no. Tuy nhin bin i Fourierc

mt nhc im cbn l vi mt tn hiu ( )f t ta khng th bit c

rng ti mt thi im t th tn hiu c cc thnh phn tn s no. Mt

php bin i tt hn bin i Fourierphi l php bin i c y

tnh nng ca bin i Fourierv c kh nng xc nh xem ti mt thi

im t bt k trong tn hiu ( )f t c thnh phn tn s no. Php bin i

Waveletra i khc phc c cc nhc im ca bin i Fourier

trong phn tch tn hiu. Bin i Waveletd ch lm vic vi cc tn hiu

mt chiu (lin tc hoc ri rc) nhng sau khi bin i xong ta thu c

mt hm s hai bin hoc mt tp cc cp gi tr ( ),W a b minh ha cc

thnh phn tn s khc nhau ca tn hiu xy ra ti thi im t. Cc gitr ( ),iW a b to thnh mt ct (i=1, 2,...., n) cho bit mt thnh phn tn s

c trong nhng thi im t no v cc gi tr ( ), iW a b to thnh hng cho

bit ti mt thi im t ca tn hiu ( )f t c cc thnh phn tn s no.

c nghin cu t trc nhng nm 80 ca th k trc v cng


34/67


Ngc Anh

c ng dng trong mt s ngnh khoa hc v cng ngh khc nhau

nhng bin i Wavelet vn l mt lnh vc ang v s tip tc c

nghin cu v pht trin cng nhng dng rng ri hn na. Tham sb

trong bin i Waveletcho bit khong dch ca hm Waveletm v

phn gii cc tn s khc nhau ca ( )f t c minh ha bi h s t l

chnh l a. Bin i Waveletngy cng c p dng rng ri c bit l

trong x l ting ni, x l nh s. Tn hiu ting ni l tn hiu mt

chiu nhng do c im ca ting ni l tn hiu khng dng nn vic s

dng Fourierl khng phn tch mt cch y cc c trng ca

ting ni. Khc vi tn hiu ting ni, x l tn hiu nh s l x l tn

hiu hai chiu v do c im ca nh s l bao gi cng c tnh nhhng v tnh nh v. Tnh nh hng ca mt nh ngha l trong nh

bao gicng c mt s t cc thnh phn tn s nhng cc thnh phn tn

s ny tri rng trn ton b khng gian nh cn tnh nh v ca nh

chnh l tnh cht biu th rng ti mt vng ca nh c th c rt nhiu

thnh phn tn s. nh biu th tnh nh v r nht chnh l nh c nhiu

bin vng phn tch r rt, ti cc ng bin bao gi cng c nhiu

thnh phn tn s khc nhau, cn hu ht cc nh c tng lin tc u l

nhng nh c tnh nh hng.

Ngoi ra ngi ta thng p dng mt cch kt hp bin i

Waveletvi cc hm Waveletthch hp vi dng tn hiu cn kho st v

php phn tch a phn gii vic x l tn hiu ting ni v hnh nh

t hiu qu cao hn. Trc khi xem xt ng dng ca phn tch a phn

gii trong nn nh, chng ta xem xt l thuyt va phn gii trong phn

tch tn hiu. Gi s chng ta cn xp x ho mt tn hiu lin tc c dng

mt hm bnh phng kh tch ( )f x bng mt tp cc gi tr ri rc (v

d hm ( )f x l hm cng sng ca nh). Php xp xn gin thc


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hin da trn l thuyt php ly trung bnh v da vo hm xp x l hm

( )x c dng:

( )[ )1 0,1

0

xx

=

cc gi tr cn li(3.13)

Vic tnh ton cc gi tr xp x ca hm ( )x theo hm ( )x sc

vit nh sau:

( ) ( )nn

A f x f x n= (3.14)

vi nf l chnh l gi tr xp x ca hm ( )f x trong khong [ ); 1n n + . y

chnh l gi tr trung bnh ca hm ( )f x trong khong [ ); 1n n + c cho

bi biu thc:

( )1n

nn

f f x+

= (3.15)

Nh vy chng ta c th xp x ho hm ( )f x bng mt tp cc hm

tng t nh hm ( )x v php xp x ho hm ( )x cho bi:

( ) ( ) ( ) ( ),n

A f x x n f x x n = % (3.16)

y ( )x% c gi l hm trng v ( )x l hm ni suy, xp x

( )x tho mn:

( ) ( ) [ ],x x n n =% (3.17)

Vic phi tho mn iu kin 3.17 l m bo rng hm ( )x c th

c xp x ho bng mt t hp tuyn tnh ca cc hm ( )x n . Ngoi

ra hai hm ( )x% v ( )x phi c chun ho tho mn:

( ) ( )2 2

1x dx x dx = = % (3.18)Trong thc t, hm ( )f x thng c gi thit l c chu k nguyn v

chng ta ch cn mt s hu hn cc t hp tuyn tnh xp x ho hm

( )f x . Chng ta c th thay i phn gii ca php xp x bng cch


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thay i h s t l ca cc hm ( )x% v ( )x . Cho ( ) ( )22 2j

j jx x = v

( ) ( )22 2j

j jx x =% % , chng ta c xp x:

( ) ( ) ( ) ( ), 2 2j j j j j

kA f x f x x k x k

=

%

(3.19)

ca hm ( )f x l cc php chiu trc giao ca hm ( )f x ln khng gian

ly ( ){ }2j jk

x k

lm cs. Vic thay i gi tr ca j s lm thay i

mc chnh xc ca php xp x hm ( )f x ca chng ta nh trn hnh

3.2.

