kiemtailieu.com-nen anh trong wavelet

5/24/2018 Kiemtailieu.com-nen Anh Trong Wavelet

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Lun vn cao hcTVT 2004 2006

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BGIO DC V O TO

TRNG I HC BCH KHOA H NI

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

LUN VN THC SKHOA HC

NN NH SDNG BIN I WAVELET V

NG DNG TRONG CC DCH VDLIU A

PHNG TIN DI NG

NGHNH: IN TVIN THNG

NGC ANH

Ngi hng dn khoa hc: PGS.TS. Nguync 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 .......................................................................................8

CHNG 1: MU..............................................................................9

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

1.2. Tchc lun vn............................................................................10

CHNG 2:TNG QUAN CC KTHUT NN TRONG M HO

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

2.1. Gii thiu chung vnn nh s .....................................................11

2.2. Phn loi cc kthut 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 kthut nn c tn hao............................................................15

2.4.1. Kthut m ho bng con ......................................................15

2.4.2. Kthut m ho da trn php bin i.................................19

2.4.2.1. Kthut m ho da trn php bin i DCT.................19

2.4.2.2. Kthut m ho da trn php bin i DWT ...............25

CHNG 3:CSL 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 shWavelet........................................................37

3.3.1. Bin i Wavelet Haar............................................................37

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


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3.3.3. Bin i Wavelet Daubechies.................................................38

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

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

3.4.2. Khnhiu ...............................................................................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 sra i v pht trin chunJPEG2000...............................41

4.2. Cc tnh nng caJPEG2000 ........................................................41

4.3. Cc bc thc hin nn nh theo chunJPEG2000 .....................42

4.3.1. Xl 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 tho - Gii lng t ho............................................44

4.3.5. M ho v kt hp dng dliu sau m ho..........................45

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

4.3.7. Phng php m hoEZW.....................................................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. Skhi 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 kthut loi b.........................................60

5.3.2. Cc kt quthc 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 snn 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 quthc nghim...............................................................62

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

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

Hng pht trin nghin cu ................................................................63PHLC..................................................................................................65

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


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CC HNH V, BNG BIU TRONG LUN VN

Hnh 2.1 Sbkhi qut hthng nn nh.........................................12

Hnh 2.2. Sminh hokthut m ho bng con M bng con .......16

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

Hnh 2.5. Sbm ho theo chunJPEG ..........................................23

Hnh 2.6. Sp xp Zigzag cc hsDCT bm ho............................23

Hnh 2.7. Skhi bgii m theo chunJPEG ..................................23

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

Hnh 2.9. Minh hoDWT hai 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 holi nhtdyadic vi cc gi trca 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 hbin i Daubechies n vi n=2, 3, 7, 8........39Hnh 4.1: Trnh tm ho (a) v gii mJPEG2000 (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 hocy tphn (a) v sphn mc (b)..........................47

Hnh 4.5: Hai cch sp xp thtcc hsbin i...............................48

Hnh 4.6: So snhJPEGvJPEG2000....................................................50

Bng 4.1: So snhJPEGvJPEG2000 ...................................................51

Hnh 4.7: Minh hotnh nng ROI...........................................................52

Bng 4.2: So snh tnh nng ca JPEG2000vi cc chun nn nh tnh

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

Hnh 5.1. Skhi 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 bshc cc hsthng cao sau php bin i Wavelet

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

Hnh 5.4: Dliu sau php bin i Waveletvi hai kthut loi bHH

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 Hthng 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 Kthut nn nh khng tn hao (khng mt dliu)

Lossy Compression Kthut nn nh c tn hao (c mt dliu)

MRA Phn tch a phn gii (Multi Resolution Analysis)

MSE Sai sbnh phng trung bnh (Mean Square Error)

PCM iu xung m (Pulse Code Modulation)

PSNR Tstn hiu nh trn nhiu (Peak Signal to Noise Ratio)

QMF Lc gng cu tphng (Quardrature Mirror Filters)

RLC M ho lot di (Run Length Coding)

ROI Kthut 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 vdliu trn mng

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

vn t ra l lm thno tm c mt kthut m ho dliu then

cht (chun), c hiu qutruyn cc dliu ny trn mng di ng.

Mc ch ca lun vn l trnh by mt kthut nn nh sdng

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

liu a phng tin trong mng di ng. So vi cc kthut nn sdng

php bin i trc y nhbin iFourier(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 sra i ca chun nnJPEG2000(da trnDWT) c tnh nng

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

cJPEG2000 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 xlv truyn trn mng. Trong lun vn trnh by mt k thut nn nh

trong mng di ng sdng bin i Wavelethiu nng khng chem

li hiu qunn, cht lng hnh nh m cn tit kim nng lng xl

ca hthng. iu ny ha hn c thxy dng mt bm ho nh tit

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

bng thng thp, rng buc vcht lng dliu trong cc mng thng

tin di ng.


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CHNG 1: MU

1.1. Csnghin cu v mc ch ca lun vnc thsdng cc dch vInternet khng dy cng nhnhiu

dch vdliu khc trn nn cc ng dng di ng cn c mt kthut

then cht c thhtrtruyn thng nhiu dng dliu trong thng tin

di ng tbo 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 nghmi ca tng

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

ca cc dch vtng lai, th phng php gim kch thc dliu bng

cc kthut 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 dliu a phng

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

trn bin i Wavelet) v chunMPEG, tuy nhin nhng kthut ny ch

tp trung vo hiu qunn v cgng nh mt cht lng nh t v th

chng bqua vn tiu hao nng lngtrong qu trnh nn v truyn

RF (trong thng tin ng). Lun vn ny trnh by mt kthut 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 kthut nn nh sdngbin i Wavelet thch nghi v hiu nng cho d liu a phng tin

trong thng tin di ng.


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1.2. Tchc lun vn

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

tc gitrnh by tm tt csnghin cu v mc ch cng nhtchc

ca lun vn.

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

nguyn l nn v nh ngha mt sthut ngc sdng rng ri nh

MSE, PSNR v SNR. Chng ny cng trnh by csl 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 shWaveletphbin v gii thiu mt s

ng dng ni bt ca Waveletngoi ng dng nn nh.

Chng 4 gii thiu tng quan vchun nn JPEG2000da 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 tchc ISO cng nhn nn chc chn s trthnh mt chun nn

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

tc gitrnh by tm tt cc bc thc hin nn nh theoJPEG200 v so

snh n vi chunJPEGv cc chun nn nh tnh khc.

