Analysis of Compact Polarimetric SAR Imaging...
Transcript of Analysis of Compact Polarimetric SAR Imaging...
Analysis of Compact Polarimetric SAR
Imaging Modes
T. L. Ainsworth1, M. Preiss2, N. Stacy2, M. Nord1,3 & J.-S. Lee1,4
1Naval Research Lab., Washington, DC 20375 USA2Defence Science and Technology Organisation, Edinburgh, SA 5111 Australia
3Applied Physics Lab., Johns Hopkins Univ., Laurel, MD 20723 USA4Center for Space and Remote Sensing Research, Central National Univ., Taiwan
Compact Polarimetry –Enhancing Dual-Pol Imagery
Pseudo Quad-Pol Data
1) Standard Quad-Pol Analysis
2) Quad-Pol Decomposition
3) Classification, etc.Polarimetric Scattering
Model
Dual-Pol SAR Imagery
e.g. π/4 Transmit with
(H, V) Receive
Compact Polarimetry –Enhancing Dual-Pol Imagery
Pseudo Quad-Pol Data
1) Standard Quad-Pol Analysis
2) Quad-Pol Decomposition
3) Classification, etc.Polarimetric Scattering
Model
Dual-Pol SAR Imagery
e.g. π/4 Transmit with
(H, V) Receive
Two Questions:
1) How appropriate is the scattering model?
2) What type of dual-pol imagery provides the best
input to the scattering model?
Compact Polarimetric Modes / Models
� Dual-Pol Data Collection Modes� Standard Linear Modes:
� Transmit H (or V) with H & V Receive
� Not Appropriate for Compact Polarimetry
� π/4 Mode: � Linear Transmit with H & V Linear Receive
� Circular Transmit Modes:
� Circular Transmit with Left & Right Circular Receive
� Circular Transmit with H & V Linear Receive
� Model Simple Natural Scatterers � Reflection Symmetry Assumption
� Random Volume Scattering Model
� Double-Bounce “Correction” to Random Volume Model
Compact Polarimetric Modes
� Dual-Pol Scattering Vectors:
� π/4 Mode Covariance Matrix
[ ]
[ ]
[ ]
[ ] 2
24/
T
HVVVHVHHCTLR
T
RLRRDC
T
HVVVHVHH
T
HVHHH
SiSiSSk
SSk
SSSSk
SSk
++=
=
++=
=
r
r
r
r
π
[ ] [ ] [ ]
( )( )
⋅ℜ⋅+⋅
⋅+⋅⋅ℜ+
+
⋅
⋅=×=
***
***
22
22
2*
*2
444/
2
2
2
1
2
1
2
1
HVVVHVVVHVHH
HVVVHVHHHVHH
HVHV
HVHV
VVHHVV
VVHHHH
SSSSSS
SSSSSS
SS
SS
SSS
SSSkkC
†πππ
Reflection Symmetry Assumption
Too Many Variables (9), Not Enough Equations (4)
� Assume Reflection Symmetry
� Define a Relationship Between |HV| and ρ
� True for a Randomly Oriented Cloud of Dipoles (Volume Scattering), but …
22
*
VVHH
VVHH
SS
SS
⋅
⋅=ρ
0**
=⋅=⋅HVVVHVHH
SSSS
( )4
122
2ρ−
=+
VVHH
HV
SS
S
DLR E-SAR Imagery
Quad-Pol Data to Simulate Compact Polarimetric Modes
Pauli Display
Red: |HH-VV|
Green: |HV|
Blue: |HH+VV|
L-band Imagery of Oberpfaffenhafen
Test of |HV| vs. ρρρρ Relationship
A Scatter Plot of
vs.
Shows a Possible Problem.
(All points should lie on the diagonal line.)
( )ρ−14
1
22
2
VVHH
HV
SS
S
+
22
2
VVHH
HV
SS
S
+
( )4
1 ρ−
Double-Bounce Correction
A Useful Mathematical Inequality:
Rewriting Yields
|SHH-SVV| / |SHV| is the Double-Bounce “Correction”
• First Estimate the |SHH-SVV| / |SHV| Ratio
• Then Apply this New Relationship
( ) ( ) 2221
VVHHVVHHSSSS −≤+− ρ
( )( )
2
222
21
HV
VVHHVVHH
HV
S
SSSS
S
−
−≈
+
ρ
Model Improvement
Use the Original Compact Polarimetry Model to Estimate the |SHH-SVV| / |SHV| Ratio.