Hnh 3.2. Phn tch a phn gii p dng cho biu din tn hiu

Hm ( )x c gi l hm t l v chng ta thy hm ny c mt

tnh cht c bit l cc hm ng vi phn gii th j (tc l c chiu

rng 2 j ) l trng hp c bit ca cc hm c phn gii th 1j +

(chiu rng 12 j ) bi v cc hm c phn gii j c th d dng biu

din t cc hm c phn gii 1j + . iu dn ti:

1j jV V+

V vy chng ta c th biu din hm ( )x theo cc mc phn gii khc

nhau da trn cc php chiu trc giao ca hm ( )x ln cc khng gian

jV . Chnh v th ngi ta nh ngha mt php phn tch a phn gii nh

sau:


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*. Mt phn tch a phn gii bao gm mt chui khng gian bao

hm nhau:

2 1 0 1 2.... ...V V V V V (3.20)

tho mn:( )2j

j Z

V L R

=U (3.21)

{ }0jj Z

V

=I (3.22)

Tnh bt bin t l

( ) ( ) 02 jjf x V f x V (3.23)

Tnh bt bin dch:( ) ( )0 0x V f x n V n Z (3.24)

Tnh tn ti ca cs

Tn ti 0V vi ( ){ }x n n Z (3.25) l mt cstrc chun ca

0V

*. Nu chng ta gi ( ) ( )mV

f x proj f x= l hnh chiu trc giao

ca ( )f x ln mV , th ta c: ( ) ( )lim mm Vproj f x f x = (3.26)Trn y l csl thuyt ca php phn tch a phn gii vi tn

hiu 1D tng qut. Vic p dng trong tn hiu nh (tn hiu 2D) c th d

dng m rng t vic phn tch a phn gii 1D, chng ta s xt ti

phn p dng trong JPEG2000phn sau

3.3. Gii thiu mt s hWavelet

3.3.1. Bin i WaveletHaar

Bin i Haar Wavelet l bin i n gin nht trong cc php

bin i Wavelet. Hnh v 3.2 cho thy dng ca hm ( )t vi bin i

Haar. Do tnh cht n gin ca bin i Haarm n c ng dng

tng i nhiu trong nn nh, khi p dng bin i ny nn nh th


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Ngc Anh

thut ton nn nh trn my tnh c mt sim khc vi cng thc ton

hc ca bin i Haar

Hnh 3.3. Hm ( )t ca bin i Haar

3.3.2. Bin i WaveletMeyer

Yves Meyerl mt trong nhng nh khoa hc t nn mng cho

php bin i Wavelet. Php bin i Waveletmang tn Meyercng l

mt php bin i thng dng, bin i ny c kh nng phn tch tnhiu tt hn nhiu so vi bin i Haar. Dng ca hm ( )t vi bin i

Meyercho hnh v:

Hnh 3.4: Hm ( )t ca bin i Meyer

3.3.3. Bin i WaveletDaubechies

Ging nhMeyer, Daubechies cng l mt nh khoa hc c cng

lao to ln trong vic nghin cu pht trin php bin i Wavelet. Bin

i Daubechies l mt trong nhng php bin i phc tp nht trong

bin i Wavelet. H bin i ny c ng dng ht sc rng ri, bin

i Waveletp dng trong JPEG2000 l mt bin i trong h bin i


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Wavelet Daubechies. Di y l mt s hm ( )t trong h bin i

WaveletDaubechies:

Hnh 3.5. Hm ( )t ca h bin i Daubechies n vi n=2, 3, 7, 8

3.4. Mt sng dng ni bt ca Wavelet

Phn ny ch nu ra cc lnh vc mang tnh cht tng qut cc ng

dng ca Waveletvi tnh cht gii thiu v gi m.3.4.1. Nn tn hiu

Do c im ca mnh, Waveletc bit tt khi s dng nn hay

phn tch cc tn hiu khng dng; c bit l tn hiu nh s v cc ng

dng nn ting ni, nn d liu. Vic s dng cc php m ho bng con,

bng lc s nhiu nhp v bin i Waveletri rc tng ng vi loi tn

hiu cn phn tch c th mang li nhng hiu qu rt r rt trong nn tn

hiu. Do tnh cht ch tn ti trong cc khong thi gian rt ngn (khiphn tch tn hiu trong min thi gian tn s) m cc h s ca bin i

Waveletc kh nng tp trung nng lng rt tt vo cc h s bin i.

Cc h s mang thng tin chi tit ca bin i Waveletthng rt nh v

c th b qua m khng nh hng ti vic m ho d liu (trong phng


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Ngc Anh

php m ho nh hay ting ni l nhng tn hiu cho php m ho c tn

tht thng tin).

3.4.2. Khnhiu

Tnh cht ca bin i Waveletm chng ta xt ti trong phn

ng dng cho nn tn hiu c m rng bi Iain Johnstone v David

Donohos trong cc ng dng kh nhiu cho tn hiu. Phng php kh

nhiu ny c gi l Wavelet Shrinkage Denoising(WSD). tng c

bn ca WSD da trn vic tn hiu nhiu s l r khi phn tch bng bin

i Waveletcc h s bin i bc cao. Vic p dng cc ngng loi

b tng ng vi cc bc cao hn ca h sWavelets c th d dng

loi b nhiu trong tn hiu.3.4.3. M ho ngun v m ho knh

SdWaveletc ng dng trong m ho ngun v m ho knh

v trong m ho ngun th chng ta cn kh nng nn vi t l nn cao

cn trong m ho knh th cn kh nng chng nhiu tt. Bin i

Waveletkt hp vi mt s phng php m ho nh m ho Huffman

hay m ho s hc c th thc hin c c hai iu trn. V th s s

dng bin i Wavelettrong m ho ngun v m ho knh l rt thch

hp.


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CHNG 4:CHUN NN NH TNH DA TRN

BIN I WAVELET JPEG2000

4.1. Lch sra i v pht trin chun JPEG2000

Nh chng ta bit, s ra i ca JPEG mang li nhiu li ch to

ln v nhiu mt. JPEG c th gim nh kch thc nh, gim thi gian

truyn v lm gim chi ph x l nh trong khi cht lng nh l kh tt.

Tuy nhin cho n nay ngi ta mi chng dng dng thc nn c tn

tht thng tin ca JPEG v m ho khng tn tht ca JPEG l kh phc

tp. vic nn nh c hiu qu hn, y ban JPEG a ra mt chun

nn nh mi l JPEG2000. JPEG2000 s dng bin i Waveletv cc

phng php m ho c bit c c nh nn u vit hn hn JPEG.

JPEG2000 hin vn ang tip tc c pht trin, nhng phn I c

t chc ISO chp nhn l chun nn nh quc t p dng cho nh tnh.

Chun nn nh JPEG2000 m xng sng l bin i Wavelet vi

tnh nng vt tri so vi JPEG chc chn sc s dng trong cc

server ni dung chuyn i nh dng nh trong mng di ng. Chnh

v th, mc ch ca chng ny khng ch gii thiu mt chun nn nhda trn bin i Waveletph bin m cn a ra mt la chn nhm gii

quyt ton cc bi ton t ra phn mu.

