B GIO DC V O TO TRNG I HC BCH KHOA H NI 0380LUN VN THC S KHOA HC NN NH S DNG BIN I WAVELET V NG DNG TRONG CC DCH v D LIU A PHNG TIN DI NGNGHNH: IN T VIN THNGNgi hng dn khoa hc: PGS.TS. Nguyn c ThunH NI 2006

NGC ANH

MC LCCC HNH V, BNG BIU TRONGLUN VN5THUT NG TING ANH7LI GII THIU8CHNG 1: M U91.1. C s nghin cu v mc ch ca lun vn91.2. T chc lun vn10CHNG 2:TNG QUAN CC K THUT NN TRONG M HO NH112.1. Gii thiu chung v nn nh s112.2. Phn loi cc k thut nn132.2.1. Nn tn hao v khng tn hao132.2.2. M ho d on v m ho da trn php bin i132.2.3. M ho bng con142.3. Tiu chun nh gi cht lng m ho nh142.4. Cck thut nn c tn hao152.4.1. K thut m ho bng con152.4.2. K thut m ho da trn php bin i192.4.2.1. K thut m ho da trn php bin i DCT192.4.2.2. K thut m ho da trn php bin i DWT25CHNG 3:C S L THUYT BIN I WAVELET303.1. C s ton hc303.1.1. Bin iWavelet lin tc303.1.2. Bin iWavelet ri rc323.2. Tnh cht ca bin i Wavelet333.3. Gii thiu mt s h Wavelet373.3.1. Bin iWavelet Haar373.3.2. Bin iWavelet Meyer383.3.3. Bin i Wavelet Daubechies383.4. Mt s ng dng ni bt ca Wavelet393.4.1. Nn tn hiu393.4.2. Kh nhiu403.4.3. M ho ngun v m ho knh40CHNG 4:CHUN NN NH TNH DA TRN BIN I WAVELET - JPEG2000414.1. Lch s ra i v pht trin chun JPEG2000414.2. Cc tnh nng ca JPEG2000414.3. Cc bc thc hin nn nh theo chun JPEG2000424.3.1. X l trc bin i424.3.2. Bin i lin thnh phn424.3.3. Bin i ring thnh phn (bin i Wavelet)434.3.4. Lngt ho - Gii lng t ho444.3.5. M ho v kt hp dng d liu sau m ho454.3.6. Phng php m ho SPIHT454.3.7. Phng php m ho EZW474.4. So snh chun JPEG2000 vi JPEG v cc chun nn nh tnhkhc49CHNG 5:NG DNG WAVELET TRONG CC DCH v D LIU A PHNG TIN TRONG THNG TIN DI NG545.1. Nn nh bang Wavelet545.2.1. S khi tng qut545.1.2. Bin i Wavelet555.1.3. Tnh ton nng lng tiu hao565.2. Thut ton nn nh bng Wavelet hiu nng - EEW585.2.1. Hiu nng ca cc k thut loi b605.3.2. Cc kt qu thc nghim625.3.2.1. nh hng n nng lng tnh ton v cht lng nh 625.3.2.2. nh hng n nng lng truyn thng v cht lng nh625.4. Cc tham s nn nh bang Wavelet625.4.1. Thay i mc bin i Wavelet625.4.2. Thay i cc mc lng t625.5. Truyn nh trn mng625.5.1. Phng php la chn tham s ng625.5.2. Kt qu thc nghim62KT LUN63Kt qu t c v ng dng ca lun vn63Hng pht trin nghin cu63PH LC65Lun vn cao hc TVT 2004 - 2006