Chng 5 cng l chng quan trng nht. Da trn kthut 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

nhvy 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 vnn nh s

Nn nh sl mt ti nghin cu rt phbin trong lnh vc x

l d liu a phng tin. Mc ch l lm thno lu trbc nh

di dng c kch thc nhhn hay di dng biu din m chyu cu

sbt 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 tchc. V thnu bc tch c tnh trt t, cu trc th sbit

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

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

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

bc nh xp xgn chnh xc so vi nh gc nhng vn thomn cht

lng yu cu, m bo thng tin cn thit.

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

c nhng tnh cht nhsau: C stng quan (dtha) thng tin vkhng gian: Trong phm

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

(dtha) gia cc im nh ln cn.

C stng quan (dtha) thng tin vph: Cc dliu thu c

tcc bcm bin ca thit bthu nhn nh tn ti stng quan

ng kgia cc mu thu, y chnh l stng quan vph.

C s tng quan (d tha) thng tin v thi gian: Trong mt

chui nh video, tn ti stng quan gia cc im nh ca cc

khung video (frame).


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Sca mt hthng nn dliu tng qut nhsau:

Hnh 2.1 Sbkhi qut hthng nn nhTrong hnh 2.1, bm ho d liu thc hin qu trnh nn bng

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

trv truyn dn trn knh. Tc bt u ra ca bm ho c tnh l

sbt cho mt mu (im nh). Bm ho knh thc hin vic chuyn

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

v truyn dn, thng bm ho knh sdng cc kthut: m ho c

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

ho shc [4]. Bgii m thc hin qu trnh ngc li so vi bm

ho.

Trong cc hthng nn, tsnn chnh l tham squan trng nh

gi khnng nn ca hthng, cng thc c tnh nhsau:

Tsnn = Kch thc dliu gc / Kch thc dliu nn

i vi nh tnh, kch thc chnh l sbt biu din ton bbc 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 kthut nn

Cc kthut nn chyu c phn loi nhsau:

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 qunn rt nh. Tri li, cc kthut nn c tn hao (lossy

compression) c tht c hiu qunn cao hn rt nhiu m iu

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

nhn c v v thvn m bo cht lng nh. Mt skthut nn c

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

tho vct VQ, m ho bin i v bng con. nh khi phc trong hthng nn c tn hao lun c ssuy gim thng tin so vi nh gc bi v:

phng php nn ny loi bnhng thng tin dtha 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 trmang thng tin

c gi hay ang sn c sc sdng don cc gi trkhc, v

chm ho ssai lch gia chng. Phng php ny n gin v rt ph

hp vi vic khai thc cc c tnh cc bca bc nh. KthutDPCM

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 nhsau:

trc tin thc hin php bin i vi nh chuyn sbiu 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 sbin 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 (sdng

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

bc nh chbng mt st cc hs, sln cc hscn 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 nhi rt nhiu. Trong phng php m ho don, sai lch

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

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

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

bin i.

2.2.3. M ho bng con

Bn cht ca kthut 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 sdng mt bm 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 nhsau:

( )22

,

1[ , ] - [ , ]q

j k

SE f j k g j k N

= = (2.1)

Trong tng ly theoj, ktnh cho tng tt ccc im nh trong nh v

Nl sim nh trong nh. CnPSNRgia hai nh (bbt cho mi im

nh,RMSE l cn bc 2 caMSE) c tnh theo cng thc dBnhsau:

12log20 10

=

b

RMSEPSNR (2.2)

Thng thng, nuPSNR 40dBth hthng mt ngi gn nhkhng

phn bit c gia nh gc v nh khi phc.

Mt tham skhc hay sdng trong cc hthng vin thng l ts

tn hiu trn nhiu - SNR, tuy vy SNRsdng cho mt hthng n nh

cng c cng thc dBnhsau:


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1010log

Encoder input energySNR

Noise energy= (2.3)

2.4.Cc kthut nn c tn hao

Trong phn ny, tc gila chn trnh by hai kthut nn tn hao

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

v m ho sdng php bin i (transform coding). y l hai kthut

nn in hnh v cho hiu qunn cng nhcht lng nh cao.

2.4.1. Kthut m ho bng con

Ttng chnh ca kthut 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 thno cc bng con

khng bchng cho ln nhau. c thphn ly tn hiu bm 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 hs2. 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 bgii m (decoder),qu trnh c thc hin ngc li: gii lng t bng con tn s, ly

mu ln vi hs2, cho i qua bank lc bng con tng hp ri cng tt

ccc u ra ca blc 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 hstn skt qu. y chnh l tnh cht quan trng m

qu trnh lc bng con cgng t c. Cc blc bng con c thit

kl cc xp xvi cc blc chn tn sl tng, trong p ng

tng hp ttt ccc blc bao trm tt cbng tn ca nh. Tuy nhin

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

lc ny chxp xvi cc blc l tng.


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Hnh 2.2 di y l stng qut gii thch kthut m ho bng con.

Hnh 2.2. Sminh hokthut m ho bng con M bng con

Cc blc sdng trong m ho bng con l cc blc gng t

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

thit kcc blc thng thp c p ngH()cn p ng ca cc b

lc thng cao lH(+)chl sdch pha 180oso vi blc thng thp.

Schnh xc ca blc phthuc vo scc hsca blc.

Mt trong cc phng php m ho bng con l p dng sphn 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 scao 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. Kthut ny rt phbin v cng c


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p dng trong cc bm sdng bin i Wavelet. u ra ca cc bng

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

bng con ssdng blng tho ring v mi blng tho ny c

tc ly mu ring (bt/mu).

Nhvy r rng m ho bng con khng t c snn, 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 slng tho (quantization).

Hnh 2.3 Minh hoqu trnh phn ly bng con cy bt phn

Trong cc hthng 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

kmc no.

Hnh 2.4 di y minh hovic phn ly 2 nh mu thnh 4 bng conLL,

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 kthut m ho bng con:

Mt trong nhng vn chyu ca kthut m ho bng con

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

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

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

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 snhc im ca k thut m ho bng

con nhsau:Kthut m ho bng con khng xc nh c hthng 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 ccc bng tn, y l do

cc blc khng phi l l tng v c schng cho nhgia cc bng

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

bng tn knhau v dliu skhng c nn hon ton.

