aucun titre de diapositive - european space agency · aucun titre de diapositive author: e pottier...

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

SAPHIR

SAPHIR

DECOMPOSITION THEOREMSDECOMPOSITION THEOREMS

EIGENVECTORS BASEDDECOMPOSITION

W.A. HOLM(1988)

S.R. CLOUDE(1985)

MODEL BASEDDECOMPOSITION

EIGENVECTORS / EIGENVALUES ANALYSIS&

MODEL BASED DECOMPOSITION

S.R. CLOUDE - E. POTTIER(1996-1997)

A.J. FREEMAN(1992)

J.J. VAN ZYL(1992)

AZIMUTHAL SYMMETRY

EIGENVECTORS / EIGENVALUES ANALYSISENTROPY / ANISOTROPY

[C ][T ][T ]

E. KROGAGER(1990)

W.L. CAMERON(1990)

COHERENTDECOMPOSITION

[S ]

[K ]

TARGETDICHOTOMY

J.R. HUYNEN(1970)

R.M. BARNES(1988)

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

SAPHIR

SAPHIR

EIGENVECTOREIGENVECTOR--BASED DECOMPOSITIONBASED DECOMPOSITION

EIGENVECTOR BASED

DECOMPOSITION

SHANE R. CLOUDE(1985-1992)

WILLIAM A. HOLM(1988)

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

SAPHIR

SAPHIR

EIGENVECTOREIGENVECTOR--BASED DECOMPOSITIONBASED DECOMPOSITION

PROPRIETY

EIGENVALUE PROBLEM IS AUTOMATICALLY

BASIS INVARIANT

GENERATE A DIAGONAL FORM OF THECOHERENCY MATRIX

PHYSICALLY INTERPRETATION AS STATISTICALINDEPENDENCE BETWEEN A SET OF VECTORS

GENERAL DECOMPOSITION INTO INDEPENDENTSCATTERING PROCESSES

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

SAPHIR

SAPHIR

EIGENVECTOREIGENVECTOR--BASED DECOMPOSITIONBASED DECOMPOSITION

[ ] [ ] [ ] [ ]321 TTTT ++=COHERENCY MATRIX

[ ] [ ] [ ] [ ]321 KKKK ++=KENNAUGH MATRIX

[ ]3S[ ]1S [ ]2SSINCLAIR MATRIX

STATISTICAL INDEPENDENCEBETWEEN THE TARGETS

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

SAPHIR

SAPHIR

EIGENVECTOREIGENVECTOR--BASED DECOMPOSITIONBASED DECOMPOSITION

COHERENCY MATRIX

[ ]

−−−++++−

=BBFjEGjHFjEBBDjCGjHDjCA2

T

0

0

0

[ ] [ ] [ ] [ ] 133 UUT −= Σ

3x3 DIAGONAL MATRIX OF EIGENVALUES[ ]

3213

2

1

000000

λλλλλ

λΣ

≥≥

=

[ ] [ ]3213 u,u,uU = SU(3) UNITARY MATRIX (EIGENVECTORS)

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

SAPHIR

SAPHIR

EIGENVECTOREIGENVECTOR--BASED DECOMPOSITIONBASED DECOMPOSITION

SHANE R. CLOUDE

(1985-1992)

DECOMPOSITION

IDENTIFICATION OF THE DOMINANTSCATTERING MECHANISM

VIA THE

EXTRACTION OF THE LARGEST EIGENVALUE

[ ] [ ][ ][ ] [ ] *T11

*T1111

133 kkuuTUUT ==⇒= − λΣ

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

SAPHIR

SAPHIR

S.R. CLOUDE DECOMPOSITIONS.R. CLOUDE DECOMPOSITION

( )dB0 BB + ( )dB0 BB −( )dB0A2

20dB 40dB0dB

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

SAPHIR

SAPHIR

S.R. CLOUDE DECOMPOSITIONS.R. CLOUDE DECOMPOSITION

λ 1 13u λ 1 12u λ 1 11u20dB 40dB0dB

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

SAPHIR

SAPHIR

S.R. CLOUDE DECOMPOSITIONS.R. CLOUDE DECOMPOSITION

0A2 BB0 + BB0 − λ 1 11u λ 1 12u λ 1 13u

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

SAPHIR

SAPHIR

S.R. CLOUDES.R. CLOUDE DECOMPOSITIONDECOMPOSITION

( )dB0A2 ( )dB0 BB −( )dB0 BB +

-15dB 0dB-30dB

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

SAPHIR

SAPHIR

S.R. CLOUDE DECOMPOSITIONS.R. CLOUDE DECOMPOSITION

λ 1 13u λ 1 12u λ 1 11u-15dB 0dB-30dB

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

SAPHIR

SAPHIR

S.R. CLOUDES.R. CLOUDE DECOMPOSITIONDECOMPOSITION

0A2 BB0 + BB0 − λ 1 11u λ 1 12u λ 1 13u

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

SAPHIR

SAPHIR

W.A HOLM DECOMPOSITIONW.A HOLM DECOMPOSITION

WILLIAM A. HOLM(1988)

DECOMPOSITION

ALTERNATIVE PHYSICAL INTERPRETATION

OF THE EIGENVALUES SPECTRUM

[ ]

=

3

2

1

000000

λλ

λΣ

[ ]

+

−

−+

−=

3

3

3

32

3221

000000

0000000

00000000

λλ

λλλ

λλλλΣ

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

SAPHIR

SAPHIR

W.A HOLM DECOMPOSITIONW.A HOLM DECOMPOSITION

[ ] *T333

*T222

*T111 uuuuuuT λλλ ++=

[ ] ( ) ( )( ) [ ]D33*T22

*T1132

*T1121 IuuuuuuT λλλλλ ++−+−=

MIXED TARGET(VARIANCE)

PURE TARGET(AVERAGE)

NOISE(UNPOLARIZED)

TARGET PLUS NOISECONCEPT OF :

HYBRID APPROACH OF THE HUYNEN MODEL

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

SAPHIR

SAPHIR

W.A HOLM DECOMPOSITIONW.A HOLM DECOMPOSITION

( )dB0 BB + ( )dB0 BB −( )dB0A2

20dB 40dB0dB

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

SAPHIR

SAPHIR

W.A HOLM DECOMPOSITIONW.A HOLM DECOMPOSITION

λ λ1 2 13− u λ λ1 2 12− u λ λ1 2 11− u

20dB 40dB0dB

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

SAPHIR

SAPHIR

W.A HOLM DECOMPOSITIONW.A HOLM DECOMPOSITION

0A2 BB0 + BB0 − λ λ1 2 11− u λ λ1 2 12− u

λ λ1 2 13− u

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

SAPHIR

SAPHIR

W.A HOLM W.A HOLM DECOMPOSITIONDECOMPOSITION

( )dB0A2 ( )dB0 BB −( )dB0 BB +

-15dB 0dB-30dB

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

SAPHIR

SAPHIR

W.A HOLMW.A HOLM DECOMPOSITIONDECOMPOSITION

λ λ1 2 13− u λ λ1 2 12− u λ λ1 2 11− u

-15dB 0dB-30dB

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

SAPHIR

SAPHIR

W.A HOLMW.A HOLM DECOMPOSITIONDECOMPOSITION

0A2 BB0 + BB0 − λ λ1 2 11− u λ λ1 2 12− u

λ λ1 2 13− u