Lun vn cao hc TVT 2004 - 2006

TI LIU THAM KHO66 Ngc Anh

Ngc Anh

CC HNH V, BANG BIU TRONG LUN VNHnh 2.1 S b khi qut h thng nn nh12Hnh 2.2. S minh ho k thut m ho bng con - M bng con16Hnh 2.3 Minh ho qu trnh phn ly bng con cy bt phn17Hnh 2.4. Phn ly hai nh mu thnh bn bng con18Hnh 2.5. S b m ho theo chun JPEG23Hnh 2.6. Sp xp Zigzag cc h s DCT b m ho23Hnh 2.7. S khi b gii m theo chun JPEG23Hnh 2.8. Bank lc khi phc l thuyt s dng DWT 1D28Hnh 2.9. Minh ho DWThai chiu cho nh28Hnh 2.10(a). Minh ho DWTkiu dyadic mc 3 nn nh28Hnh 2.10(b). Minh ho DWTkizu dyadic mc 3 nn nh29Hnh 3.1. Minh ho li nh to dyadic vi cc gi tr ca m v n33Hnh 3.2. Phn tch a phn gii p dng cho biu din tn hiu36Hnh 3.3. Hm y/t) ca bin i Haar38Hnh 3.4: Hm y/(t) ca bin i Meyer38Hnh 3.5. Hm y/(t) ca h bin i Daubechies n vi n=2, 3, 7,839Hnh 4.1 : Trnh t m ho (a) v gii m JPEG2000 (b)42Hnh 4.2: Minh ho nh vi RGB v YCrCb43Hnh 4.3: Phng php Lifting ID dng tnh ton bin i Wavelet44Hnh 4.4: Minh ho cy t phn (a) v s phn mc (b)47Hnh 4.5: Hai cch sp xp th t cc h s bin i48Hnh 4.6: So snh JPEG v JPEG200050Bng 4.1: So snh JPEG v JPEG200051Hnh 4.7: Minh ho tnh nng ROI52Bng 4.2: So snh tnh nng ca JPEG2000 vi cc chun nn nh tnhkhc53Hnh 5.1. S khi qu trnh nn nh bang Wavelet54Hnh 5.2. (a) Bin i Wavelet 2D mc 3 v (b) Minh ho bng nhCASTLE56Hnh 5.3. Phn b s hc cc h s thng cao sau php bin i Waveletmc 259Hnh 5.4: D liu sau php bin i Wavelet vi hai k thut loi b HH v H*61THUT NG TING ANHCWTBin i Wavelet lin tc (Continuous Wavelet Transform)DCTBin i Cosine ri rc (Discrete Cosine Transform)DFTBin i Fourier ri rc (Discrete Fourier Transform)DPCMiu xung m vi sai (Differized Pulse Code Modulation)DWTBin i Wavelet ri rc (Discrete Wavelet Transform)EZWWavelet cy zero (Embedded Zerotree Wavelet)HVSH thng cm nhn hnh nh ca mt ngi(Human Visual System)IDWTBin i Wavelet ri rc ngcJPEGChun nn nh ca y ban JPEG quc t(Joint Photographic Experts Group)JPEG2000Chun nn nh JPEG2000Lossless CompressionK thut nn nh khng tn hao (khng mt d liu)Lossy CompressionK thut nn nh c tn hao (c mt d liu)MRAPhn tch a phn gii (Multi Resolution Analysis)MSESai s bnh phng trung bnh (Mean Square Error)PCMiu xung m (Pulse Code Modulation)PSNRT s tn hiu nh trn nhiu (Peak Signal to Noise Ratio)QMFLc gng cu t phng (Quardrature Mirror Filters)RLCM ho lot di (Run Length Coding)ROIK thut m ha nh theo vng (Region Of Interest) - Mttnh nng mi ni bt ca JPEG2000 SPIHTPhng php m ho phn cp theo vng(Setpartitioning in hierarchical trees)STFTBin i Fourier thi gian ngn (Short Time FourierTransform)WaveletBin i bng con WaveletWavelet Decomposition Cy phn gii Wavelet TreeLI GII THIUTrong 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 Wavelet cho 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 l v truyn trn mng. Trong lun vn trnh by mt k thut nn nh trong mng di ng s dng bin i Wavelet hiu nng khng ch em 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.CHNG 1: M U1.1. C s nghin 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 tr truyn 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: bng thng ca mng di ng t bo, nhiu knh, gii hn ca pin cho cc ng dng, tnh tng thch d liu 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 lng trong 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 dng bin i Wavelet thch nghi v hiu nng cho d liu a phng tin trong thng tin di ng.1.2. T chc lun vnLun vn c trnh by thnh 5 chng v 1 ph lc. Chng 1, tc gi trnh by tm tt c s nghin 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 ng c s dng rng ri nh MSE, PSNR v SNR. Chng ny cng trnh by c s 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 Wavelet ri rc (DWT).Chng 3 trnh by c s ton 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 h Wavelet ph bin v gii thiu mt s ng dng ni bt ca Wavelet ngoi 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 DCT m cn a ra mt la chn gii quyt bi ton t ra trong lun vn. JPEG2000 ang 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 bang 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).CHNG 2:TNG QUAN CC K THUT NN TRONG M HO NH2.1. Gii thiu chung v nn nh sNn 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 hon 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 mt chui nh video, tn ti s tng quan gia cc im nh ca cc khung video (frame).

