[PDF] SAR Image Filtering Based on the Heavy-Tailed Rayleigh Model

View - Download SAR Image Filtering Based on the Heavy-Tailed Rayleigh Model

Previous PDF

Next PDF

ISSN 0249-6399 ISRN INRIA/RR--5493--FR+ENG

apport de recherche

ThèmeCOG

SARImageFilteringBasedonthe

Heavy-TailedRayleighModel

AlinAchim-ErcanE.Kuruoglu-JosianeZerubia

N°5493

February2005

UnitéderechercheINRIASophiaAntipolis

Heavy-TailedRayleighModel

ThèmeCOGSystèmescognitifs

ProjetAriana

Filtraged'ImagesRadarRSOFondésur

leModèledeRayleighàQueueLourde enleverlebruitdechatoiement.

Contents

1Introduction4

2StatisticalmodelingofSARimages5

3AdaptiveMAPlteringofspecklenoise9

4ExperimentalResults14

5Conclusions18

6Acknowledgement18

RRn°5493

4A.Achim,E.E.Kuruoglu&J.Zerubia

1Introduction

limitationsofinfraredimagers. transform[11,12,13,14]. INRIA

2StatisticalmodelingofSARimages

RCS.

2.1Statisticsoflog-transformedspeckle

RRn°5493

6A.Achim,E.E.Kuruoglu&J.Zerubia

components,respectively,onecanwrite: y(u;v)=x(u;v)(u;v)+(u;v);(u;v)2Z2(1) rewrite(1)as y(u;v)=x(u;v)(u;v)(2) functiononbothsidesof(2): logy(u;v)=logx(u;v)+log(u;v):(3)

Expression(2)canberewrittenas

Y(u;v)=X(u;v)+N(u;v);(4)

2.1.1IntensityImage

INRIA p

I()=LLL1eL

(L)(5) kI(1)=(L)log(L) kI(2)=(1;L)(6) p

I(N)=LLeNLeLeN

(L)(7)

2.1.2AmplitudeImage

p

A(x)=2xpI(x2)(8)

kA(r)=(1

2)r~kI(r)(9)

p

A()=2LL2L1eL2

(L)(10) kA(1)=1

2((L)log(L))

kA(2)=1

4(1;L)(11)

p

A(N)=2LLe2NLeLe2N

(L)(12)

RRn°5493

8A.Achim,E.E.Kuruoglu&J.Zerubia

2.2ThegeneralizedRayleighmodel

2.2.1SymmetricAlpha-StableDistributions

tion '(!)=exp(|! j!j)(13) locationparameter,and determines

Gaussiandistribution.

2.2.2AHeavy-TailedRayleighmodel

INRIA p(x)=xZ 1 0 uexp( u)J0(ux)du(14) obtain p(x)=x 2 exp(x24 )(15) model p(x)=x (x2+

2)3=2(16)

p

A(x)=2xpI(x2).Thus,oneobtain

p

I(x)=1

2Z 1 0 uexp( u)J0(upx)du(17) p

A(X)=e2XZ

1 0 uexp( u)J0(ueX)du(18) p

I(X)=eX

2Z 1 0 uexp( u)J0(ueX

2)du(19)

whereX=lnx.

3AdaptiveMAPlteringofspecklenoise

Y=X+N(20)

RRn°5493

10A.Achim,E.E.Kuruoglu&J.Zerubia

012345670

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Data, x

P(x) a=0.5 a=1 a=1.5 a=2 =1.

X(Y)=argmaxXPXjY(XjY)(21)

P

XjY(XjY)=PYjX(YjX)PX(X)

PY(Y);(22)

INRIA =argmaxXPN(N)PX(X)(23) parametersXand cumulants.

3.1.1Mellintransform

(s)=M[f(u)](s)=Z +1 0 us1f(u)du(24) f(u)=M1[(s)](u)=1 2jZ c+j1 cj1us(s)ds(25)

Thetransform(s)existsiftheintegralR+1

0jf(x)jxk1dxisboundedforsomek>0,in

Transform[21,22]

ˆSecond-kindrstcharacteristicfunction

(s)=Z +1 0 xs1p(x)dx(26) (s)=log((s))(27)

RRn°5493

12A.Achim,E.E.Kuruoglu&J.Zerubia

ˆrthordersecond-kindmoments

~mr=dr(s) dsr s=1=Z +1 0 (logx)rp(x)dx(28)

ˆrthordersecond-kindcumulants

kr=dr(s) dsr s=1(29) asfollows ~k1=1 NN X i=1[log(yi)] ~k2=1 NN X i=1[(log(yi)^ ~k1)2](30) [0;1]as (f^ g)(y)=Z +1 0 f(x)g(y x)dxx=Z +1 0 f(yx)g(x)dxx(31) (s)=2s(s+1 2) s1(1s) (1s2)(32) second-kindcumulantsofthemodel kA(1)= (1)1 +log(2 1 kA(2)= (1;1) 2(33) INRIA followingexpressionsforthelog-cumulants kI(1)=2 (1)1 +log(4 2 kI(2)=4 (1;1) 2(34) metersand p p y(y)=Z +1 0 p yjx(yjx)px(x)dx=Z +1 0 p (y x)px(x)dxx=p^ px(35) kindcumulantsofthesameorderofxand[21] ky(r)=~kx(r)+~k(r)(36) ^=2v u u t (1;1) ~k(2) (1;L) =[exp(^ ~k(1)+2 (1)1 (L)+log(L)

4]=2(37)

empiricallog-cumulantsin(30)weget ^=v u u t (1;1) ~k(2)14 (1;L) =[exp(^ ~k(1)+ (1)1

12( (L)log(L))

2](38)

RRn°5493

14A.Achim,E.E.Kuruoglu&J.Zerubia

4ExperimentalResults

4.1SyntheticDataExamples

(S/MSE)ratio,denedas[25]:

S=MSE=10log10(KX

i=1S 2i=KX i=1(^SiSi)2)(39) =(S

S;dSdS)q

(SS;SS)(dSdS;dSdS)(40) (S1;S2)=KX i=1S

1iS2i:(41)

INRIA

ENL=1ENL=3ENL=9ENL=12

MethodS=MSES=MSES=MSES=MSE

4.2RealSARImageryExamples

wasacquiredinApril1993byERS. meansofKuan,Frost,MAPandMBD[33]lters. theheavy-tailednatureofSARdata.

RRn°5493

16A.Achim,E.E.Kuruoglu&J.Zerubia

(a) (b) (c) (d) (e) (f) tailedRayleighmodel. INRIA (a) (b) (c) (d) (e)

RRn°5493

18A.Achim,E.E.Kuruoglu&J.Zerubia

quotesdbs_dbs28.pdfusesText_34

[PDF] La radioactivité - Le Repaire des Sciences

[PDF] 14 Traitement en radiothérapie - accueil

[PDF] (RAMED) - l Ecole Nationale de Santé Publique - Ministère de la

[PDF] Relations internationales - Cavej

[PDF] Relativité générale - LUTh OBSPM - Observatoire de Paris

[PDF] Relativit¶e restreinte - ENS-phys

[PDF] Réparation mobile smartphones tablette

[PDF] Représentation de l 'information

[PDF] La reproduction humaine

[PDF] PDF 357 ko Cours GRH - FOAD

[PDF] Le circuit RLC en régime forcé Cours - TuniSchool

[PDF] Résonance Magnétique Nucléaire - FSR

[PDF] CHAPITRE LES ROCHES MAGMATIQUES A INTRODUCTION Le

[PDF] rotation - Maths-et-tiques

[PDF] TP : Configuration de routeurs CISCO - LACL