4.2. Cc tnh nng ca JPEG2000

JPEG2000 c nhiu chc nng c bit hn mi chun nn nh

tnh khc nh JPEG hay GIF. Di y l cc chc nng u vit ca

JPEG2000 so vi cc chun nn nh tnh khc

Cho cht lng nh tt nht khi p dng nn nh tnh c tntht.

S dng c vi truyn dn v hin th lu tin v cht lng, phn gii, cc thnh phn mu v c tnh nh v khng gian.

S dng cng mt cch nn nh cho c hai dng thc nn. Truy nhp v gii nn ti mi thi im trong khi nhn d liu.


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Gii nn tng vng trong nh m khng cn gii nn ton bnh

C kh nng m ho nh vi t l nn theo tng vng khc nhau Nn mt ln nhng c th gii nn vi nhiu cp cht lng tu

theo yu cu ca ngi s dngHin ti, ISO v u ban JPEG a ra khuyn ngh thay th

JPEG bng JPEG2000.

4.3. Cc bc thc hin nn nh theo chun JPEG2000

nh m ho

X l trcbin i

Bin ithun linthnh phn

Bin ithun ringthnh phn

Lng tho

M ho

Gii m hoGii lng

t ho

Bin i

ngc ringthnh phn

Bin i

ngc linthnh phn

X l saubin i

nh sau khim honh gc

nh khi phc

(a)

(b)

Hnh 4.1: Trnh tm ho (a) v gii m JPEG2000 (b)

4.3.1. Xl trc bin i

Do s dng bin i Wavelet, JPEG2000 cn c d liu nh u

vo dng i xng qua 0. X l trc bin i chnh l giai on m

bo d liu a vo nn nh c dng trn. pha gii m, giai on x l

sau bin i s tr li gi tr gc ban u cho d liu nh.

4.3.2. Bin i lin thnh phn

Giai on ny s loi b tnh tng quan gia cc thnh phn ca

nh. JPEG2000 s dng hai loi bin i lin thnh phn l bin i mu

thun nghch (ReversibleColorTransform - RCT) v bin i mu khng

thun nghch (Irreversible Color Transform - ICT) trong bin i

thun nghch lm vic vi cc gi tr nguyn, cn bin i khng thunnghch lm vic vi cc gi tr thc. ICTv RCTchuyn d liu nh t

khng gian mu RGB sang YCrCb. RCTc p dng trong c hai dng

thc nn c tn tht v khng tn tht, cn ICTch p dng cho nn c

tn tht. Cng thc ca bin i thun v ngc ca hai php bin i


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ICT v RCT cho phn ph lc. Vic p dng cc bin i ny trc khi

nn nh khng nm ngoi mc ch lm tng hiu qu nn. Cc thnh

phn Cr, Cb c nh hng rt t ti s cm nhn hnh nh ca mt trong

khi thnh phn chi Yc nh hng rt ln ti nh. Chng ta c th

thy r hn iu ny trn hnh v 4.3:

Hnh 4.2: Minh honh vi RGB v YCrCb

4.3.3. Bin i ring thnh phn (bin i Wavelet)

Bin i ring thnh phn c p dng trong JPEG2000 chnh l

bin i Wavelet. m bo tnh ton vn thng tin cng phi p dng

cc php bin i thun nghch hoc khng thun nghch. Do php bin

i Waveletkhng phi l mt php bin i trc giao nh bin i DCT

m l mt php bin i bng con nn cc thnh phn sc phn chiathnh cc bng tn s khc nhau v mi bng sc m ha ring r.

JPEG2000 p dng bin i Waveletnguyn thun nghch 5/3(IWT) v

bin i thc khng thun nghch Daubechies 9/7. Vic tnh ton bin i

trong JPEG2000 ny sc thc hin theo phng php Lifting(Cng

thc c th ca phng php Liftingv bin i Wavelettrong JPEG2000

cho phn ph lc). S ca phng php Lifting1D p dng trong

JPEG2000 trn hnh 4.3.Vic tnh ton bin i Wavelet 2D suy ra t

bin i Wavelet 1D theo cc phng php phn gii nh tu chn. Trong

JPEG2000 c 3 phng php phn gii nh nhng phng php c s

dng nhiu nht chnh l phng php kim tthp.


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Odd / Even

Split U-P

+

+

X[n]

Xe[n] c[n]

d[n]Xo[n]

Ke

Ko

MergeP-U

+

+

X[n]

c[n]

d[n]

1/Ke

1/Ko

Hnh 4.3: Phng php Lifting 1D dng tnh ton bin i Wavelet

Do bin i Wavelet 5/3 l bin i thun nghch nn c th p

dng cho nn nh theo c hai phng php, c tn tht v khng tn tht

trong khi bin i 9/7ch p dng cho nn nh theo phng php c tntht thng tin.

4.3.4.Lng tho - Gii lng tho

Cc h s ca php bin i sc tin hnh lng t ho. Qu

trnh lng t ho cho php t t l nn cao hn bng cch th hin cc

gi tr bin i vi chnh xc tng ng cn thit vi mc chi tit ca

nh cn nn. Cc h s bin i sc lng t ho theo php lng t

ho v hng. Cc hm lng t ho khc nhau sc p dng cho cc

bng con khc nhau v c thc theo biu thc:

( )( )

( ),

, sgn ,U x y

V x y U x y

=

(4.1)

vi l bc lng t, ( ),U x y l gi tr bng con u vo; ( ),V x y l gi

tr sau lng t ho. Trong dng bin i nguyn, t bc lng t bng

1.Vi dng bin i thc th bc lng t sc chn tng ng cho

tng bng con ring r. Bc lng t ca mi bng do phi c

trong dng bt truyn i pha thu c th gii lng t cho nh. Cng

thc gii lng t ho l:

( ) ( ) ( ), , sgn ,U x y V x y r V x y= + (4.2)


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r l mt tham s xc nh du v lm trn, cc gi tr ( ) ( ), ; ,U x y V x y

tng ng l cc gi tr khi phc v gi tr lng t ho nhn c.

JPEG2000 khng cho trc rtuy nhin thng chn 12r= .

4.3.5. M ho v kt hp dng dliu sau m hoJPEG2000 theo khuyn ngh ca u ban JPEG quc t c th s

dng nhiu phng php m ho khc nhau cng nh nhiu cch bin i

Waveletkhc nhau c th thu c cht lng nh tng ng vi ng

dng cn x l. iu ny gip cho JPEG2000 mm do hn nhiu so vi

JPEG. Vic p dng cc phng php m ho khc nhau cng c m

rng sang lnh vc nn nh ng bng bin i Wavelet. Trong thc t

cc phng php m ho nh c p dng khi nn nh bng bin i

Waveletcng nhJPEG2000 th c hai phng php c coi l csv

c p dng nhiu nht: phng php SPIHT v phng php EZW.

