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8/10/2019 NguyenVanThien_De12

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TRNG I HC BCH KHOA H NI

VIN CNG NGH THNG TIN V TRUYNTHNG

*

BI TP LN

XL NH

ti:Tm hiu bi ton khi phc nh, m hnh quan st nhkthut lc Wiener v kho st ng dng

Ging vin hng dn: Nguyn ThHong Lan

Sinh vin thc hin: Nguyn Vn Thin

Lp: KSTN-CNTT-K56

MSSV: 20112282

H NI


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MC LC1. Bi ton khi phc nh. ...................................................................................................................... 3

2. M hnh quan st nh. ......................................................................................................................... 4

2.1. M hnh nh b xung cp bi nhiu cng ngu nhin................................................................ 42.1.1. B lc Wiener........................................................................................................................ 4

2.2. M hnh nh b xung cp v nhe............................................................................................... 8

2.3. M hnh nh b xung cp bi c nhe v nhiu cng. ................................................................ 9

2.4. M hnh nh nhiu ph thuc tn hiu........................................................................................ 10

3. Kho st ng dng ca b lc Wiener.............................................................................................. 11

4. Ti liu tham kho ............................................................................................................................ 15

Danh mc cc hnh vHnh 1. M hnh nhiu cng ................................................................................................................... 4

Hnh 2. S khi thc hin blc ....................................................................................................... 5

Hnh 3. M phng blc Wiener ........................................................................................................... 6

Hnh 4. nh bnho ................................................................................................................................ 8

Hnh 5. nh bnhe nhng khng bit vhm gy nhe ...................................................................... 9

Hnh 6. M hnh blc trng hp nhiu cng nhe ........................................................................... 10

Hnh 7. Kt qukhi phc nh bnhiu ............................................................................................... 12

Hnh 8. Kt qukhi phc nh bnhe do chuyn ng ...................................................................... 13

Hnh 9. Kt qukhi phc nh do nhe v nhiu ................................................................................. 14


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1. Bi ton khi phc nh.

Khi nim: Khi phc nh cp ti cc k thut loi b hay ti thiu ho cc nh hng

ca mi trng bn ngoi hoc t cchthng thu nhn v lu tr nh n nh thu nhn c.

Ni cch khc: nu coi x m l nh sgc, y m l nh sbgim cht lng (u vo) v x m l

nh s xl (u ra). Mc ch ca bi ton khi phc nh l lm cho nh xl x m gn

ging nh nh ban u x m .

Kthut khi phc nh nhm c thc lng li nh gc hay nh l tng tnh quan st c

bng cch o ngc li nhng hin tng gy bin dng. V vy khi phc c nh c kt qu,

iu cn thit l phi bit c cc nguyn nhn, cc hm (hay dng) gy ra bin dng nh. Cc

nguyn nhn bin dng thng do: Do camera, u thu nh cht lng km.

Do mi trng, nh sng, hin trng (scene), kh quyn, nhiu xung.

Do cht lng.

Vic khi phc nh ph thuc vo loi hnh xung cp hay khi phc nh l nhm xc nh m hnh

ton hc ca qu trnh gy ra bin dng. Cc loi hnh xung cp ta xt l nhiu cng ngu nhin,

nho v nhiu ph thuc tn hiu, nh nhiu nhn. Cc thut ton lm gim nhiu cng ngu nhin

khc vi cc thut ton lm gim nho nh.

c lng s xung cp: C hai cch tip cn c thng tin v s xung cp.

Mt cch tip cn l thu thp thng tin t chnh nh b xung cp. Nu ta c th tm ra cc

vng cng xp x ng u trong nh, chng hn bu tri, th c th c lng ph cng sut

hoc hm mt xc sut ca nhiu nn ngu nhin t s thng ging cng trong cc vng c

nn ng u. Mt v d khc nh, khi nh b nho nu ta tm c trong nh xung cp mt vng

m tn hiu gc bit, th c th c lng hm nho .n m K hiu tn hiu nh gc mt vngc bit ca nh l x m v nh b xung cp trong vng l y m , th quan h gn ng gia

y m v x m l:

y m x m n m


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Theo gi thit x m v y m u bit, nn c th c c lng c .n m

Mt cch tip cn khc hiu bit v s xung cp l nghin cu c ch gy ra xung cp. V d,

xt mt nh tng t b nho bi s dch chuyn phng ca my nh lc chp. Mt v d khc

s xung cp c th c c lng t c ch ca n l nhiu ht ca phim, lm nho nh l do nhiu

x quang v gy ra nhiu lm m.