Kthut m ho bng con khng hiu qukhi thc hin b chuyn ng

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

(sai sdon l rt ln).

2.4.2. Kthut m ho da trn php bin i

Mt php bin i l mt hm ton hc c sdng bin i

mt tp cc gi trny thnh mt tp gi trkhc v to ra mt cch biudin mi cho cng mt ngun tin. Tt ccc php bin i m chng ta

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

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

xc bt kmc no. Nhng hu ht cc kthut m ho u c tn

hao bc lng tho do c slm trn gi trcho cc hsphp bin

i.

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

i c sdng trong nn nh.

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

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

(c) Kthut m ho da trn php bin i DWT

2.4.2.1. Kthut m ho da trn php bin i DCT

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

bin i thng tin nh tmin khng gian sang min tn sc thbiu

din di dng gn hn. Tnh cht ca n tng tnhbin iFourier,

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 kthut ny trc ht ta cn tm hiu bin

iFourier.

Bin i Fourier FT

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

thun nghch, n cho php schuyn i thun nghch gia thng tin

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

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

c thhin. Ngha l tn hiu trong min khng gian khng c sxut

hin thng tin vtn sv tn hiu sau bin iFourierkhng c sxut

hin thng tin vthi gian.

FTcho bit thng tin tn sca tn hiu, cho bit nhng tn snoc 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 skhng thay i theo thi gian) th vic xc nh cc thnh

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

Php bin iFTthun v nghch c nh ngha nhsau:

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 nhchng ta chquan tm n thnh phn phno

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 iFTkhng c khnng p ng c

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

c bin iFourierri 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 sphp 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 bngDFTngc nhsau:

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 N mu c nh ngha

nhsau:

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

CDCTvIDCTu 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 caDCTvIDCTl khng bt thng(non-singular)

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

ton thon v. Cng nhbin iFT, DCT cng coi dliu u vo l

tn hiu n nh (bt bin).

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

vIDCTc 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 iDCT hai chiu bm

ho v p dng bin iIDCTbgii m.

Bin iDCTvIDCT8 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 DCTvIDCTl: thc hin php bin i 1-Dln

lt cho hng ri n ct ca ma trn.

So snhDCT vKLT

Hiu quca 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 dliu kha cnh thng k bi: n c thgii

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 shsca 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 trongJPEG

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 hinDCT, sau lng t

ho cc hsri m ho entropy sau lng t.

i vi nhng nh muRGB, p dng kthut nn ny, trc

ht phi chuyn sang chmu 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

trongJPEGc thc hin cho thnh phn chi ri mu.

Skhi bm ho v gii m caJPEGnhsau:


23/67


Ngc Anh

Hnh 2.5. Sbm ho theo chunJPEG

Hnh 2.6. Sp xp Zigzag cc hsDCT bm ho

Hnh 2.7. Skhi bgii m theo chunJPEG

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 trcc im

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

dng bin i DCT sto ra cc hsAC c di gi trt-1023 n

+1023 (c thc m ho bi 11 bt c du). Nhng hsDC li c

gii gi trt0 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 sAC.

Chnh v thvic trgi trmi im nh i 128 l sau khi bin

i DCT ccc hsDC v AC c cng di gi trthun li cho vic

xl v biu din.

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

to ra mng hai chiu cc hsbin i. Hsc tng ng vi tnskhng gian thp nht nhng li c gi trln nht c gi l hs

DC (mt chiu), n tlvi chi trung bnh ca ckhi nh 8x8.

Cc hscn li gi l cc hsAC (xoay chiu). Theo l thuyt,

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

n chchuyn 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 tha tlng nht. Ngha l cc hssc lng tho

ring lv c lp. Qu trnh lng tho l da trn sinh l ca h

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

tn scao v c nhy tt hn cc hsc tn sthp. V thcc

hsc chn sao cho thc hin lng tho th i vi cc hs

tn scao v lng tho tinh i vi cc hsc tn sthp. Bng

lng tho c ly t lto ra cc mc nn thay i tu theo

tc bt v cht lng nh. Vic lng tho sto ra rt nhiu gi

tr0, c bit l tn scao. Qu trnh lm trn trong khi lng t

ho chnh l nguyn nhn chnh gy ra stn hao nhng li l nhn

tchnh em li hiu sut nn.


25/67


Ngc Anh

(d) tn dng u im ca cc hs c lng tc gi trgn

bng 0, mng hai chiu cc hs c lng tsc 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

trbng 0 lin tip. Cng theo cch sp xp ny, cc hsDC c

tch khi cc hsAC v sdng kthut m ho iu xung m vi

sai DPCM.

(e) Bc cui cng ca bm ho l sdng m ho entropy chng hn

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

tng thm hiu qunn cng nhgim thiu li.

pha gii m, lung bt m ho c gii m entropy, sau mng haichiu cc hsDCT c lng tho c gii sp xp Zigzag v

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

IDCT ri cng mi gi trvi 128 xp xto thnh cc khi nh con

kch thc 8x8. Ch l bng lng tho 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. Kthut m ho da trn php bin i DWT

Mi quan hgia bin i Waveletv Fourier

Khng ging nhbin iFourierchthch hp khi phn tch nhng tn

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

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

p ng tn sthay i theo thi gian.

khc phc nhng hn chca bin i FT, php bin iFourierthi

gian ngn STFT c xut. Chc mt skhc bit nhgia STFT

vFT: Trong bin i STFT, tn hiu c chia thnh cc khong nhv


26/67


Ngc Anh

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

kthut ny cn chn mt hm ca swsao 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 iFTta khng thc hin c.

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

X(f,t) =

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

Trong di thi gian ca ca sl (t-),chng ta c thdch chuyn

vtr ca ca sbng cch thay i gi trtv thu c cc p ng

tn skhc nhau ca on tn hiu ta thay i gi tr .Gii thch bin i STFTbng nguyn l bt nhHeissenber, nguyn l

ny pht biu l:Khng thbit c 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 sdng. Nu hm ca scng hp th phn gii cng tt

hn v ginh tn hiu l n nh cng c chnh xc nhng phn

gii tn sli km i. Ta c cc hqusau:

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 vphn 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 tnhnhn vi hm ca s

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

hiu khc nhau trong min thi gian ti cc tn skhc 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 skhc 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 stt v phn gii thi gian

km cc tn sthp. Nhvy kthut ny rt thch hp vi nhng tn

hiu: c cc thnh phn tn scao 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 nhcc tnh cht ca bin i Wavelet lin tc s

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

Bc ny c thhiu php bin iDWT nhl p dng mt tp cc b

lc: thng cao v thng thp. Thit kcc blc ny tng ng nhk

thut m ho bng con (subband coding)ngha l: chcn thit kcc b

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

thpHv Gri c ly mu xung (down sampling)hs2 to thnh

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

(up sampling)hs2 ri sdng cc blc khi phcH, G(l tng

lHv Gchnh lH, G).