Hin nay JPEG2000 vn c p dng m ho bng hai phng php

ny v mt phng php pht trin t hai phng php ny l phng

php m ho mt phng bt. V thy chng ta s xem xt hai phng

php ny. Vic kt hp dng d liu sau m ho ca JPEG2000 thc cht

l thc hin cc tnh nng c bit ca JPEG2000 nh tnh nng ROI

v.v...

4.3.6. Phng php m ho SPIHT

C th thy rng d p dng bin i Waveletno hay cng vi n

l mt php phn gii nh no th trong cc bng con c s th t thp

cng l nhng thnh phn tn s cao (mang thng tin chi tit ca nh)

trong khi nhng bng con c s th t cao hn th s cha nhng thnhphn tn s thp (mang thng tin chnh vnh). iu ngha l cc h

s chi tit s gim dn t bng con mc thp (HH1 chng hn) (ng vi

thnh phn tn s cao) xung bng con mc cao (ng vi thnh phn tn

s thp) v c tnh tng t v khng gian gia cc bng con, v d nh


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mt ng bin ca hnh v trong nh s tn ti cng mt v tr trn cc

bng con (tng ng vi mc phn gii ca bng con y). iu ny

dn ti s ra i ca phng php SPIHT (Set partitioning in

hierarchical trees - phng php m ho phn cp theo phn vng).

Phng php SPIHTc thit k ti u cho truyn dn lu tin. iu

ny c ngha l ti mi thi im trong qu trnh gii nn nh theo

phng php m ho ny th cht lng nh hin th ti thi im y l

tt nht c tht c vi mt s lng bt a vo gii m tnh cho ti

thi im y. Ngoi ra, phng php ny s dng k thut embedded

coding; iu c ngha l mt nh sau nn vi kch c(lu tr) ln (t

l nn thp) s cha chnh d liu sau nn ca nh c kch c (lu tr)nh (t l nn cao). B m ho ch cn nn mt ln nhng c th gii nn

ra nhiu mc cht lng khc nhau. Gi s gi cc pixeltrong mt nh p

cn m ho l pi, j. p dng mt php bin i WaveletTno cho cc

pixeltrong nh to ra cc h s ca php bin i Waveletl ci, j. Cc

h s ny to ra mt nh bin i l C. Php bin i ny c vit di

dng ton t nh sau: C=T(p). Trong phng php truyn dn lu tin

vi nh th b m ho s bt u qu trnh khi phc (gii nn) nh bng

cch t cc gi tr ca nh khi phc t cc h s bin i l c . S dng

cc gi tr gii m ca cc h s bin i to ra mt nh khi phc (vn

cha p dng bin i ngc Wavelet) l c v sau p dng bin i

ngc Wavelet to ra nh cui cng l p . Chng ta c th vit di

dng ton t nh sau: ( )1 p T c= . Nguyn tc quan trng ca phng

php truyn dn nh theo kiu lu tin chnh l phng php ny lun

truyn i cc gi tr mang thng tin quan trng hn ca nh i trc. S

dlm nh vy l do cc thng tin chnh l cc thng tin s lm gim

thiu nhiu nht mo dng ca nh (s sai khc gia nh gc v nh

khi phc). y chnh l l do ti sao phng php SPIHTlun truyn i


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cc h s ln trc v cng l mt nguyn tc quan trng ca phng

php ny. Mt nguyn tc na l cc bt c trng s ln bao gi cng

mang thng tin quan trng nht trong d liu nh phn. Phng php

SPIHTs dng c hai nguyn tc ny; n sp xp cc h s bin i v

truyn i cc bt c trng s ln nht. Qu trnh gii m c th dng li

bt k mt bc no ng vi gi trnh cn m ho yu cu. y chnh l

cch m phng php m ho SPIHTlm tn tht thng tin.

4.3.7. Phng php m ho EZW

Phng php m ho EZW(Embedded Zerotree Wavelet Encoder)

cng da trn csphp m ho lu tin (progressivecoding) ging nh

phng php m ho SPIHT. Phng php ny ch yu da trn khinim v cy zero (zerotree). V c bn, thut ton ny da trn hai

nguyn tc nh trnh by phn phng php m ho SPIHT. Sau y

chng ta s xem xt cc khi nim cbn ca thut ton:

Cy tphn: Sau khi p dng bin i Waveletng vi cc mc

phn gii khc nhau chng ta c th biu din cc h s bin i di

dng mt cy. Ta thy rng vi cy biu din ny c mi nt cha th c 4

nt con. Sdc c iu ny l do qu trnh bin i Waveletcc t

l khc nhau. Ta gi y l cc cy t phn (quadtree). S cy t phn

c minh hohnh 4.5.

Level 3

Level 2

Level 1

LL

LH1

HL1

HH1

(a) (b)

Hnh 4.4: Minh ho cy tphn (a) v sphn mc (b)


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Cy zero (zerotree): Cy zero l mt cy t phn, trong tt c

cc nt ca n u nh hn nt gc. Mt cy nh vy khi m ho sc

m ho bng mt i tng duy nht v khi gii m th chng ta cho tt

c cc gi tr bng khng. Ngoi ra c th m ho c cc h s

Wavelet trong trng hp ny, gi tr ca nt gc phi nh hn gi tr

ngng ang c xem xt ng vi h sWavelet

Sau khi c cc khi nim cn thit v cy t phn v cy zero,

chng ta c th trnh by nguyn l hot ng ca thut ton. Thut ton

s m ho cc h s theo th t gim dn. Chng ta s dng mt gi tr

gi l ngng (threshold) v s dng ngng ny tin hnh m ho

cc h s bin i. Cc h sc m ho theo th t t vng tn s thpn vng tn s cao. V ch nhng h s c gi tr tuyt i ln hn hoc

bng ngng th mi c m ho. Tip theo gim ngng v tip tc

lm nh vy cho ti khi ngng t ti mt gi tr nh hn gi tr ca h

s nh nht. Cch gim gi tr ngng y thc hin tng i c bit,

gi tr ca ngng gim xung mt na so vi trc . B gii m phi

bit cc mc ngng ny th mi c th gii m nh thnh cng. Nhng

khi ta i t nt cha n nt con trong cy t phn th n vn c 3 nt con.