2. M hnh quan st nh.Nh nu trn, qu trnh gy ra bin dng nh gc ph thuc vo h thng quan st v to

nh. Do vy, trc ht ta cn xem nh quan st c biu din th no, trn c s m hnh ho

nhiu sinh ra. Tip theo l dng bin i ngc (lc ngc) khnhiu v thu linh gc. l c

sl thuyt ca k thut khi phc nh.

2.1. M hnh nh b xung cp bi nhiu cng ngu nhinXt mt nhx quan st c c thm nhiu cng nc th hin trong cng thc sau:

y m x m n m

Hnh 1. M hnh nhiu cng

Gi thit nhiu cng ngu nhin c lp vi tn hiu (khng tng quan).

2.1.1. B lc Wiener.Mt trong nhng phng php u tin c trin khai lm gim nhiu cng ngu nhin

trong nh l php lc Wiener.


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Nguyn l da trn c lng c thc hin bng cch hthp sai sbnh phng trung bnh (Mean

Square Error) gia tn hiu mong mun v tn hiu c lng. Trong xl nh sth l sai sgia

nh gc v nh ang c.

Mt blc Wiener c thl mt trong hai loi IIR hoc FIR. Tuy nhin blc Wiener thngc gn vi cc cng trnh xy dng blc FIR. iu ny l bi v cc hsblc Wiener thay i

theo thi gian, v blc IIR c thtrnn khng n nh cho cc gi trhsnht nh. ngn

chn iu khng n nh ny, chng ta thng xy dng cc blc thch nghi vi cu trc FIR.

Blc Wiener c biu din bi mt vector trng s 0 1 1, ,..., ,T

Pw w w w

Quan hlc gia u vo v u ra: 1

0

w wP

T

k

k

x m y m k y

V Tw y l mt v hng nn bng chuyn vca n, tc l: .T Tw y yw

Tn hiu li m c xc nh bi s sai khc gia tn hiu mong mun x m vi tn hiu thu

c x m c tnh bng:

T Tm x m x m x m w y x m y w

Hnh 2. S khi thc hin blc

i vi b lc Wiener, hm hiu nng c chn l sai sbnh phng trung bnh 2E m .

Trong k hiu l kvng thng k.

2

2 =

T T

T T T T

E m E x m w y x m y w

E x m w E yx m E x m y w w E yy w


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Ta nh ngha vectortng quan cho gia u vo v tn hiu mong mun l ,xyr E x m y m

v ma trn ttng quan ca tn hiu u vo l : ,TyyR E y m y m ta c :

2

0 2

T T

xy yx yyE m r w r w R w

thu c cc trng sng vi 2E m c gi tr cc tiu, ta cn phi gii hphng trnh

c to thnh to hm bc nht caEi vi mi trng sbng khng, tc l:

20

2 2 =0

2 2 0

T T

T

yx yy

E mw

E x m y m w E y m y m

r w R

Trong ton tgradian c xc nh:0 1 1

, ,...,

T

Pw w w w

Do : 1yy yx yy yxR w r w R r

khi :

2 0 Txy yyE m r w R w .

Hnh 3. M phng blc Wiener

(ngun: Tham kho [2])

Trong min tn s, nhiu cng c biu din:

Y f X f N f


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Khi sai khc gia X f thu c vi mong mun X f bng:

f X f X f X f W f Y f

X f W f X f N f

Bnh phng sai khc:

2

2E f E X f W f X f N f

Tng tcch lm trn, ta tnh o hm theo W thu c:

2

2 2 22 2

E fE W X N X

W

Cho 2

0E f

W

ta thu c p ng xung ca blc Wiener bng:

1XXXX NN

P fW f

P f P f

Trong XX

P vNN

P l phcng sut ca tn hiu v nhiu.Nu gi thit rng ph cng sut XXP v

NNP ca chng bit, th c th nhn c c lng tuyn tnh ti u sai s qun phng ti thiu

ca X f bng cch cho Y f qua b lc Wiener m p ng tn s W f .

Trong nhng bi ton thng gp, c lng ph cng sut nhiu NNP tng i d lm, nhng c

lng ph cng sut nh XXP th khng n gin. Mt phng php c s dng l ly trung bnh

2

X f cho nhiu nh x m khc nhau.

Chia ctcmu ca (1) choNN

P v t

XX

NN

P fSNR f

P f l tstn hiu trn nhiu ta thu c:

1

SNR f W f

SNR f

Khi 0SNR th W f

Trong nhiu cng, p ng xung ca blc Wiener l mt sthc v 0 1W f

By gichng ta hy xem xt hai trng hp:

i)

nh khng c nhiu 0NNP SNR v 1W f

ii) nh ton nhiu 0 0XXP SNR v 0W f

Nh vy b lc Wiener gi nguyn SNR ca cc phn hp thnh tn s cao nhng lm gim SNR

ca cc phn hp thnh tn s thp. c im b lc Wiener l thng thp.