28/67


Ngc Anh

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

Tbin iDWTmt chiu c thmrng nh ngha bin iDWThai

chiu theo cch: Sdng cc blc ring bit, thc hin bin i DWT

mt chiu dliu 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 sbini. Qu trnh bin i DWT hai chiu c thminh ho nh hnh 2.12

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

tng ng thc hin lc theo hng, chci thhai tng ng thc

hin lc theo ct).

Hnh 2.9. Minh hoDWT hai 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 sdngDWT in hnh

So vi bin php bin iDCTsdng trong chun nnJPEGra

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

Tuy nhin ci tin mang tnh t ph sdngDWTnn nh bt u l

kthut 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 qunn 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)sdng to cc bin i Waveletsnguyn. Kthutny sdng cc blc Wavelettrc giao em li hiu qurt 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 thl bt kmt hm sthc

hoc phc lin tc no thomn cc tnh cht sau y:

Tch phn suy rng trn ton btrc 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 khtch ( )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 av 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 thvit 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 hschun 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 vtrn trc thi gian. Do b c gi l tham sdch.t tham sdch 0b= ta thu c:

( ),01

a

tt

aa

=

(3.7)

iu cho thy rng a l tham stl.

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 iFourierca ( )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 nhsau:

( ) ( ) ( ),21 1

, a bf t W a b t dadbC a

= (3.9)

vi gi trca Cc nh ngha l:

( )2

C d

= (3.10)

Bin i CWT chtn ti nu Cdng 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 th3 m mt hm cn phi thomn c

thc la chn lm hm Wavelet. Chng ta c thxem 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 bt . Cc hng ca ma trn tng ng vi cc gi

trca av cc ct tng ng vi cc gi trca 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 hsWaveletti tt ccc tll 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 chchn ra mt tp

nhcc gi trtlv cc vtr tin hnh tnh ton. Hn na nu vic

tnh ton c tin hnh ti cc tlv cc vtr trn cslutha cs

2th kt quthu c shiu quv 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 iDWTthccht l s ri rc ho bin i Wavelet lin tc (CWT); vic ri rc ho

c thc hin vi sla chn cc hsa vb nhsau:

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

Vic tnh ton hsca bin i Waveletc thddng thc hin

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

trong xl tn hiu.


33/67


Ngc Anh

Shift n

m = -2

m = -1

m = 0

m = 1

m = 2

Hnh 3.1. Minh holi nhtdyadic vi cc gi trca m v n

3.2. Tnh cht ca bin i Wavelet

Tt cchng 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 tmin thi gian

sang min tn s. Sdng bin iFourierta c thbit c trong tn

hiu ( )f t c cc thnh phn tn sno. Tuy nhin bin i Fourierc

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

rng ti mt thi im t th tn hiu c cc thnh phn tn sno. Mt

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

tnh nng ca bin iFourierv c khnng xc nh xem ti mt thi

im tbt ktrong tn hiu ( )f t c thnh phn tn sno. Php bin i

Wavelet ra i khc phc c cc nhc im ca bin i Fourier

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

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

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

thnh phn tn skhc 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 tca tn hiu ( )f t c cc thnh phn tn sno.

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 Waveletmv

phn gii cc tn skhc nhau ca ( )f t c minh ha bi hs 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

dngFourierl 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 st cc thnh phn tn snhng 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 thrng ti mt vng ca nh c thc rt nhiu

thnh phn tn s. nh biu thtnh nh vr nht chnh l nh c nhiu

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

thnh phn tn skhc 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 giivic xl tn hiu ting ni v hnh nh

t hiu qucao 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. Gischng ta cn xp xho mt tn hiu lin tc c dng

mt hm bnh phng khtch ( )f x bng mt tp cc gi trri rc (v

dhm ( )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 xl hm

( ) c dng:

( ) [ )1 0,1

0

xx

=

cc gi tr cn li (3.13)

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

vit nhsau:

( ) ( )nn

A f x f x n= (3.14)

vi nf l chnh l gi trxp xca hm ( )f x trong khong [ ); 1n n + . y

chnh l gi trtrung 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 tnhhm ( ) v php xp xho 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

( ) thomn:

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

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

c xp xho bng mt thp tuyn tnh ca cc hm ( )n . Ngoi

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

( ) ( )2 2

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

chng ta chcn mt shu hn cc thp tuyn tnh xp xho hm

( )f x . Chng ta c ththay i phn gii ca php xp xbng cch


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thay i hstlca cc hm ( )% v ( )x . Cho ( ) ( )22 2j

j jx = 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 trca j slm thay i

mc chnh xc ca php xp xhm ( )f x ca chng ta nhtrn hnh

3.2.

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

Hm ( )x c gi l hm tlv 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 thddng biu

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

1j jV V+

V vy chng ta c thbiu 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 thngi 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)

thomn:( )2j

j Z

V L R

=U (3.21)

{ }0jj Z

V

=I (3.22)

Tnh bt bin tl

( ) ( ) 02jjf 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 1Dtng qut. Vic p dng trong tn hiu nh (tn hiu 2D) c thd

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

phn p dng trongJPEG2000phn sau

3.3. Gii thiu mt shWavelet

3.3.1. Bin i WaveletHaar

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

bin i Wavelet. Hnh v3.2 cho thy dng ca hm ( )t vi bin i

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

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


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

hc ca bin iHaar

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 tn

hiu tt hn nhiu so vi bin iHaar. 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, Daubechiescng 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. Hbin i ny c ng dng ht sc rng ri, bin

i Waveletp dng trongJPEG2000l mt bin i trong hbin i


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

WaveletDaubechies:

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

3.4. Mt sng dng ni bt ca Wavelet

Phn ny chnu 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 sdng nn hay

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

dng nn ting ni, nn dliu. Vic sdng cc php m ho bng con,

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

hiu cn phn tch c thmang li nhng hiu qurt r rt trong nn tn

hiu. Do tnh cht ch tn ti trong cc khong thi gian rt ngn (khi

phn tch tn hiu trong min thi gian tn s) m cc hsca bin i

Waveletc khnng tp trung nng lng rt tt vo cc hsbin i.