Hnh 2.1 S b khi qut h thng nn nh

Trong 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 so hc [4]. B gii m thc hin qu trnh ngc li so vi b m ho.S ca mt h thng nn d liu tng qut nh sau:

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:T s nn = Kch thc d liu gc/ Kch thc d liu 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).

2.2. Phn loi cc k thut nnCc k thut nn ch yu c phn loi nh sau:2.2.1. Nn tn hao v khng tn haoTrong 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 th t 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 vct - VQ, m ho bin i v bng con. nh khi phc trong h thng 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 d on v m ho da trn php bin ii vi m ho d on (predictive coding) cc gi tr mang thng tin c gi hay ang sn c s c s dng d on 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 d in 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 hon rt nhiu so vi phng php nn d on 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 hon s b loi b sau khi lng t ho v nh vy lng d liu phi truyn nh i rt nhiu. Trong phng php m ho d on, sai lch gia nh gc v nh d on vn c ngha (cn s dng bc tip theo) sau khi lng t ho, chnh iu ny lm cho phng php m ho d on c nhiu d liu c truyn i hn so vi phng php m ho bin i.2.2.3. M ho bng conBn 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 nh nh 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). MSE thng c gi l phng sai lng t - 2q (quantization error variance). MSE gia nhgc v nh khi phc c tnh nh sau:MSE = ] =k] - gj, k])2(2.1)N j*Trong tng ly theo j, k tnh cho tng tt c cc im nh trong nh v N l s im nh trong nh. Cn PSNR gia hai nh (b bt cho mi im nh, RMSE l cn bc 2 ca MSE) c tnh theo cng thc dB nh sau:PSNR = -20 logl0 ~~~~(2.2)A 1Thng 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:sm = mogME^oderinputenergy Noise energy2.4. Cc k thut nn c tn haoTrong 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 conT 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. e 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 s c ly mu xung s ln lt c: lng t ho c lp bng cc b lc v hng khc nhau, m ho entropy, lu tr v 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 thit k 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 gi t c do nhng b lc ny ch xp x vi cc b lc l tng.Hnh 2.2 di y l s tng qut gii thch k thut m ho bng con.

Bandpass synthesis filter bank 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(co) cn p ng ca cc b lc thng cao l H(co+7r) ch l s dch pha 180 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 b nh 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 p dng trong cc b m s dng bin i Wavelet. u ra ca cc bng con sau khi gin lc s c 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 d nh gc v tp trung nng lng ca nh vo mt s bng con. Nn ch t 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 min tn 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 HH mc u tin.hDrliontal ar>lhhtm

1IT T*

1 LiHa.... iLi]

HHhHH

Horizontal low and high Horizontal and verticalirixcmtal high trGuaorl

' iC ;

rc '1 bt/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.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 d on l rt ln).2.4.2. K thut m ho da trn php bin iMt 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 biu din 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 DWT2.4.2.1. K thut m ho da trn php bin i DCTPhp 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 bin theo thi gian. e hiu r k thut ny trc ht ta cn tm hiu bin i Fourier.Bin i Fourier - FTBin 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 Fourier khng c s xut hin thng tin v thi gian.FT cho bit thng tin tn s ca tn hiu, cho bit nhng tn s no c trong tn hiu, tuy nhin n khng cho bit tn s xut hin khi no trong tn hiu. Neu 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 FT thun v nghch c nh ngha nh sau:X(f) = xt)e-2J*dt(2.4)0000x(t) = x)eMdf(2.5)00Php bin i FT cng c th c p dng cho tn hiu khng n nh (non-statonary) 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 FT khng c kh nng p ng c yu cu ny, y cng l hn ch ca php bin i ny.e c bin i Fourier ri 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.