Vy ta phi i theo nhnh c nt con no trc. Hay ni mt cch y

hn ta di chuyn t h s ny n h s khc theo th t nh th no. C

nhiu cch di chuyn khc nhau, tuy nhin hai cch di chuyn trnhnh

4.6 c s dng nhiu nht.

Raster Scan Morton Scan

Hnh 4.5: Hai cch sp xp thtcc h s bin i


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Vic sp xp ny cn phi c quy c thng nht gia qu trnh

m ho v qu trnh gii m vic gii m nh c thnh cng. Trn

y ch l nguyn l cbn ca phng php m ho EZW. Chi tit v

thut ton m ho c th xem phn chng trnh. Hin nay phng

php m ho ny c p dng ngy cng nhiu nn nh ng. Phng

php ny cho t l nn v tin cy gii m cao. Ngoi ra phng php

EZWrt d trin khai trn my tnh bi phng php ny khng yu cu

vic lp trnh qu phc tp.

4.4. So snh chun JPEG2000 vi JPEGv cc chun nn nh tnh

khc

Mt tnh nng quan trng v l u im r nt nht ca JPEG2000so vi JPEG cng nh cc chun nn nh khc nhMPEG 4 VTChay

JPEG- LSv. v.... l JPEG2000a ra c hai k thut nn c tn tht v

khng tn tht theo cng mt c ch m ho ngha l JPEG2000 thc

hin tt c cc dng thc ca JPEG ch bng mt cch m ho duy nht.

Nu xt v s tn ti ca hai k thut ny th JPEG cng c kh nng nn

nh c tn tht v khng tn tht thng tin. Tuy nhin vi JPEG th c

ch m ho vi hai dng ny l khc nhau v rt kh s dng c hai

dng ny cng lc cho cng mt ng dng. Do , c th thy rng JPEG

c tnh mm do hn bt k chun nn nh tnh no trc y. Hn th,

chng ta thy rng tt c cc phng php thit k cho chun

JPEG2000u u vit v c nhiu tnh nng hn so vi JPEG; ngoi ra

nhng thng k v thc t cho thy vi cng mt t l nn v mt loi

nh th nh c nn bi JPEG2000 hu nh lun c cht lng tt hn

so vi JPEG. Chng ta xem xt hai nh trn hnh 4.7 thy r iu ny,

nh bn tri c nn theo JPEG cn nh bn phi c nn theo

JPEG2000


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JPEG JPEG2000

JPEG JPEG2000

Hnh 4.6: So snh JPEGv JPEG2000

Tnh nng u vit th hai ca JPEG2000 so vi JPEG chnh l

trong dng thc nn c tn tht thng tin, JPEG2000 c tha ra t l

nn cao hn nhiu so vi JPEG. Cc phn mm nn nh JPEG hin ti

(k c Photoshop) cng ch thit k c th nn c ti t l 40:1

nhng vi JPEG2000 th t l nn c th ln ti 200:1. Theo cng thc

tnh PSNR trong n v dB, chng ta c: (b l s bt dng biu din mtpixeltrn nh gc)

=

12

RMSElog20)dB(PSNR

b

Vi hai nh hnh 4.6, s so snh v tham sPSNR cho trn bng

4.1. c th so snh d dng hn, ta xt nh c nn vi cc t l khc

nhau (o lng bi h sbt/pixelhay bpp). Tt c cc s liu trn bng

u cho thy JPEG2000 nn nh tt hn l JPEG; hn th h sPSNR

m chng ta xt trong bng c o trong hn vlogarit.


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Bit per pixel 0. 125 0. 50 2.00

nh 1 theo JPEG 24.42 31.17 35. 15

nh 1 theo JPEG2000 28. 12 32.95 37. 35

nh 2 theo JPEG 22.6 28. 92 35. 99nh 2 theo JPEG2000 24.85 31.13 38. 80

Bng 4.1: So snh JPEGv JPEG2000

Tnh nng u vit th 3 ca JPEG2000 so vi JPEG l chun nn

nh ny c th hin thc cc nh vi phn gii v kch thc khc

nhau t cng mt nh nn. Vi JPEG th iu ny l khng th thc hin

c. Sdc iu ny l do JPEG2000 s dng k thut phn gii nh

v m ho nh km m chng ta ni ti phn m ho nh theo

JPEG2000.

Tnh nng ny l mt li thc bit quan trng ca JPEG2000,

trong khi JPEG cng nh cc chun nn nh tnh trc y phi nn

nhiu ln thu c cht lng vi tng ln nn khc nhau th vi

JPEG2000 ta ch cn nn mt ln cn cht lng nh th sc quyt

nh tu theo ngi s dng trong qu trnh gii nn nh theoJPEG2000

.Mt tnh nng u vit na ca JPEG2000 l tnh nng m ho nh quan

trng theo vng (ROI- Region of Interest) m chng ta cp trong

phn m ho nh theo JPEG2000. Cht lng ca ton bnh cng c

thy r trn hnh 4.7.


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Hnh 4.7: Minh ho tnh nng ROI

Nh chng ta thy trn hnh 4.7, cht lng ca vng nh c la

chn tng cao hn khi vng c p dng phng php nn nh ROI.

JPEG2000 cn c mt kh nng c bit u vit hn so vi JPEG, chnh l kh nng vt tri trong khi phc li. l khi mt nh

c truyn trn mng vin thng th thng tin c th b nhiu; vi cc

chun nn nh nhJPEG th nhiu ny sc thu vo v hin th, tuy

nhin vi JPEG2000, do c trng ca php m ho c th chng li,

JPEG2000 c th gim thiu cc li ny ti mc hu nh khng c.