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2.2. M hnh nh b xung cp v nheMt nh b xung cp v nho c th m hnh ho nh sau:

*y m x m h m

Trong m hnh trn nh b xung cp y m l kt qa nhn chp nh gc x m vi mt p ngxung h m . h m c gi l hm nho.

Hnh 4. nh bnho

(Ngun: http://www.svi.nl/BlindDeconvolution)

S xung cp ny c th c m hnh ho bng nhn chp vi nho do cc nguyn nhn nh thu

knh lch tiu c, my b rung v nhiu lon ca kh quyn. Bi ton lm gim nho c th chia thnh

hai loi. Loi th nht l gii tch chp (deconvolution), trong khi hm nho h bit, mt cch

tip cn kh nho l b lc ngc. T:

*

Y fY f X f N f X f

N f

Loi th hai l gii tch chp m (blind deconvolution), trong nhe h l khng bit v phi clng t nhng thng tin sn c trc khi a ti b lc ngc.


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Hnh 5. nh bnhe nhng khng bit vhm gy nhe

(Ngun: http://www.svi.nl/BlindDeconvolution)

V ta mun chia chp y m khi khng c hiu bit chi tit v h m , nn php x l ny c gi lbi ton chia chp m.Trong phm vi ti bi tp ln ny khng i su vo gii quyt vn ny.

2.3. M hnh nh b xung cp bi c nhe v nhiu cng.

Thc t th s xung cp ca nh thng l t hp ca nhe v nhiu.

Thng thng ta ch xt trng hp nhiu nhe nh l mt b lc tuyn tnh vi p ng xung h m

v nhiu l nhiu cng n m . Tn hiu u ra c m hnh di dng:

1

0

*P

k

y m x m h m n m x k h m k n m

Mt cch tip cn hp l khi phc nh x m l p dng mt h lm gim nhiu t y m c

lng *u m x m h m sau p dng mt h kh nho t u m c lng ra x m

Cch tip cn ln lt kh cc loi xung cp tng ci mt, cho php chng ta khai trin nhng thutton khi phc ring cho mi loi, sau c kt hp chng li mt cch n gin nu nh b xung

cp v nhiu loi nguyn nhn khc nhau.

Trong min tn s, m hnh nhiu c dng: *Y f X f H f N f


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Hnh 6. M hnh blc trng hp nhiu cng nhe

(ngun: Tham kho [1])

Li: f X f X f , gi thit x m v n m l nhng mu c lp tuyn tnh. Ngoi ra, gi

thit h m bit. Vy th b c lng tuyn tnh ti u (optimal linear estimator) c th ti thiu

ho 2

E X f X f

l mt h LSI, tng t nh bin i trn (mc 2.1.1) ta s thu c p

ng xung ca b lc Wiener trn min tn s:

*

2

XX

XX NN

P f H fW f

P f H f P f

Trong gi thit nhiu v tn hiu khng tng quan vi nhau. Nu khng c nhiu th 0NNP f

v b lc Wiener tr thnh b lc ngc vi 1W f H f

2.4. M hnh nh nhiu ph thuc tn hiu. Mt nh b xung cp y m bt k c th biu din bi m hnh:

y m D x m x m d m

Trong D[.] l ton t xung cp c p dng vox.Nu d m khng l hm ca tn hiu x m

th n c gi l nhiu cng khng ph thuc tn hiu. Nu d m l hm ca tn hiu x m th

d m c gi l nhiu cng ph thuc tn hiu. Nhng v d v nhiu ph thuc tn hiu l nhiu

m, nhiu ht trn phim v nhiu lng t.Mt cch tip cn lm gim nhiu ph thuc tn hiu l bin i y m vo mt min, nhiu

tr thnh nhiu cng khng ph thuc tn hiu v sau lm gim nhiu khng ph thuc tn hiu.

Mt cch tip cn khc l lm gim nhiu trc tip trong min tn hiu. Trong phm vi bi tp ln ny

khng i su vo gii quyt m ch nu vn .


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3. Kho st ng dng ca b lc Wiener

Vic kho st ng dng ca b lc da trn cng c Matlab 7.11.0 (R2010b), y l mt cng

c mnh cho x l, h tr nhiu hm cho vic thc hin nhanh chng v thun tin.

Dng 1 nh c cht lng tt, coi nh l nh l To ra sxung cp ln nh nh to nhiu hay lm tc ng quang hc do chuyn ng

Khi phc li bng cc hm sdng blc weiner c chng trnh Matlab cung cp sn.

Cc hm sdng:

Hm c nh: I = imread(filename)c nh lu ma trn im nh vo ma trn I.