H s php bin i DFT th k ca mt chui gm N mu x(n)} c nh ngha:X(k) = I\x(n)W , k=0, N-l(2.6)n=0Trong WN = e~jmN = COS (2ft/N) -j sin (27/N), cn chui fx(n)} c th khi phc bang DFT ngc nh sau:x(n) = y X(kW^ , n=0,, N-l(2.7)N tnh ngha v cc tnh cht ca bin i DCTBin i DCT thun v ngc mt chiu gm N mu c nh ngha nh sau:DCT = X(k) = ck Yx(n)cos\{2n + )k7, k= 0,1,,N-1 (2.8),n=0,l,,N-1 (2.9)

N s2N (2 n + X)kn

IDCT = x(n) = y'cytX(:)cos N2N

rrAr\l/y2,k= 0Trong ck= \[1, k ^ 0C DCT v IDCT u 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 DCT \ DCT l khng bt thng (non-sngular) v thc th bin i ngc ca chng c th t 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 IDCT c kch thc 8 mu. Bc nh hoc khung nh video kch thc NxN c 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 IDCT b gii m.Bin i DCT v IDCT 8 mu to thnh cc ma trn 8x8 theo cng thc:

2-D DCT = xkl =Xm n cospmj (2.10)Trong k, l = 0,1,,72-DIDCT=xm, = c{k)c(l) X tJcos|^(2m +1 )k cos(2n +1 )br j (2.11) Trong m,n = 0,1,,7' /7 1 //>= fl/V2,*&/ = 0v c(k),c(l) = \\l,k2 + l2 *0Thut ton tnh 2-D DCT v IDCT l: thc hin php bin i 1-D ln lt cho hng ri n ct ca ma trn.So snh DCTxKLTHiu 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 MSE gia nh khi phc v nh gc.Nn v gii nn nh da theo php bin i DCT trong JPEGJPEG l chun nn s quc t u tin cho cc nh tnh c tng mu lin tc gm c nh on 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 (7 l thnh phn chi, u v V l 2 thnh phn mu). Thnh phn chi l nh on sc xm. Hai thnh phn mu cn li cha thng tin v mu. Vic m ho v gii m nh trong JPEG c thc hin cho thnh phn chi ri mu.S khi b m ho v gii m ca JPEG nh sau:

Hnh 2.5. S b m ho theo chun JPEG

-tojr--ki

T'/t7

?////4

V//>ts*/J/,1

///4

V/f r ,r/T

//.*/*

1 i Jw'iv'LT

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 mi khi khi nh s c tr i 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 th c 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 tn s 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 on gin n ch chuyn thng tin nh sang min khng gian mi thut li hon 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 l ng nht. Ngha l cc h s s c 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 hon cc h s tn s cao v c nhy tt hn cc h s c tn s thp. V th cc h s c 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.(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 s c 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 so 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 hai chiu 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 s c bin i 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 s c ni suy thnh kch thc gc.2.2.2. K thut m ho da trn php bin i DWT Mi quan h gia bin i Wavelet v FourierKhng ging nh bin i Fourier ch thch hp khi phn tch nhng tn hiu n nh (stationary), Wavelet l php bin i c s dng phn tch cc tn hiu khng n nh (non-statonary) - l nhng tn hiu c p ng tn s thay i theo thi gian.e khc phc nhng hn ch ca bin i FT, php bin i Fourier thi gian ngn - STFT c 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 trong khong tn hiu c gi nh l tn hiu n nh. e thc hin k thut ny cn chn mt hm ca so w sao cho di ca ca s ng 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 FT ta khng thc hin c.Bin i STFT i vi tn hiu lin tc thc c nh ngha nh sau:X(f,t) = j[x(t)w (t-T)']e-M>dt(2.12)00Trong di thi gian ca ca s l (t-), chng ta c th dch chuyn v tr ca ca s bng cch thay i gi tr t v thu c cc p ng tn s khc nhau ca on tn hiu ta thay i gi tr T.Gii thch bin i STFT bng nguyn l bt nh Hessenber, nguyn l ny pht biu l: Khng th bit c chnh xc c biu din thi gian - tn so ca mt tn hiu (hay khng th bit cc thnh phn pho ca 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. Neu hm ca s cng hp th phn gii cng tt hon v gi nh tn hiu l n nh cng c chnh xc nhng phn gii tn s li km i. Ta c cc h qu sau:Ca s hp -> phn gii thi gian tt, phn gii tn so km Ca s rng -> phn gii tan so tt, phn gii thi gian kmTrn c s cch tip cn bin i STFT, bin i Wavelet c pht trin gii quyt vn v phn gii tn hiu (min thi gian hoc tn s) m STFT vn cn hn ch. Bin i Wavelet c 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 cn nh vy cn c gi l: phn tch a phn gii - MRA (Mult Resolution Analysis)', phn tch tn hiu cc tn so 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 so km cc tn so cao; phn gii tn s tt v phn gii thi gian km cc tn so thp. 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 nh nh v khung nh video.C s ton hc cng nh cc tnh cht ca bin i Wavelet lin tc s c trnh by chi tit trong chng 3.Bin i Wavelet ri rc -DWTBc ny c th hiu php bin i DWT nh 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 180. Tuy nhin khc vi m ho bng con, cc b lc trong DWT c thit k phi c p ng ph phng, 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 H v 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 H v chnh l H, G).

