POLARIMETRIC SPECKLE FILTERING - Earth Online · polarimetric speckle filtering should filter all...

© E. Pottier, L. Ferro-Famil (01/2004)

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POLARIMETRICSPECKLE FILTERING

POLARIMETRICPOLARIMETRICSPECKLE FILTERINGSPECKLE FILTERING

0

$x

$y( )rE z t,

$z


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SPECKLE FILTERINGSPECKLE FILTERING

SPECKLE SPECKLE PHENOMENONPHENOMENON


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SPECKLE FILTERINGSPECKLE FILTERINGOBSERVATION POINT

SURFACE ROUGHNESSWAVELENGTH

SCATTERING FROM DISTRIBUTEDSCATTERERS

COHERENT INTERFERENCES OF WAVES SCATTERED FROM MANY RANDOMLY

DISTRIBUTED ELEMENTARY SCATTERERSINSIDE THE RESOLUTION CELL

GRANULAR NOISE

SPECKLE PHENOMENON


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SPECKLE PHENOMENON

DISTORTION OF THE INTERPRETATION

SPECKLE FILTERING

HOMOGENEOUS AREA HETEROGENEOUS AREA

SPECKLE REDUCTION(RADIOMETRIC RESOLUTION)

DETAILS PRESERVATION(SPATIAL RESOLUTION)


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SPECKLE REDUCTIONMULTI-LOOK SAR PROCESSING (BoxCar)

Averaging Amplitude / Intensity (Not complex images) ofneighboring pixels

Good Noise Smoothing

Spatial Resolution Loss - blurring edges - erasing thin linesLoss of linear or point features …


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LINEAR SPECKLE FILTERS

Median FilterMAP Filter (Kuan)Gradient FilterNagao Filter (Nagao)Sigma Filter (Lee)Frost Filter (Frost)Geometrical Filter (Crimmins)Morphological Filter (Safa, Flouzat)

.

.

.

.Local Statistics Filter (Lee 80)


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SPECKLE : MULTIPLICATIVE NOISE MODEL« SPECKLE is a scattering phenomenon and not a noise.However, from the image SAR processing point of vue, thespeckle can be modeled as multiplicative noise for extended target » (Lee, IGARSS-98)

=

=

=

VVVV

HVHV

HHHH

VV

HV

HH

VV

HV

HH

VV

HV

HH

nxnxnx

xxx

n000n000n

yyy

y

REFLECTIVITYDENSITY

SCATTERINGFIELD

NOISE

pqpqpqpq*pqpqpqpq vXyyY == *

pqpqpqpqpqpq yyYA ==

INTENSITY AMPLITUDE


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HOMOGENEOUS AREA

NUMBER OF ELEMENTARY SCATTERERS IS IMPORTANT

CENTRAL LIMIT THEOREM

CIRCULARGAUSSIAN

( ) ( )( )( ) ( )

⇒∈⇒+=

==

=

==

212Q

pq2I

pq

Qpq

Ipq

Qpq

Ipq

Q,Ipq

Qpq

Ipqpq

nEnE

0nnE

0nEnE

)21,0(nnnn Νj

NOISE INTENSITY

( ) ( ) ( ) 1vEnnnnv pq2Q

pq2I

pq*pqpqpq =⇒+==


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HOMOGENEOUS AREA

0pqpq XX =CONSTANT SPATIAL REFLECTIVITY

pqpqpqpqpqpq vXY =

( ) ( ) ( ) 0pqpqpqpqpqpqpqpq XXEvXEYE ===

( ) ( ) ( )pqpq20pqpqpqpqpqpq vvarXvXvarYvar ==

( )( ) ( ) vpqpq

pqpq

pqpqY CVvvar

YEYvar

CV ===

( ) 2YpqpqYv CVvvarCVCV ==


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SPECKLE FILTERINGSPECKLE FILTERINGHOMOGENEOUS AREA N LOOK CASE

INTENSITY AMPLITUDE

COEFFICIENTOF

VARIATION

VARIANCE

MEAN

DENSITY

N LOOK

( ) ( )