Hm hin thnh I: imshow(I)hin thnh c lu bng ma trn im nh I.

Hm to p ng xung: h = fspecial(type, parameters)p ng xung ny khi nhn chp

vi nh gc to ra cc hiu ng do typetruyn vo nh:

motion: to nhe ging my nh chp b rung khi chp hay vt thchuyn ng nhanh qua

ng knh khi bm my

gaussan: to nhiu Gaussian

parameters: tham sbsung cho type

Hm to nhiu: J = imnoise(I,type,parameters)to ra cc loai nhiu nh gaussian, 'salt

& pepper'

Hm imfilter(A,H,option1,) hm ny s ty theo option x l A v H, trong th

nghim option = conv dng tch chp nh ban u A v H( l hiu ng quang hc chuyn

ng).

Hm gii chp sdng thut ton ca blc Wiener:

o deconvwnr(I,H,SNR)deconvolves nh I dng blc wiener khi bit gi trca nh

hng quang hc (motion) v tham svnhiu (y l tsSNR).


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o Ngoi ra ta cn 1 hm Wiener2 l hm lc nhiu nhng sdng nh mt phng thc

lc trung bnh

o wiener2 (I,[m n],noise) vi [m n] l kch thc p ng xung

Th nghim lc nhiu bng b lc Wiener

newImageRGB = imread('test2.PNG');

%% Chuyn nh sang nh xm

grayImage = rgb2gray(newImageRGB);

figure;

imshow(grayImage);

title('Anh goc');

%% Thm nhiu vo nh .afferNoise = imnoise(grayImage,'gaussian',0,0.025);

figure;

imshow(afferNoise);

title('Anh Nhieu');

%% Lc nhiu nh bng blc Wiener

afterWiener = wiener2(afferNoise,[6 6]);

figure, imshow(afterWiener);

title('Anh sau khi loc');

Kt qu chy th nghim:

Hnh 7. Kt qukhi phc nh bnhiu


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Thnghim blc trong trng hp nh chuyn ng khng nhiu

newImageRGB = im2double(imread('test2.PNG'));

I = rgb2gray(newImageRGB);

figure;

imshow(I);

title('Anh goc');

%% Tao anh bi mo do chuyen dong

LEN = 21;

THETA = 11;

PSF = fspecial('motion', LEN, THETA);

blurred = imfilter(I, PSF, 'conv', 'circular');

figure, imshow(blurred)

title('Anh bi mo do chuyen dong');

%% Khoi phuc anh bi mo do chuyen dong

wnr1 = deconvwnr(blurred, PSF, 0);figure, imshow(wnr1);

title('Anh khoi phuc do chuyen dong');

Kt qu:

Hnh 8. Kt qukhi phc nh bnhe do chuyn ng

Thnghim blc bng cch thm nhiu vo nh bmdo chuyn ng

%% Tao anh bi mo do chuyen dong va them nhieu

noise_mean = 0;

noise_var = 0.0001;

blurred_noisy = imnoise(blurred, 'gaussian', noise_mean, noise_var);

figure, imshow(blurred_noisy)


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title('Anh bi mo va co nhieu')

%% Khoi phuc

estimated_nsr = 0;

wnr2 = deconvwnr(blurred_noisy, PSF, estimated_nsr);

figure, imshow(wnr2)

title('Khoi phuc anh bi mo va co nhieu, Su dung ti so NSR = 0' )

%% Khoi phuc anh bi mo va co nhieu co su dung ti so NSR

estimated_nsr = noise_var / var(I(:));

wnr3 = deconvwnr(blurred_noisy, PSF, estimated_nsr);

figure, imshow(wnr3)

title('Khoi phuc anh bi mo va co nhieu co su dung ti so NSR' );

Kt quthnghim

Hnh 9. Kt qukhi phc nh do nhe v nhiu

Trong trng hp SRN hay 0NSR th ta c ththy ngay blc Wiener tng ng vi lc

ngc v rt nhy vi nhiu.


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4. Ti liu tham kho

[1] Chap 6. Advanced Digital Signal Processing and Noise Reduction, Second Edition. Saeed V.

Vaseghi

[2] Two-dimentional Signal and image processing JAE Slim

[3]http://www.mathworks.com/help/images/examples/deblurring-images-using-a-wiener-filter.html
http://www.mathworks.com/help/images/examples/deblurring-images-using-a-wiener-filter.htmlhttp://www.mathworks.com/help/images/examples/deblurring-images-using-a-wiener-filter.htmlhttp://www.mathworks.com/help/images/examples/deblurring-images-using-a-wiener-filter.htmlhttp://www.mathworks.com/help/images/examples/deblurring-images-using-a-wiener-filter.html

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