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

T bin i DWT mt chiu c th m rng nh ngha bin i DWT hai 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 DWT mc 1, s to ra 4 nhm h s bin i. Qu trnh bin i DWT hai 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).IMAGEDWTLHDWTLLHL

theo hngtheo ctLHHH

Hnh 2.9. Minh ho DWThai chiu cho nh

Ttng cao

Hnh 2.10(a). Minh ho DWT\n dyadic mc 3 nn nh

Mc 3

Hnh 2.10(b). Minh ho DWT\u dyadic mc 3 nn nh Hai thut ton nn s AxmgDWT in hnhSo vi bin php bin i DCT s 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 Wavelet a 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 partitatonng n 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 Wavelet s nguyn. K thut ny s dng cc b lc Wavelet trc 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.CHNG 3:C S L THUYT BIN I WAVELET3.1. C s ton hc3.1.1. Bin i Wavelet lin tcBin i Wavelet lin tc (Continuous Wavelet Transform - CWT) ca mt hm f(t) c bt u t mt hm Wavelet m (motherWavelet) /(t). Hm Wavelet m /(t) c th l bt k mt hm s thchoc phc lin tc no tho mn cc tnh cht sau y:Tch phn suy rng trn ton b trc t ca hm y/(t) l bng 0. Tc l:J \(t)dt- 0(3.1)-00Tch phn nng lng ca hm trn ton b trc t l mt s hu hn, tc l:J |^()|2 dt < 00(3.2)-00iu kin (3.2) c ngha l hm y/(t) phi l mt hm bnh phng kh tch ngha l hm y/(t) thuc khng gian 2(^) cc hm bnh phng kh tch.Sau khi hm Wavelet y/(t) c la chn, bin i Wavelet lin tc ca mt hm bnh phng kh tch /(t) c tnh theo cng thc:w(a,b)= f(3.3)^ J\a\ V a JBin i ny l mt hm ca hai tham s thc a v b. Du * k hiu l lin hip phc ca y/(t). Nu chng ta nh ngha mt hm ab(t) theobiu thc:'". M=-oM ^ a'chng ta c th vit c:w(a,b) = f(t)y/a b (t)dt (3.5)-00Theo ton hc ta gi y l tch v hng ca hai hm f(t) v /ah(t). Gi tr Lr l h s chun ho m bo rng tch phn nng lng ca /hm /a h () s c lp vi a v b :J \Vajb (0|2 dt=\\v (0|2 dt (3 -6)00 00Vi mi gi tr ca a th \/ ft() l mt bn sao ca \ 0() cdch i b n v trn trc thi gian. Do b c gi l tham s dch. t tham s dch b = 0 ta thu c:V'*At) = -f("fri (3-7)vll Wiu cho thy rng a l tham s t l.Khi a > 1 th hm Wavelet s c tri rng cn khi 0 < a < 1 th hm s c co li. Sau y chng ta s nh ngha php bin i ngc ca bin i Wavelet lin tc. Gi '()) l bin i Fourier ca y/(t):= I [t)e~j(tdt (3.8)-00Nu w(a,b) l bin i CWT ca /(/) bng hm Wavelet th bin i ngc ca bin i CWT s c tnh nh sau:/ w = V^t)dadb (3.9) avi gi tr ca c nh ngha l:C=\_dc0 (310J J^ \)\Bin i CWT ch tn ti nu dng v hu hn. Do c gi l iu kin tn ti ca bin i Wavelet. Cng vi hai iu kin nu trn, y l iu kin th 3 m mt hm cn phi tho mn c th c 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 f(t) v y/a h (). Cc hng ca ma trn tng ng vi cc gitr ca a v cc ct tng ng vi cc gi tr ca b do cch tnh bin i Wavelet theo tch v hng trnh by trn:{f(t),g(t))=lsf(t)g'{t)dt^(f(t),,iih(t))=^f{t)v/l,ll(i)dt (3-11)3.1.2. Bin i Wavelet ri rcVic tnh ton cc h so Wavelet ti tt c cc t l l mt cng vic ht sc phc tp. Neu tnh ton nh vy s to ra mt lng d liu khng l. e 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 c s lu tha c s 2 th kt qu thu c s hiu qu v chnh xc hon 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 Wavelet ri rc (.DWT). Do , vic tnh ton bin i DWT thc cht l s ri rc ho bin i Wavelet lin tc (CWT); vic ri rc ho c thc hin vi s la chn cc h s a v b nh sau: a = 2m;b = 2mn; m,neZ (3.12)Vic tnh ton h s ca bin i Wavelet c th d dng thc hin bng cc bng lc s nhiu nhp a knh, mt l thuyt rt quen thuc trong x l tn hiu.