Sau khi xem xt cc tnh nng vt tri ca JPEG2000 so vi

JPEG (chun nn nh thng dng nht hin nay) chng ta so snh chc

nng ca JPEG2000 vi mt s chun nn nh nh l JPEG- LS; PNG;

MPEG 4 VTCqua bng 4.2 (Du + biu th chun c chc nng tng

ng, s du + cng nhiu th chun thc hin chc nng tng ng

cng tt) du - biu th chun tng ng khng h trtnh nng )


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JPEG2000JPEG -

LSJPEG

MPEG -4VTC

PNG

Kh nng nn nhkhng tn tht

+++ ++++ + - +++

Kh nng nn nh ctn tht +++++ + +++ ++++ -

Kh nng lu tin trongkhi phc nh

+++++ - ++ +++ +

K thut m ho theovng ROI

+++ - - + -

Kh nng tng tc vicc vt th c hnh dngbt k

- - - ++ -

Kh nng truy nhpngu nhin dng bt canh nn

++ - - - -

Tnh n gin ++ +++++ +++++ + +++Kh nng khi phc li +++ ++ ++ +++ +Kh nng thay i t lnn

+++ - - + -

Tnh mm do (khnng nn nhiu loi nhkhc nhau)

+++ +++ ++ ++ +++

Bng 4.2: So snh tnh nng ca JPEG2000 vi cc chun nn nh tnh khc

T bng trn chng ta c th thy cc tnh nng vt tri v kh

nng u vit ca JPEG2000 so vi cc chun nn nh tnh trc y.


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CHNG 5:NG DNG WAVELET TRONG CC

DCH V D LIU A PHNG

TIN TRONG THNG TIN DI NG

5.1. Nn nh bng Wavelet

Trong cc chng trc chng ta thy c u im ca

Wavelet trong ng dng nn nh tnh. Chng ny xin a ra mt gii

php l va s dng bin i Wavelet khai thc kh nng nn cao,

cht lng hnh nh m bo (k thut nn nh bng Wavelet thng

thng) m vn ph hp vi mi trng thng tin di ng c bng thnghp, tc bt thp v thng xuyn b nhiu knh, hiu ng fading. Mt

cch tip cn p ng c cc yu cu trn l: kthut nn nh bng

Wavelet hiu nngvi hai c tnh quan trng trong thut ton: (i) gim

thiu nng lng tnh ton thc hin nn nh v (ii) gim thiu

nng lng khi truyn thng cho cc ng dng a phng tin trong

mng di ng m vn m bo cht lng ca nh. Chi tit ca k thut

s trnh by phn di y.5.2.1. S khi tng qut

Hnh 5.1. S khi qu trnh nn nh bng Wavelet

Hnh 5.1 ch ra s khi qut qu trnh nn nh (m ho ngun).

Qu trnh nh sau: nh mu c a qua mt php bin i to

thnh tp h s bin i. Cc h s ny tip tc c lng t ho (chia

cho cc gi tr cnh cho trc) gim dung lng d liu. u ra ca


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bc ny l mt lung cc s nguyn m mi mt trong s tng ng

vi mt ch s nh phn c lng t ho. Bc cui cng l m ho:

cc lung d liu c chuyn thnh chui cc t m nh phn (binary

symbol) theo cch: cc t m nh phn c di ngn m ho cho cc s

nguyn c xc sut xut hin cao. iu ny lm gim s bt cn truyn.

Cc nguyn l m ho nh vy l: Huffman [4] v RLC (m chy di) [4].

C nhiu thut ton s dng cho nn nh nh: da theo php bin

i, lng t ho vcthoc m ho bng con. Vic la chn thut ton

trong truyn thng a phng tin di ng khng ch ph thuc vo t s

nn t c, cht lng nh khi phc m cn lin quan n nng lng

tiu hao cng nh kh nng trng li li bt cao hn.Gn y nhm JPEG pht trin chun nn nh da trn bin i

Wavelet gi l JPEG2000 vi nhiu u im. Tuy nhin thng k cho

thy bc bin i Wavelet trong qu trnh nn tiu tn hn 60% thi

gian CPU. Nh vy nu ti u cc c im ca thut ton bc bin

i th nng lng v hiu sut nn c thc ci thin ng k. Do

ta tp trung vo ti u nng lng tiu hao bc bin i.

5.1.2. Bin i WaveletPhp bin i Waveletthun s dng s phn ly 1D (mt chiu)

chuyn tp cc mu 1D thnh hai bng: bng con thng thp (Li) v bng

con thng cao (Hi). Bng Li l phin bn c phn gii thp ca nh gc

c ly mu xung (downsampled), bng Hi biu th thng tin d tha

ca nh gc (ch cn thit khi cn khi phc hon ton nh gc t bng

thng thp). Qu trnh phn ly bng con 2D ch l s mrng qu trnh

phn ly bng con 1D. Ton b qu trnh chnh l s thc hin qu trnh

phn ly 1D hai ln: u tin theo hng, ri theo ct. Theo cch ny, bng

con thng thp Li to thnh khi phn ly theo hng li tip tc c phn

ly theo ct to thnh bng con LLi v LHi. Tng t nh vy, bng con Hi

tip tc c phn ly thnh HLi v HHi. Sau mc bin i u tin, nh


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c th tip tc c phn ly bng cch p dng qu trnh phn ly 2D cho

bng con LLi. Nh vy nh c thc bin i nhiu mc. Hnh 5.2

di y minh ho qu trnh phn ly nh 3 mc.

Hnh 5.2. (a) Bin i Wavelet2D mc 3 v (b) Minh ho bng nh CASTLE

5.1.3. Tnh ton nng lng tiu hao

thc hin bin i Waveletcn chn mt b lc cho n. y

ta chn b lc c cp Daubechies 5-tap / 3-tap do nhng u im sau ca

n:

Kt qu sau b lc Waveletc cha thng tin im nh ln cn v

nh th loi bc hiu ng khi m bin i DCTgp phi

C tnh cht i xng v nh v cho php d dng pht hin ngvin, tnh ton nhanh, nh nn c cht lng cao.

D dng thc hin bng phn cng v n ch gm cc b cng v

b dch nh phn (khng phi l cc b ghp knh v b chia).

(thc t c th chn nhiu cp b lc khc nhau cho bin i Wavelet, la

chn cp Daubechies 5-tap/ 3-tap mc ny v cc mc sau u mang

tnh cht cc b, kt qu cui cng vn khng mt tnh tng quan)

Phng trnh ca b lc Daubechies 5-tap/3-tap l:

+++=+

++++++=

2

]22[]12[2]2[]12[

4

2]22[]12[2]2[6]12[2]22[]2[

nxnxnxnH

nxnxnxnxnxnL

(5.1)


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xc nh hiu nng ca mi thut ton, chng ta s dng mt

ma trn khng ph thuc vo vic thc hin thut ton. Chng ta phn

tch hiu nng ca n bng cch xc nh s ln cc php ton cbn

c thc hin khi u vo cho trc, tip xc nh nh lng cc

hot ng chuyn mch v chnh l nng lng tiu hao. Ly v d,

trong php phn ly Waveletthun s dng b lc trn, cn 8 php ton

cng - A(Add) v dch - S(Shift) chuyn nhng im nh mu thnh

mt h s thng thp. Tng t nh vy, s phn ly thng cao cn 2 php

ton dch v 4 php ton cng. Chng ta lp m hnh tiu hao nng lng

ca s phn ly thng thp/cao bng cch m s cc php ton v xem

chng nh l ti tnh ton(computational load). Nh vy c 8*S(phpdch) + 8*A (php cng) l ti tnh ton cn cho mt im nh trong qu

trnh phn ly thng thp v 2S + 4A php ton cho thng cao.