Cc hsmang thng tin chi tit ca bin i Waveletthng rt nhv

c thbqua m khng nh hng ti vic m ho dliu (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 khnhiu cho tn hiu. Phng php kh

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

bn ca WSDda trn vic tn hiu nhiu slr khi phn tch bng bin

i Waveletcc hsbin i bc cao. Vic p dng cc ngng loi

b tng ng vi cc bc cao hn ca h sWavelet sc thddng

loi bnhiu 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 khnng nn vi t lnn cao

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

Waveletkt hp vi mt sphng php m ho nhm ho Huffman

hay m ho shc c th thc hin c chai iu trn. V th s s

dng bin i Wavelet trong 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 chunJPEG2000

Nhchng ta bit, sra i caJPEGmang li nhiu li ch to

ln vnhiu mt.JPEGc thgim nhkch thc nh, gim thi gian

truyn v lm gim chi ph xl 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 caJPEGv m ho khng tn tht caJPEGl kh phc

tp. vic nn nh c hiu quhn, y banJPEG a ra mt chun

nn nh mi l JPEG2000. JPEG2000sdng bin i Waveletv cc

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

JPEG2000hin vn ang tip tc c pht trin, nhng phn I c

tchcISOchp nhn l chun nn nh quc tp dng cho nh tnh.

Chun nn nhJPEG2000m 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 chgii thiu mt chun nn nhda trn bin i Waveletphbin m cn a ra mt la chn nhm gii

quyt ton cc bi ton t ra phn mu.

4.2. Cc tnh nng caJPEG2000

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

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

JPEG2000so vi cc chun nn nh tnh khc

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

Sdng c vi truyn dn v hin thlutin vcht lng,phn gii, cc thnh phn mu v c tnh nh vkhng gian.

Sdng cng mt cchnn nh cho chai dng thc nn. Truy nhp v gii nn ti mi thi im trong khi nhn dliu.


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

C khnng m ho nh vi tlnn theo tng vng khc nhau Nn mt ln nhng c thgii nn vi nhiu cp cht lng tu

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

JPEGbngJPEG2000.

4.3. Cc bc thc hin nn nh theo chunJPEG2000

nh m ho

X l trcbin i

Bin ithun linthnh phn

Bin ithun ringthnh phn

Lng tho

M ho

Gii m ho Gii l

ngt 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 mJPEG2000(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. Xl trc bin i chnh l giai on m

bo dliu a vo nn nh c dng trn. pha gii m, giai on xl

sau bin i strli gi trgc ban u cho dliu nh.

4.3.2. Bin i lin thnh phn

Giai on ny sloi btnh tng quan gia cc thnh phn ca

nh.JPEG2000sdng 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 trnguyn, cn bin i khng thunnghch lm vic vi cc gi trthc. ICTv RCTchuyn d liu nh t

khng gian muRGBsang YCrCb.RCTc p dng trong chai dng

thc nn c tn tht v khng tn tht, cn ICTchp 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 phlc. 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, Cbc nh hng rt t ti scm 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 v4.3:

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 trongJPEG2000chnh 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 nhbin iDCT

m l mt php bin i bng connn cc thnh phn sc phn chia

thnh cc bng tn skhc nhau v mi bng sc m ha ring r.

JPEG2000p dng bin i Waveletnguyn thun nghch 5/3(IWT)v

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

trongJPEG2000ny sc thc hin theo phng phpLifting (Cng

thc cthca phng phpLifting v bin i Wavelet trongJPEG2000

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

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

bin iWavelet 1Dtheo cc phng php phn gii nh tuchn. Trong

JPEG2000c 3phng php phn gii nh nhng phng php c s

dng nhiu nht chnh lphng 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 chai phng php, c tn tht v khng tn tht

trong khi bin i 9/7chp dng cho nn nh theo phng php c tn

tht thng tin.

4.3.4.Lng tho - Gii lng tho

Cc hsca php bin i sc tin hnh lng tho. Qu

trnh lng tho cho php t tlnn cao hn bng cch thhin cc

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

nh cn nn. Cc hsbin i sc lng tho theo php lng t

ho v hng. Cc hm lng tho 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 trbng con u vo; ( ),V x y l gi

trsau lng tho. Trong dng bin i nguyn, t bc lng tbng

1.Vi dng bin i thc th bc lng tsc chn tng ng chotng bng con ring r. Bc lng t ca mi bng do phi c

trong dng bt truyn i pha thu c thgii lng tcho nh. Cng

thc gii lng tho 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.

JPEG2000khng cho trc rtuy nhin thng chn 12r= .

4.3.5. M ho v kt hp dng dliu sau m hoJPEG2000 theo khuyn ngh ca uban JPEGquc tc th s

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

Waveletkhc nhau c ththu c cht lng nh tng ng vi ng

dng cn xl. iu ny gip choJPEG2000mm 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

Wavelet cng nhJPEG2000th 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 sxem xt hai phng

php ny. Vic kt hp dng dliu sau m ho caJPEG2000thc chtl thc hin cc tnh nng c bit caJPEG2000nhtnh nngROI

v.v...

4.3.6. Phng php m hoSPIHT

C ththy 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 sthtcao hn th scha nhng thnhphn tn sthp (mang thng tin chnh vnh). iu ngha l cc h

schi tit sgim dn tbng con mc thp (HH1chng hn) (ng vi

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

sthp) v c tnh tng tvkhng gian gia cc bng con, v dnh


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mt ng bin ca hnh vtrong nh stn ti cng mt vtr 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 thti thi im y l

tt nht c tht c vi mt slng 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

lnn thp) scha chnh d liu sau nn ca nh c kch c (lu tr)nh(tlnn cao). Bm ho chcn nn mt ln nhng c thgii nn

ra nhiu mc cht lng khc nhau. Gisgi ccpixeltrong mt nhp

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

pixeltrong nh to ra cc hsca php bin i Waveletl ci, j. Cc

hsny 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 bm ho sbt u qu trnh khi phc (gii nn) nh bng

cch t cc gi trca nh khi phc tcc hsbin i l c . Sdng

cc gi trgii m ca cc hsbin 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 thvit 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 luntruyn i cc gi trmang thng tin quan trng hn ca nh i trc. S

dlm nhvy l do cc thng tin chnh l cc thng tin slm gim

thiu nhiu nht mo dng ca nh (ssai 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

SPIHTsdng chai nguyn tc ny; n sp xp cc hsbin i v

truyn i cc bt c trng sln nht. Qu trnh gii m c thdng li

bt kmt 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 hoEZW

Phng php m ho EZW(Embedded Zerotree Wavelet Encoder)

cng da trn csphp m ho lutin (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 sxem 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 cmi nt cha th c 4

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

lkhc nhau. Ta gi y l cc cy tphn (quadtree). Scy tphn

c minh hohnh 4.5.