N523.01

)N()N(NCV

N1CV

)N()N(N

NX)Avar(

NX)Yvar(

)N()N(

NX)A(EX)Y(E

eX)N(AN2X/APe

X)N(YNX/YP

YN1AY

N1Y

yyAyyY

212

2

NANY

2212

020

21

00

XNA

N0

1N2N

0NAXNY

N0

1NN

0NY

ii

ii

*pqpqpqpq

*pqpqpqpq

0

2

0

≈−+

==

+−==

+==

==

==

==

−−−−

∑∑

ΓΓ

ΓΓ

ΓΓ

ΓΓ


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LOCAL STATISTICS LINEAR FILTER

( ) j,iYj,ij,i YbaYbYEaX +=+= µ

222XY EXEEYXY νµµµν ν ===with:

( ) ( )1CVEYYvarCV 2Y

2Y

22Y

2Y +== µ

µ

M.M.S.E ( )( )

2j,ij,ib,a

XXEJmin\b,a −=

)Yvar()Xvar(b0

bJb1a0

aJ

νν

µ∂∂

µ∂∂ =⇒=−=⇒=

( )νµµµµµ b21EXEYba2ab2aJ 222YX

2Y

2Y

2 −++−+=


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( ))Y(EYb)Y(EX j,ij,i −+=νµ

2Y

2X

CVCV1

)Yvar()Xvar(b

νν µ

µ ==

( )

( ) ( )( )1CV

CVCVCVCVEv

CVCVEvEv

EY1EXCV

2v

2v

2Y2

v2Y2

2v

2v

2Y22

X

2Y

2v

2Y

2

2

2X

2X

2X

22X

+−

=−=

−=

−=

−=

µµµ

µµ

µµµ

with:

and:

( )22Y

22Y

CV1CVCVCV1

)Yvar()Xvar(b

ν

ν

νν µ

µ+−

==


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1)(E == ννµor:

( )

[ ] [ ]2v2v

2

2v

2Y

2v

2Y

j,ij,i

1)Yvar()Y(E)Yvar(

CV1CVCVCV

)Yvar()Xvar(k

)Y(EYk)Y(EX

σσ

+−

=+−

==

−+=

LOCAL STATISTICS LINEAR FILTER

( ) ( ) )Y(EYEYvar,)Y(E 222 −=LOCAL STATISTICS

( )N1CVvvar 2

Y2v ===σA PRIORI INFORMATION

IMAGE NUMBER OF LOOK


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POLSAR SPECKLE FILTERINGPOLSAR SPECKLE FILTERINGVECTORIAL SPECKLE FILTER

[ ] [ $ ] $ $* *C yy C xxT T= =FILTER

COVARIANCE MATRIX

LOPES - GOZE - NEZRY - TOUZY (1990 - 1992) and SERY (1997) FILTERS, LEE FILTER (1997)

POLARIMETRIC SPECKLE FILTERING SHOULD FILTER ALL ELEMENTS OF THECOVARIANCE MATRIX

AVOIDING CROSS-TALK BETWEEN CHANNELS DUE TO THE FILTERING PROCESS

PRESERVING POLARIMETRIC INFORMATION AND THE STATISTICALCORRELATION BETWEEN THE CHANNELS

PRESERVING SPATIAL RESOLUTION, FEATURES, EDGE SHARPNESSAND POINT TARGETS


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POLSAR SPECKLE FILTERINGPOLSAR SPECKLE FILTERING

EXTENSION OF THE LOCAL STATISTICLINEAR FILTER

VECTORIZATION OF THE COVARIANCE MATRIX

[ ]