Vi mt nh u vo cho trc kch thc M x Nv qu trnh phn

ly c p dng vi L mc bin i, khi chng ta c thnh gi c

tng ti tnh ton nh sau: Gi s trc tin chng ta p dng qu trnh

phn ly theo chiu ngang. Nhng do tt c cc im nh v tr chn

c phn ly thnh cc h s thng thp v cc im nh v tr lc

phn ly thnh cc h s thng cao, tng ti tnh ton trong qu trnh phn

ly chiu ngang s l 1/2MN(10S+12A). Lng ti tnh ton trong qu

trnh phn ly theo chiu dc cng d nhn ra. Do kch thc ca nh gim

theo h s 4 sau mi mc bin i, tng ti tnh ton c th c biu

din bng cng thc sau:

Ti tnh ton vi bin i Wavelet thng CW:

=

+

+=+=

K

ll

L

lSAMNSAMNSAMNC

11W

)1012(34

4141

)1012(41

)1012(

(5.2)

Ngoi cc php ton s hc, bc bin i cng bao gm mt s

lng ln cc ln truy nhp b nh. Do vy nng lng tiu hao trong cc


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ln truyn d liu ni v ngoi h thng c thng k, chng ta c

lng ti truy nhp d liu (data-acces load) bng cch m tng s cc

ln truy nhp b nhtrong qu trnh thc hin bin i Wavelet. Ti mt

mc bin i, mi im nh sc c hai ln v c ghi hai ln. Do

vy, vi cng mt iu kin cng nh cng phng php nh gi nh

trn, tng ti truy nhp d liu rt ra bng s cc ton tc v ghi

Ti truy nhp dliu vi bin i Wavelet thng:

=

==

L

llREAD

MNCC1

1WRITE_WW_ 38

41

2 (5.3)

Nng lng tnh ton tng c tnh bng tng trng s ca ti tnh

ton v ti truy nhp d liu. T kt qu tin hnh thc nghim, ta thyrng thc hin cc php cng tiu tn nng lng gp i so vi thc

hin php dch v nng lng tiu tn cho ti truy nhp d liu gp 2.7

ln ti tnh ton. Chng ta cng c lng nng lng truyn thngbng

C*R, trong Cl kch thc ca nh nn (tnh bng bt) v R l tn hao

nng lng truyn mt bt bng b pht RF.

Nh vy ta phn tch bin v ngun gc ca tn hao nng

lng trong bin i Wavelet, tip theo chng ta s trnh by cc k thut ti thiu nng lng tiu hao cng nh nng lng truyn thng yu

cu cho vic nn nh bng Waveletv truyn v tuyn.

5.2. Thut ton nn nh bng Wavelethiu nng - EEW

Trong phn ny, chng ta trnh by thut ton EEW (Effective Energy

Wavelet) - mt thut ton bin i bng Waveletm mc ch l tit kim

nng lng trong khi cht lng nh ch bnh hng t nht.

EEWkhai thc phn b s hc ca cc h s thng cao kho lo

loi b mt s lng ln cc mu trong qu trnh nn nh. Hnh 5.3 minh

ho phn b cc h s thng cao (high-pass coefficients) sau khi p dng

bin i Wavelet hai mc cho nh mu Lena kch thc 512 x 512.

Chng ta cng quan st thy l cc h s thng cao thng c biu


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din bng cc gi tr s nguyn nh. Ly v d, 80% cc h s thng cao

mc 1 (level 1)u khng vt qu 5. Chnh bi s phn b s hc ca

cc h s thng cao v nh hng ca bc lng t ho i vi cc h

s c gi tr nh, chng ta c th lm trn cc h s thng cao bng 0 (v

do loi bc php ton lin quan n chng) v do suy hao cht

lng nh chmc nh. Cch tip cn ny c hai u im chnh. Th

nht, bi v cc h s thng cao khng cn phi tnh ton, EEW lm gim

nng lng tnh ton tiu hao trong qu trnh nn nh bng Waveletbng

cch gim s lng cc php ton c thc hin. Th hai, bi v b

m ho v gii m l k thut lm trn (c lng), v th khng c thng

tin yu cu c truyn qua knh v tuyn, do gim c nng lngtiu hao cn c.

Hnh 5.3. Phn b s hc cc h s thng cao sau php bin i Waveletmc 2

S dng k thut c lng trn chng ta xy dng c

thut ton gm hai k thut hn ch tiu hao nng lng: hn ch tnh

ton v truyn thng cho cc h s thng cao: K thut u tin l loi b

bng con t ngha nht. Trong s 4 bng con ta thy bng con ng

cho (HHi) l t ngha nht (xem hnh 5.2), v l ng c vin sng gi

loi btrong bc bin i Wavelet. Chng ta gi k thut ny l k

thut loi b HH. k thut th 2, th ch nhng bng con c ngha

nht (cha thng tin phn gii thp, LLi) c gi li cn cc bng


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thng cao khc (LHi, HLi v HHi) u c loi b. Chng ta gi k thut

ny l k thut loi b H*(tt c cc bng con thng cao u b loi b

trong bc bin i).

Tip theo chng ta s trnh by chi tit v cc k thut loi b HH

v H* v so snh hiu nng ca hai k thut ny vi thut ton s dng

Waveletnguyn bn (c xem l thut ton bin i Waveletkhng loi

b thng tin ( c cp trong mc 5.2.2 v 5.2.3).