Level 3

Level 2

Level 1

LL

LH1

HL1

HH1

(a) (b)

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


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

cc nt ca n u nhhn nt gc. Mt cy nhvy 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 hsWavelet

Sau khi c cc khi nim cn thit vcy tphn v cyzero,

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

sm ho cc hstheo thtgim dn. Chng ta sdng mt gi tr

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

cc hsbin i. Cc hsc m ho theo thttvng tn sthpn vng tn scao. V chnhng hsc gi trtuyt i ln hn hoc

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

lm nhvy cho ti khi ngng t ti mt gi trnhhn gi trca h

snhnht. Cch gim gi trngng y thc hin tng i c bit,

gi trca ngng gim xung mt na so vi trc . Bgii m phi

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

khi ta i tnt cha n nt con trong cy tphn 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 thsny n hskhc theo thtnhthno. C

nhiu cch di chuyn khc nhau, tuy nhin hai cch di chuyn trnhnh

4.6 c sdng nhiu nht.

Raster Scan Morton Scan

Hnh 4.5: Hai cch sp xp thtcc hsbin 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 tlnn v tin cy gii m cao. Ngoi ra phng php

EZWrt dtrin khai trn my tnh bi phng php ny khng yu cu

vic lp trnh qu phc tp.

4.4. So snh chun JPEG2000vi JPEGv cc chun nn nh tnh

khc

Mt tnh nng quan trng v l u im r nt nht caJPEG2000so vi JPEG cng nhcc chun nn nh khc nhMPEG 4 VTC hay

JPEG- LSv. v.... lJPEG2000a ra chai kthut nn c tn tht v

khng tn tht theo cng mt c ch m ho ngha l JPEG2000 thc

hin tt ccc dng thc caJPEGchbng mt cchm ho duy nht.

Nu xt vstn ti ca hai kthut ny thJPEGcng c khnng nn

nh c tn tht v khng tn tht thng tin. Tuy nhin vi JPEGth c

chm ho vi hai dng ny l khc nhau v rt kh sdng chai

dng ny cng lc cho cng mt ng dng. Do , c ththy rngJPEG

c tnh mm do hn bt kchun 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 viJPEG; ngoi ra

nhng thng k v thc tcho thy vi cng mt t lnn v mt loi

nh th nh c nn biJPEG2000hu nhlun c cht lng tt hn

so viJPEG. 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 snhJPEGvJPEG2000

Tnh nng u vit th hai ca JPEG2000 so vi JPEG chnh l

trong dng thc nn c tn tht thng tin,JPEG2000c tha ra tl

nn cao hn nhiu so vi JPEG. Cc phn mm nn nh JPEGhin ti

(k cPhotoshop) cng ch thit k c th nn c ti t l 40:1

nhng viJPEG2000th tlnn c thln ti 200:1. Theo cng thc

tnhPSNRtrong n vdB, chng ta c: (b l sbt dng biu din mtpixeltrn nh gc)

=

12

RMSElog20)dB(PSNR

b

Vi hai nh hnh 4.6, sso snh vtham sPSNRcho trn bng

4.1. c thso snh ddng hn, ta xt nh c nn vi cc tlkhc

nhau (o lng bi hsbt/pixelhay bpp). Tt ccc sliu trn bng

u cho thy JPEG2000nn nh tt hn l JPEG; hn thh 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 theoJPEG 24.42 31.17 35. 15

nh 1 theoJPEG2000 28. 12 32.95 37. 35

nh 2 theoJPEG 22.6 28. 92 35. 99nh 2 theoJPEG2000 24.85 31.13 38. 80

Bng 4.1: So snhJPEGvJPEG2000

Tnh nng u vit th3 caJPEG2000so viJPEGl chun nn

nh ny c thhin thc cc nh vi phn gii v kch thc khc

nhau tcng mt nh nn. ViJPEGth iu ny l khng ththc hin

c. Sdc iu ny l doJPEG2000sdng kthut 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

JPEG2000ta chcn nn mt ln cn cht lng nh th sc quyt

nh tutheo ngi sdng trong qu trnh gii nn nh theoJPEG2000.Mt tnh nng u vit na caJPEG2000l tnh nng m ho nh quan

trng theo vng (ROI - Region of Interest) m chng ta cp trong

phn m ho nh theoJPEG2000. Cht lng ca ton bnh cng c

thy r trn hnh 4.7.


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Hnh 4.7: Minh hotnh nng ROI

Nhchng 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 nhROI.

JPEG2000cn c mt khnng c bit u vit hn so viJPEG, chnh l kh nng vt tri trong khi phc li. l khi mt nh

c truyn trn mng vin thng th thng tin c thbnhiu; vi cc

chun nn nh nhJPEGth nhiu ny sc thu vo v hin th, tuy

nhin vi JPEG2000, do c trng ca php m ho c th chng li,

JPEG2000c thgim thiu cc li ny ti mc hu nhkhng 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 caJPEG2000 vi mt schun nn nh nhl JPEG- LS; PNG;

MPEG 4 VTCqua bng 4.2 (Du + biu thchun c chc nng tng

ng, s du + cng nhiu th chun thc hin chc nng tng ng

cng tt) du - biu thchun tng ng khng htrtnh nng )


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JPEG2000JPEG-

LSJPEG

MPEG -4

VTCPNG

Kh nng nn nhkhng tn tht

+++ ++++ + - +++

Kh nng nn nh ctn tht +++++ + +++ ++++ -

Khnng lutin trongkhi phc nh

+++++ - ++ +++ +

K thut m ho theovngROI

+++ - - + -

Khnng tng tc vicc vt thc hnh dngbt k

- - - ++ -

Kh nng truy nhpngu nhin dng bt canh nn

++ - - - -

Tnh n gin ++ +++++ +++++ + +++Khnng khi phc li +++ ++ ++ +++ +Khnng thay i tlnn

+++ - - + -

Tnh mm do (khnng nn nhiu loi nhkhc nhau)

+++ +++ ++ ++ +++

Bng 4.2: So snh tnh nng caJPEG2000vi cc chun nn nh tnh khc

Tbng trn chng ta c th thy cc tnh nng vt tri v kh

nng u vit caJPEG2000so 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 sdng bin i Waveletkhai thc khnng 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 bnhiu 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 kthut

strnh by phn di y.5.2.1. Skhi tng qut

Hnh 5.1. Skhi qu trnh nn nh bng Wavelet

Hnh 5.1 chra skhi qut qu trnh nn nh (m ho ngun).