=⇒==

VVVV

HVVV

HVHV

HHVV

HHHV

HHHH

VVVV

*

HVVV

*

HHVV

HVVVHVHV

*

HVHV

HHVVHHHVHHHH*T

YYYYYY

YYYYYYYYYY

yyC

VECTORIAL MULTIPLICATIVE MODEL

[ ]XVY =


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VECTORIAL MULTIPLICATIVE MODEL

[ ]XVY =

==

VVVV

HVVV

HVHV

HHVV

HHHV

HHHH

VVVV

HVVVV

HVHV

HHVV

HHHV

HHHH

VVVV

HVVV

HVHV

HHVV

HHHV

HHHH

XXXXXX

v000000v000000v000000v000000v000000v

YYYYYY

Y

VECTORIAL LOCAL STATISTICS LINEAR FILTER

[ ] ( ) [ ]YBYEAX +=


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M.M.S.E[ ] [ ]( )

[ ][ ]( )( ) ( )[ ]*T2

B,AXXXXEXXEJmin\B,A −−=−=

[ ] [ ] [ ] [ ] [ ]( )

[ ] [ ] ( ) [ ]( ) ( )YcovVEXcovB0BJ

VEBIdA0AJ

1*T −=⇒=

−=⇒=

∂∂∂∂

( ) [ ] ( )( )

[ ] ( ) [ ]( ) ( )YcovVEXcovk

YYEkYEX

1*T −=

−−=


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VECTORIAL LOCAL STATISTICS LINEAR FILTER

( ) [ ] ( )( )

[ ] ( ) [ ]( ) ( )YcovVEXcovk

YYEkYEX

1*T −=

−−=

DERIVATION AND COMPUTATION OF THE COV(X) MATRIX IS RATHERCOMPLICATED (ILL-CONDITIONING)

IN THE COVARIANCE MATRIX, THE CO-POL INTENSITIES CHANNELSCAN BE MODELED AS MULTIPLICATIVE NOISE MODEL.

BUT THE CROSS-POL (OFF-DIAGONAL) INTENSITIES CHANNELS AREDIFFICULT TO DEFINE : NEITHER MULTIPLICATIVE NOR ADDITIVE


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10n

0

0.5

1

1.5

2

2.5

3

3.5

4

HVVV r (Nwin = 7)

-10 -5 0 5 100

1

2

3

4

5

6

7

8

9

10

10n

0

0.5

1

1.5

2

2.5

3

3.5

4HHHH (Nwin = 7)

ECAR

T TY

PE

0 2 4 6 8 100

1

2

3

4

5

6

7

8

9

1010n

0

0.5

1

1.5

2

2.5

3

3.5

4HVHV (Nwin = 7)

ECAR

T TY

PE

0 2 4 6 8 100

1

2

3

4

5

6

7

8

9

1010n

0

0.5

1

1.5

2

2.5

3

3.5

4VVVV (Nwin = 7)

MOYENNE

ECAR

T TY

PE

0 2 4 6 8 100

1

2

3

4

5

6

7

8

9

10

10n

0

0.5

1

1.5

2

2.5

3

3.5

4

HHHVr (Nwin = 7)

ECAR

T TY

PE

-10 -5 0 5 100

1

2

3

4

5

6

7

8

9

1010n

0

0.5

1

1.5

2

2.5

3

3.5

4

HHVVr (Nwin = 7)

ECAR

T TY

PE

-10 -5 0 5 100

1

2

3

4

5

6

7

8

9

10

10n

0

0.5

1

1.5

2

2.5

3

3.5

4

HHHVi (Nwin = 7)

-10 -5 0 5 100

1

2

3

4

5

6

7

8

9

1010n

0

0.5

1

1.5

2

2.5

3

3.5

4

HHVVi (Nwin = 7)

ECAR

T TY

PE

-10 -5 0 5 100

1

2

3

4

5

6

7

8

9

1010n

0

0.5

1

1.5

2

2.5

3

3.5

4

HVVV i (Nwin = 7)

