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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)
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EIGENVECTOREIGENVECTOR--BASED DECOMPOSITIONBASED DECOMPOSITION
EIGENVECTOR BASED
DECOMPOSITION
SHANE R. CLOUDE(1985-1992)
WILLIAM A. HOLM(1988)
© E. Pottier, L. Ferro-Famil (01/2004)
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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
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EIGENVECTOREIGENVECTOR--BASED DECOMPOSITIONBASED DECOMPOSITION
[ ] [ ] [ ] [ ]321 TTTT ++=COHERENCY MATRIX
[ ] [ ] [ ] [ ]321 KKKK ++=KENNAUGH MATRIX
[ ]3S[ ]1S [ ]2SSINCLAIR MATRIX
STATISTICAL INDEPENDENCEBETWEEN THE TARGETS
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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)
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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
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S.R. CLOUDE DECOMPOSITIONS.R. CLOUDE DECOMPOSITION
( )dB0 BB + ( )dB0 BB −( )dB0A2
20dB 40dB0dB
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S.R. CLOUDE DECOMPOSITIONS.R. CLOUDE DECOMPOSITION
λ 1 13u λ 1 12u λ 1 11u20dB 40dB0dB
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S.R. CLOUDE DECOMPOSITIONS.R. CLOUDE DECOMPOSITION
0A2 BB0 + BB0 − λ 1 11u λ 1 12u λ 1 13u
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S.R. CLOUDES.R. CLOUDE DECOMPOSITIONDECOMPOSITION
( )dB0A2 ( )dB0 BB −( )dB0 BB +
-15dB 0dB-30dB
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S.R. CLOUDE DECOMPOSITIONS.R. CLOUDE DECOMPOSITION
λ 1 13u λ 1 12u λ 1 11u-15dB 0dB-30dB
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S.R. CLOUDES.R. CLOUDE DECOMPOSITIONDECOMPOSITION
0A2 BB0 + BB0 − λ 1 11u λ 1 12u λ 1 13u
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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
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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
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W.A HOLM DECOMPOSITIONW.A HOLM DECOMPOSITION
( )dB0 BB + ( )dB0 BB −( )dB0A2
20dB 40dB0dB
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W.A HOLM DECOMPOSITIONW.A HOLM DECOMPOSITION
λ λ1 2 13− u λ λ1 2 12− u λ λ1 2 11− u
20dB 40dB0dB
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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
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W.A HOLM W.A HOLM DECOMPOSITIONDECOMPOSITION
( )dB0A2 ( )dB0 BB −( )dB0 BB +
-15dB 0dB-30dB
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W.A HOLMW.A HOLM DECOMPOSITIONDECOMPOSITION
λ λ1 2 13− u λ λ1 2 12− u λ λ1 2 11− u
-15dB 0dB-30dB
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W.A HOLMW.A HOLM DECOMPOSITIONDECOMPOSITION
0A2 BB0 + BB0 − λ λ1 2 11− u λ λ1 2 12− u
λ λ1 2 13− u