Qu trnh nhsau: nh mu c a qua mt php bin i to

thnh tp hsbin i. Cc hsny tip tc c lng tho (chia

cho cc gi trcnh cho trc) gim dung lng dliu. u ra ca


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bc ny l mt lung cc snguyn m mi mt trong s tng ng

vi mt ch snhphn c lng tho. Bc cui cng l m ho:

cc lung d liu c chuyn thnh chui cc tm nhphn (binary

symbol) theo cch: cc tm nhphn c di ngn m ho cho cc s

nguyn c xc sut xut hin cao. iu ny lm gim sbt cn truyn.

Cc nguyn l m ho nhvy l:Huffman[4]v RLC (m chy di)[4].

C nhiu thut ton sdng cho nn nh nh: da theo php bin

i, lng tho vcthoc m ho bng con. Vic la chn thut ton

trong truyn thng a phng tin di ng khng chphthuc vo ts

nn t c, cht lng nh khi phc m cn lin quan n nng lng

tiu hao cng nhkhnng trng li li bt cao hn.Gn y nhmJPEG 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. Nhvy 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 Wavelet

Php bin i Waveletthun sdng sphn ly 1D(mt chiu)

chuyn tp cc mu 1Dthnh hai bng: bng con thng thp (Li)v bng

con thng cao (Hi). BngLil phin bn c phn gii thp ca nh gc

c ly mu xung (downsampled), bng Hibiu ththng tin dtha

ca nh gc (chcn thit khi cn khi phc hon ton nh gc tbng

thng thp). Qu trnh phn ly bng con 2Dchl smrng qu trnh

phn ly bng con 1D. Ton bqu trnh chnh l sthc hin qu trnh

phn ly 1Dhai ln: u tin theo hng, ri theo ct. Theo cch ny, bng

con thng thpLito thnh khi phn ly theo hng li tip tc c phn

ly theo ct to thnh bng conLLivLHi. Tng tnhvy, bng conHi

tip tc c phn ly thnh HLivHHi. Sau mc bin i u tin, nh


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c thtip tc c phn ly bng cch p dng qu trnh phn ly 2Dcho

bng con LLi. Nhvy nh c thc bin i nhiu mc. Hnh 5.2

di y minh hoqu trnh phn ly nh 3 mc.

Hnh 5.2. (a) Bin i Wavelet2D mc 3 v (b) Minh hobng nh CASTLE

5.1.3. Tnh ton nng lng tiu hao

thc hin bin i Waveletcn chn mt blc cho n. y

ta chn blc c cp Daubechies 5-tap / 3-tap do nhng u im sau ca

n:

Kt qusau blc Waveletc cha thng tin im nh ln cn v

nhthloi bc hiu ng khi m bin iDCTgp phi

C tnh cht i xng v nh vcho php ddng pht hin ngvin, tnh ton nhanh, nh nn c cht lng cao.

Ddng thc hin bng phn cng v n chgm cc bcng v

bdch nhphn (khng phi l cc bghp knh v bchia).

(thc tc thchn nhiu cp blc 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 qucui cng vn khng mt tnh tng quan)

Phng trnh ca blc 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 sdng 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 c bn

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 sdng blc trn, cn 8 php ton

cng - A(Add)v dch - S(Shift) chuyn nhng im nh mu thnh

mt hsthng thp. Tng tnhvy, sphn ly thng cao cn 2 php

ton dch v 4 php ton cng. Chng ta lp m hnh tiu hao nng lng

ca sphn ly thng thp/cao bng cch m scc php ton v xem

chng nh l ti tnh ton(computational load). Nhvy 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 + 4Aphp ton cho thng cao.

Vi mt nh u vo cho trc kch thcM x Nv qu trnh phn

ly c p dng viL mc bin i, khi chng ta c thnh gi c

tng ti tnh ton nh sau: Gistrc 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 hsthng thp v cc im nh vtr lc

phn ly thnh cc hsthng 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 dnhn ra. Do kch thc ca nh gim

theo h s4 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(3

4

41

41)1012(

4

1)1012(

(5.2)

Ngoi cc php ton shc, bc bin i cng bao gm mt s

lng ln cc ln truy nhp bnh. 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 dliu (data-acces load)bng cch m tng scc

ln truy nhp bnhtrong 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 nhcng phng php nh gi nh

trn, tng ti truy nhp dliu rt ra bng scc ton tc v ghi

Ti truy nhp dliu vi bin i Wavelet thng:

=

==

L

llREAD

MNCC1

1WRITE_WW_ 3

8

4

12 (5.3)

Nng lng tnh ton tng c tnh bng tng trng sca ti tnh

ton v ti truy nhp d liu. Tkt qutin 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 dliugp 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) vRl tn hao

nng lng truyn mt bt bng bpht RF.

Nh vy ta phn tch bin v ngun gc ca tn hao nng

lng trong bin i Wavelet, tip theo chng ta strnh by cc kthut ti thiu nng lng tiu hao cng nhnng 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 chbnh hng t nht.

EEW khai thc phn bshc ca cc hsthng cao kho lo

loi bmt slng ln cc mu trong qu trnh nn nh. Hnh 5.3 minh

hophn bcc hsthng 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 trsnguyn nh. Ly v d, 80% cc hsthng cao

mc 1 (level 1)u khng vt qu 5. Chnh bi sphn bshc ca

cc hsthng cao v nh hng ca bc lng tho i vi cc h

sc gi trnh, chng ta c thlm trn cc hsthng 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 hsthng cao khng cn phi tnh ton,EEW lm gim

nng lng tnh tontiu hao trong qu trnh nn nh bng Waveletbng

cch gim slng cc php ton c thc hin. Thhai, bi v b

m ho v gii ml kthut lm trn (c lng), v thkhng c thng

tin yu cu c truyn qua knh v tuyn, do gim c nng lngtiu hao cn c.