5.2.1. Hiu nng ca cc k thut loi b

thc hin cc k thut loi bHHv H*(EEW), chng ta thay

i php bin i Waveletnh m t trong hnh 5.4. Nh gii thch

mc 5.2.2, trong qu trnh bin i Wavelet, mi nh u vo c thchin php bin i theo hng ri n ct v phn ly nh thnh bn bng

con (LL, LH, HL, HH). Tuy nhin, thc hin k thut loi bHH, th

sau khi thc hin bin i theo hng, cc h s thng cao chc a

vo b lc thng thp m khng c a vo b lc thng cao trong

bc bin i theo ct tip theo (trong hnh 5.4 bn di , k hiu l nhng hnh c bng sng). Cch lm ny loi

b bng con ng cho HH. Cn thc hin k thut loi bH*, nh

u vo c x l ch cho qua b lc thng thp trong c qu trnh thc

hin bin i hng v ct. V nh vy chng ta cng loi bc tt c

cc bc phn ly thng cao trong qu trnh bin i.


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Hnh 5.4: Dliu sau php bin i Waveletvi hai k thut loi b HH v H*

c lng hiu nng ca cc k thut EEW trn, chng ta s tin

hnh tnh ti tnh ton v ti truy nhp d liu theo phng php

cp trong mc 5.2.3. Chng ta gi thit rng, cc k thut tnh ton ch

c p dng E mc bin i u tin trong tng s L mc. L do l

bi v u im ca cc h s thng cao thc hin loi b cng ngha

cc mc bin i thp.

Trong k thut loi bHH, ti tnh ton trong qu trnh thc hin

bin i theo hng bng vi thut ton Waveletthng. Tuy nhin, trongqu trnh thc hin bin i theo ct bng con thng cao l kt qu t

php bin i theo dng trc, bng con HHkhng c tnh. Kt qu

trong mc 5.2.3 ch ra rng lm nh vy c th tit kim 1/4MN(4A+2S)

cc php ton cho ti tnh ton ( ngha l tit kim c 7.4% so vi thut

ton Waveletthng). V v th, tng ti tnh ton c thc tnh nh

sau:

1 11 1

(22 19 ) 1 1(12 10 )2 4 4

E L

HH l ll l E

MN A S C MN A S

= = +

+= + + (5.4)

Bi v bng con thng cao sau php bin i theo hng vn cn

tnh bng con HL trong php bin i theo ct nn chng ta c th tit

kim s ln c trong k thut loi bHH. Tuy nhin, chng ta ch tit


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kim c 1/4 cc ln ghi (tit kim 25%) trong qu trnh thc hin

php bin i theo ct. Do vy kt qu bng con HHc gn trc bng

0 trc khi qu trnh bin i c thc hin. Do vy, tng ti truy cp

d liu sc tnh:

= +=

+==

E

l

L

ElllHHWRITEWREADHHREAD

MNMNCCC1 1

11___ 4

12

4

1

4

7, (5.5)

K thut loi b H* cho kt qung k trong vic tit kim nng

lng tnh ton bi c 3 trong tng s 4 bng con c loi b. Phn

ti chng ta s tp trung m t v minh ho cc k thut trn

5.3.2. Cc kt qu thc nghim

Phn ny chng ta s tin hnh thc nghim xem xt kt qu titkim nng lng tnh ton t vic p dng k thut loi b trn. Thc

cht l chng ta s tp trung vo kh nng tit kim nng lng tnh ton

v truyn thng s dng cc k thut trn ng thi cng xt nh hng

ca chng n cht lng nh.

5.3.2.1. nh hng n nng lng tnh ton v cht lng nh

5.3.2.2. nh hng n nng lng truyn thng v cht lng nh

5.4. Cc tham s nn nh bng Wavelet5.4.1. Thay i mc bin i Wavelet

5.4.2. Thay i cc mc lng t

5.5. Truyn nh trn mng

5.5.1. Phng php la chn tham sng

5.5.2. Kt qu thc nghim


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KT LUN

Kt qut c v ng dng ca lun vn

Lun vn trnh by cc k thut nn nh, cc nguyn l nn v

mt s khi nim quan trng trong lnh vc x l nh. Tc gi cng tp trung trnh by cc nguyn l nn c tn hao in hnh ang l cc k

thut ct li ca cc chun nn (JPEG, JPEG2000, MPEG,).

Vi mc ch ca lun vn l nghin cu v k thut nn nh s

dng bin i Wavelett p dng trong cc d liu a phng tin di

ng, nn tc gi cng i su nghin cu csl thuyt ca php bin

i ny ng thi cng gii thiu chun nn nh JPEG2000 l chun

nn ph bin da trn bin i Wavelet. Hn na chun ny cng s l

mt la chn hiu qu b sung chun JPEGang c s dng trong cc

server chuyn i nh dng nh.

Lun vn cng gii thiu mt thut ton nn nh bng Wavelet

hiu nng khng ch cho hiu sut nn nh cao, cht lng nh truyn

m bo do u im ca Wavelet, m trn ht cn tit kim nng lng

x l, nng lng truyn thng cho nh trn mng. iu ny ha hn c

th xy dng mt b m ho nh tit kim nng lng x l, thi gian

truyn m vn ph hp vi iu kin bng thng thp, rng buc v cht

lng d liu trong cc mng thng tin di ng.

Hng pht trin nghin cu

Tc gi xin cp mt s hng nghin cu trong tng lai:

Lun vn mi a ra ng dng Waveletcho nh tnh trong d liu

a phng tin di ng. Nhng u im ca Waveletkhin n cth p dng cho m thanh, video, kh nhiu, bo mt,

C rt nhiu h Wavelet kh dng, c th la chn nhiu cp

Wavelet khc m khng nht thitch la chn cp 5-tap/3-tap.


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Nghin cu kh nng ng dng chun JPEG2000 cho d liu a

phng tin trong thng tin di ng nhm tng thch d liu hnh

nh gia cc thu bao, kh nhiu, khi phc li mt gi tin nh,

Nghin cu thm v cc gii thut SPIHT, EWZ ng dng trong

thng tin di ng.


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PH LC


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TI LIU THAM KHO

1. Martin Vetterli - Jelena Kovacevic - Wavelet and Subband Coding(1995)

2. Satish Kumar - An Introduction to Image Compression (10/2001)

3. Jin Li - Image Compression - the Mechanics of the JPEG2000(2001)4. David Salomon - Data Compression - The Complete Reference (2001)

5. Lng Mnh B - TS. Nguyn Thanh Thu - Nhp mn x l nh

s(1999)

6. Nguyn Kim Sch Xl nh v video s NXB KHKT, 1997

7. Hong Tin, Vc L Truyn hnh s NXB KHKT, 2000

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tai lieu wavelet

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