a stable model-based three-component decomposition approach for polarimetric sar data
TRANSCRIPT
A STABLE MODEL-BASED THREE-COMPONENT DECOMPOSITION
APPROACH FOR POLARIMETRIC SAR DATA
Zhihao Jiao, Jiong Chen, Jian Yang
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Tsinghua University
outline
• Polarimetric decomposition and the Freeman decomposition
• Stability or instability• Negative powers in the Freeman decomposition• An improved three-component decomposition
approach• Experiment results• Conclusion and expectation
2
Polarimetric decomposition
3
coherent decompositions: [S]Pauli decompositionSDH decomposition (Krogager, 1990)Cameron decomposition (Cameron et al. 1996)SSCM decomposition (Touzi et al. 1996)
incoherent decompositions: [T], [C] or [M]Huynen decomposition (Huynen, 1978)Eigenvalue based decomposition
- Cloude decomposition (Cloude, 1986)- Holm decomposition (Holm et al. 1988)
Model-based decomposition methods ：-Freeman decomposition (Freeman et al. 1998)-Yamaguchi decomposition (Yamaguchi, 2005)
Freeman Decompositions surface d double v volumeP P P= + +T T T T
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11 12
12 22
33
2
2
0
0
0 0
1 0 0 2 0 0
0 1 0 0 1 04
0 0 0 0 0 0 0 0 1
vs d
T T
T T T
T
ff f
β α αβ β α
∗
∗
∗
=
= + +
Stable decomposition
5
To measure the stability of decomposition:
1 2 3
1 2 3' ' '
T T T T
T T T T T
= + ++ ∆ = + +
1 1 2 2 3 3
:
|| ' || || ' || || ' ||
|| ||F F F
F
noise sensitivity factor
T T T T T Ta
T
− + − + −=∆
Stable: A=min a exists, and, A is small (e.g., A<5 )
For standard Freeman decomposition, “a” is limitless
Example
6The standard Freeman decomposition is unstable ！
0 0 0
0 0
1.0
.01
1 1 0 0 0 0
1 0 0
0 0 0
1.01 1 0
1 0.99 0
0 0 0
0.0
1
1.01
0
0.99
1.
0 0 0
0 0 0 0 0
0.99 1 0
1 1.0
0
0, , 0.01
1.0 2 0 0
0 0 2 0
1 1 0
1 0
0 0
0 0
0 0
2
00 0 00
sv dff f
T
αβ
= = + +
= =⇒
+ ∆ = = +
==
=
T
T
0 0 0
0 0 0
0 0 0
0 0, , 1.02.02
0.98
0
sv df f f
αβ
+
=
=
= =
=
⇒
Pauli Decomposition and Freeman Decomposition
Pauli decomposition Freeman decomposition
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Calculation of Freeman Decomposition2
11
222
12
33
1| |
21
| |4
1
44 5
d s v
d s v
d s
v
T f f f
T f f f
T f f
T f
functions with variables
α
β
α β
= + + = + + ⇒ = + =
11 12*
12 22
33
T T
T T
T
v 33
11 11 33
22 22 33
4
2
P T
x T T
x T T
== −= −
11 22x x>
12 110 , T xα β= =
2
s 11 12 11
2
d 22 12 11
P x T x
P x T x
= +
= −
12 220 , T xβ α= =
Yes No
2
d 22 12 22
2
s 11 12 22
P x T x
P x T x
= +
= − 8
ill-posed problem!
211
222
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| |
| |
3 4
d s
d s
d s
X f f
X f f
T f f
functions with variables
αβ
α β
= +
= + = +
Negative powers
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11 33
22 332
11 33 22 33 12
2
( 2 )( ) | |
T T
T T
T T T T T
< < − − <
Three reasons leading to negative powers
(Wentao An, 2010)
Decomposition based on Tikhonov regularization
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ill-posed problem
well-posed problems with a parameter
2( ) || ( ) || ( )J F λ= − + Ωx y x x
Tikhonov regularization:
( )minimize J x a stable solution⇒
Regulation term 2 2|| || || ||α βΩ = +Choose:
2 2 2( , , , , ) || || (|| || || || )d s v FJ f f f α β λ α β= ∆ + +T
Standard Freeman decomposition:
0 0orα β⇒ ⇒
2
* 2 *
1 0 | | 0 2 0 0
= | | 0 1 0 0 1 0
0 0 0 0 0 0 0 0 1s d v
where
f f f
β α αβ β α
∆ − + +
0T T
objective function :
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The selection of regularization parameter
• fixed to a constant• L-curve method
– posterior rule– almost most effective parameter
• L-curve– abscissa:– ordinate:– Point on it: a regularization parameter and the
corresponding optimal solution
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20log(|| ( ) || )F−y x
0log ( )Ω x
Decomposition with fixed regularization parameter
Pauli decomposition Freeman decomposition
λ=0.1 λ=613
Process mapping of proposed approach
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deorientationT
11 33 22 33
22 33 11 33
| 2 | 5 | |
| | 5 | 2 |
T T T T
or T T T T
− > −− > −
yes no
Standard Freeman decomposition
minimize objective function0, 0, 0d s vf f and f≥ ≥ ≥
λselected
constraint：
Experiment results
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Freeman decomposition proposed approach
Conclusion and expectation
• improvement:– More stable– With no negative powers– More reliable
• defect:– Large calculation amount
• expectation:– With more regularization parameters
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2 21 2. ., || || || ||e g λ α λ βΩ = +
Thank you!
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