Hnh 5.3. Phn bshc cc hsthng 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 hsthng cao: Kthut u tin l loi b

bng con t ngha nht. Trong s4 bng con ta thy bng con ng

cho (HHi)l t ngha nht (xem hnh 5.2), v l ng cvin sng gi

loi btrong bc bin i Wavelet. Chng ta gi kthut ny l k

thut loi bHH. kthut th2, th chnhng 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, HLiv HHi) u c loi b. Chng ta gi kthut

ny l kthut loi bH*(tt ccc bng con thng cao u bloi b

trong bc bin i).

Tip theo chng ta strnh by chi tit vcc kthut loi bHH

vH* v so snh hiu nng ca hai kthut ny vi thut ton sdng

Waveletnguyn bn (c xem l thut ton bin i Waveletkhng loi

bthng tin ( c cp trong mc 5.2.2 v 5.2.3).

5.2.1. Hiu nng ca cc kthut loi b

thc hin cc kthut loi bHHvH*(EEW), chng ta thay

i php bin i Waveletnhm ttrong 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 kthut loi bHH, th

sau khi thc hin bin i theo hng, cc hsthng 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

bbng con ng choHH. Cn thc hin kthut loi bH*, nh

u vo c xl chcho qua blc thng thp trong cqu trnh thc

hin bin i hng v ct. V nhvy 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 kthut loi bHH 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 sL mc. L do l

bi v u im ca cc hsthng cao thc hin loi bcng ngha

cc mc bin i thp.

Trong kthut loi bHH, ti tnh ton trong qu trnh thc hin

bin i theo hng bng vi thut ton Wavelet thng. 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 chra rng lm nhvy c thtit kim 1/4MN(4A+2S)

cc php ton cho ti tnh ton ( ngha l tit kim c 7.4% so vi thut

ton Wavelet thng). 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 SC 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 sln c trong kthut loi bHH. Tuy nhin, chng ta chtit


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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 qubng conHHc gn trc bng

0 trc khi qu trnh bin i c thc hin. Do vy, tng ti truy cp

dliu sc tnh:

= +=

+==

E

l

L

ElllHHWRITEWREADHHREAD

MNMNCCC1 1

11___ 4

12

4

1

4

7, (5.5)

Kthut loi bH*cho kt qung ktrong vic tit kim nng

lng tnh ton bi c 3 trong tng s4 bng con c loi b. Phn

ti chng ta stp trung m tv minh hocc kthut trn

5.3.2. Cc kt quthc nghim

Phn ny chng ta stin hnh thc nghim xem xt kt qutitkim nng lng tnh ton t vic p dng k thut loi b trn. Thc

cht l chng ta stp trung vo khnng tit kim nng lng tnh ton

v truyn thng sdng cc kthut 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 snn 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 quthc nghim


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KT LUN

Kt qut c v ng dng ca lun vn

Lun vn trnh by cc kthut nn nh, cc nguyn l nn v

mt skhi nim quan trng trong lnh vc x l nh. Tc gicng 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 vk thut nn nh s

dng bin i Wavelett p dng trong cc dliu a phng tin di

ng, nn tc gicng i su nghin cu csl thuyt ca php bin

i ny ng thi cng gii thiu chun nn nh JPEG2000 l chun

nn phbin da trn bin i Wavelet. Hn na chun ny cng s l

mt la chn hiu qubsung chunJPEGang c sdng 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

xl, nng lng truyn thng cho nh trn mng. iu ny ha hn c

thxy dng mt bm ho nh tit kim nng lng x l, thi gian

truyn m vn ph hp vi iu kin bng thng thp, rng buc vcht

lng dliu trong cc mng thng tin di ng.

Hng pht trin nghin cu

Tc gixin cp mt shng nghin cu trong tng lai:

Lun vn mi a ra ng dng Waveletcho nh tnh trong dliu

a phng tin di ng. Nhng u im ca Waveletkhin n cthp dng cho m thanh, video, khnhiu, bo mt,

C rt nhiu h Wavelet kh dng, c th la chn nhiu cp

Wavelet khc m khng nht thitchla 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 dliu hnh

nh gia cc thu bao, khnhiu, khi phc li mt gi tin nh,

Nghin cu thm v cc gii thut SPIHT, EWZ ng dng trongthng tin di ng.


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PHLC


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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

8. PGS. TS. HAnh Tu - Xl tn hiu s (2002)

9. Thomas Sikora MPEG-1 and MPEG-2 Digital Video CodingStandards.

10.Borko Furht, Stephen W.Smoliar, Hong Jiang Zhang Video and Image

Processing in multimedia systems.

11.Thomas Sikora Digital Video Coding Standards and Their Role in

Video Communications - Signal Processing for Multimedia, J.S. Byrnes

(Ed), IOS Press, 1999.

12.Anil K. Jain - Fundamental of Digital Image Processing(1994)13.Geoffrey Davis - Arina Nosratinia - Waveled-Based Image Encoding -

Overview (1997)

14. Michael David Adams - JPEG2000 - The Next Standard for Still Image

Compressing (12/2002)

15. Y. Kheong Chee - Information Theory and Its Application to Image

Coding (11/1995)

16. Geoffrey Davis - Roger Claypoole - Wim Sweldens - Richard G.Baraniuk -Nonlinear Wavelet transform for Image Coding via lifting (8/1999)

17. Michael David Adams - Reversible Wavelet Transform and their

Application to embedded image compression(1999)


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Ngc Anh

18. Michael David Adams - Faouzi Kossentini - Touraji Ebrahimi -

JPEG2000: The Next Generation Still Image Compression Standard

(2000)

19. R. Calderbank - I. Daubechies - Wim Sweldens - Wavelet transform that

map integer to integer(1998)

20. Website: http://www.citeseer.nj.nec.com

21. Website: http://research.microsoft.com

22. Website: http://www.JPEG.org/JPEG2000.html

ISO/IEC Standard 15444 JPEG2000- Final Committee Draft (2001)

kiemtailieu.com-nen anh trong wavelet

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