-10 -5 0 5 100

1

2

3

4

5

6

7

8

9

10

HHHH

HHHVr

HHHVi

VVVV

HVVVr

HVVVi

HVHV

HHVVr

HHVVi

1/N


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POLARIMETRIC VECTORIAL SPECKLE FILTER

[ ] T*xxC =[ ] [ ]( ) [ ]( ) [ ][ ]CCEkCEC −−=[ ] T*yyC =

VVVVHVHVHHHHS YY2YS ++=

SPAN IMAGE

( )( ) [ ]2v2

SS

2v

2SS

S 1CV

CV

Svar

Svark

σ

σ

+

−==

LINEAR SCALARLEE FILTER( ) ( )[ ]SSS SSEkSES −−=

J.S. LEE

Homogeneous Areas( ) ( )SSES0k0Svar =⇒=⇒≈

Highly Inhomogeneous Areas( ) ( ) Ss SS1kSvarSvar =⇒=⇒a

REFINED FILTER


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POLARIMETRIC VECTORIALSPECKLE LEE FILTER

[ ] [ ]( ) [ ]( ) [ ][ ]CCEkCEC −−=

EACH ELEMENT OF THE COVARIANCE MATRIX IS FILTERED

BY THE SAME AMOUNT AVOIDING CROSS-TALK AND PRESERVINGPOLARIMETRIC INFORMATION AND CORRELATIONS

SIMILAR TO THE MULTI LOOK PROCESSING BY AVERAGING THECOVARIANCE MATRICES OF NEIGHBORING PIXELS

BY WEIGHTING THE COVARIANCE MATRIX OF THE CENTER PIXELOF THE SLIDING WINDOW WITH THE MEAN OF COVARIANCE MATRICES FROM SELECTED NEIGHBORING PIXELS PRESERVINGSPATIAL RESOLUTION, FEATURES, EDGES … REFINED LEE FILTER


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EDGE DIRECTED WINDOW 10

LOCAL HETEROGENEITY &NOISY EDGE BOUDARIES

THE EDGE DIRECTED WINDOWS ARE USED TO

COMPUTE THE LOCAL MEANAND VARIANCE

DIRECTION 1 DIRECTION 2 DIRECTION 3 DIRECTION 4

DIRECTION 5 DIRECTION 6 DIRECTION 7 DIRECTION 8

POLARIMETRIC LEE FILTER

[ ] [ ]( ) [ ]( ) [ ][ ]( )( ) [ ]2v2

S

2v

2S

S 1CVCV

SvarSvark

CCEkCEC

S

S

σσ+

−==

−−=

FOR EACH PIXEL, THE k VALUE IS COMPUTED IN AN EDGE DIRECTED WINDOW


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OPOP--AIRFIELD LAIRFIELD L--BandBand


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POLARIMETRIC SPECKLE FILTERING IS NOT AN EXACT SCIENCESUBJECTIVE, IMAGE DEPENDENT

Quantitative Criteria (J.S. Lee - IGARSS 98)

Speckle Reduction (E.N.L)

Edge Sharpness Preservation

Line and Point Target Contrast Preservation

Retention of Mean Values in Homogeneous Regions

Retention of Texture Information

Retention of Polarimetric Information (co, cross-correlations)

Computational Efficiency

Implementation Complexity

THE POLARIMETRIC SPECKLE LEE FILTERIS TODAY A GOOD COMPROMISE

[ ] [ ]( ) [ ]( ) [ ][ ]CCEkCEC −−=


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[ ] [ $ ] $ $* *C yy C xxT T= =FILTER

AVERAGING DATA

SECOND ORDER STATISTICS

COVARIANCE / COHERENCY MATRICES

SMOOTHING AVERAGING

CONCEPT OF THE

DISTRIBUTED TARGETDISTRIBUTED TARGET


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POLARIMETRIC SPECKLE FILTERING - Earth Online · polarimetric speckle filtering should filter all...

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