Hnh 3.1. Minh ho li nh t dyadic vi cc gi tr ca m v n3.2. Tnh cht ca bin i WaveletTt c chng ta u bit rng bin i Fourier l mt bin i v ang c p dng rng ri trong nhiu ngnh khoa hc v k thut khc nhau. Bin i Fourier chuyn mt hm tn hiu t min thi gian sang min tn s. S dng bin i Fourier ta c th bit c trong tn hiu f(t) c cc thnh phn tn s no. Tuy nhin bin i Fourier cmt nhc im c bn l vi mt tn hiu f(t) ta khng th bit crng ti mt thi im t th tn hiu c cc thnh phn tn s no. Mt php bin i tt hon bin i Fourier phi l php bin i c y tnh nng ca bin i Fourier v 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 iWavelet ra i khc phc c cc nhc im ca bin i Fourier trong phn tch tn hiu. Bin i Wavelet d 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 ccthnh phn tn s khc nhau ca tn hiu xy ra ti thi im t. Cc gi tr w(ai,b) to thnh mt ct (7=7, 2,...., n) cho bit mt thnh phn tn sc trong nhng thi im t no v cc gi tr Va,^) to thnh hng chobit 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 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 nh ng dng rng ri hn na. Tham s b trong bin i Wavelet cho bit khong dch ca hm Wavelet m v phn gii cc tn s khc nhau ca c minh ha bi h s t lchnh l a. Bin i Wavelet ngy 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 Fourier l 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 nh hng v tnh nh v. Tnh nh hng ca mt nh ngha l trong nh bao gi cng 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 Wavelet vi cc hm Wavelet thch 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 hon. Trc khi xem xt ng dng ca phn tch a phn gii trong nn nh, chng ta xem xt l thuyt v a 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 / (x) bng mt tp cc gi tr ri rc (vd hm f(x) l hm cng sng ca nh). Php xp x on gin thchin da trn l thuyt php ly trung bnh v da vo hm xp x l hm (x) c dng:x1xs[:l)(3.13)[occ gi tr cn liVic tnh ton cc gi tr xp x ca hm f(x) theo hm (x) s c vit nh sau:^[/W]=Z-/X*-w) (3-14)nvi fn l chnh l gi tr xp x ca hm f(x) trong khong [n;n +1). y chnh l gi tr trung bnh ca hm f(x) trong khong [n;n + l) c cho bi biu thc:/="'/(*) (3.15)Nh vy chng ta c th xp x ho hm f(x) bng mt tp cc hm tng t nh hm (p[x) v php xp x ho hm /(jc) cho bi: ^[/(x)]=Z(^(x_'2)/(x))^(x_,)(3.16)n y () c gi l hm trng v