Use this Estimate to Determine the Ratio of
To
And Solve for the Pseudo Quad-Pol Data
22
2
VVHH
HV
SS
S
+
( )ρ−1
( )( )221
VVHHSS +− ρ
2
VVHHSS −
ππππ/4 Mode vs. Quad-Pol
ππππ/4 Mode vs. Quad-Pol
CTLR Mode vs. Quad-Pol
CTLR Mode vs. Quad-Pol
Pseudo Quad-Pol Comparison
Original Quad-Pol Imagery
Red: |HH-VV|
Green: |HV|
Blue:|HH+VV|
Dual-Circ Compact Polarimetric Imagery
π/4 ModeCompact Polarimetric Imagery
Circ X-mit / Linear Rec. Compact Polarimetric Imagery
Graphic Dual-Pol Analysis
� Dual-Pol Receives Two Orthogonal Polarizations
� Can Synthesize Any Receive
Polarization, in Principle
� Ellipticity and Orientation Fully
Characterize the Polarization of
the Received Signal
� Dual-Pol Decompositions
� Entropy is Entropy, but …
� Alpha Angle – No Longer Just a Scattering Mechanism
ab
a
b====χχχχtan
Linear Dual-Pol Signatures
Linear Horizontal Transmit Polarization
Dihedral Response Surface Response
ππππ/4 Dual-Pol Signatures
Linear π/4 Transmit Polarization
Dihedral Response Surface Response
Dual-Pol Circular Signatures
Right-hand Circular Transmit Polarization
Dihedral Response Surface Response
H Transmit
Looks like the Dihedral and
Surface Plots!
π/4 Transmit
Looks like the Surface Plot.
Dual-Pol Vegetation Signatures
H Transmit
Looks like the Dihedral and
Surface Plots!
π/4 Transmit
Looks like the Surface Plot.
Dual-Pol Vegetation Signatures
Right-hand Circular
This one is Different.
Pol Vegetation Signatures
Circular-Transmit, Dual-Pol Conclusions
� Circular Dual-Pol Separates Scatterers
� Dihedrals, Rough Surfaces, Dipoles, Vegetation
� Signature Plots Differ for These Scatterers
� Circular Does Not Detect Target Orientation
� Except for Single Dipole Scatterers
� Extracting Terrain Slopes May be Difficult Without
an Orientation Angle Response
Example of Dual-Pol ImageryPISAR X-band Imagery, Tsukuba, Japan
Quad-Pol ImageryPauli Basis Display
Dual-Pol Display
Example of Dual-Pol ImageryPISAR X-band Imagery, Tsukuba, Japan
Quad-Pol ImageryPauli Basis Display
Dual-Pol Display
Ingara Quad-Pol X-Band Dataset
Quad-Pol Standard Display:
Hue: α-angle
Sat.: Entropy
Value: Span
(HH, HV) Dual-Pol Imagery
Dual-Pol Display:
Red: |HH|
Green: |HV|
Blue: |HH⋅HV*|
Rotated Dihedral Scatterer
Unrotated Dihedral 30º Rotated Dihedral
Linear Horizontal Transmit Polarization
Rotated Dipole Scatterer
Unrotated Rotated 30º
Linear Horizontal Transmit Polarization
Rotated Surface Scatterer
Unrotated Surface 30º Rotated Surface
Linear Horizontal Transmit Polarization
H Transmit, Dual-Pol Information
� Linear Dual-Pol Can Distinguish Between
� Rotated Dihedrals (or Dipoles)
� Rough Surfaces (Trihedrals)
� Randomly Oriented Dipole Distributions
� Typical Vegetation Models
� Linear Dual-Pol Cannot Distinguish Between
� Dihedrals and Dipoles, Either Rotated or Not
� Unrotated Dihedrals (or Dipoles) and Any Rough
Surface
Linear Dual-Pol Decomposition
� Eigen Decomposition of the 2x2 Covariance Matrix
� Define Angle and Entropy as
with
=
−
−
ιϕ
ιϕ
ιϕιϕαα
αα
λ
λ
αα
αα
e
e
eeCC
CC
HVHVHHHV
HVHHHHHH
22
11
2
1
21
21
,,
,,
sincos
sincos
sinsin
coscos
α
( )12112211 2 απλαλαλαλα −+=+=
( ) 2lnlnlnEntropy 2211 λλλλ +−=
( )21 λλλλ +=ii
H Transmit, Dual-Pol Entropy-Alpha Plot
Allowed Dual-Pol α / Entropy Region
Blue: Surface Scattering
Green: Vegetation – Random Dipole
Distribution
Cyan: Vegetation – Surface Mix
Red: Single Dipoles or Double Bounce
Magenta: Dihedral – Surface Mix
Yellow: Dihedral – Vegetation Mix
White: High Entropy – Low
Polarimetric Content
Orange: Rotated Dihedral / Dipole Mix,
|HV|>|HH| with ⟨HH⋅HV*⟩ ~ 0
Linear Dual-Pol Decomposition
(HH, HV) Dual-Pol Imagery
Hue: α-angle
Sat.: Entropy
Value: Span
Summary
� Compact Polarimetry Results Depend Upon:
� The Reflection Symmetry Assumption
� An Appropriate Scattering Model Matched to the Transmitted Polarization
� The Double-Bounce “Correction” Appears to Give Fairly Good, Robust Results
� Dual-Pol Signature Plots:
� Complete Polarimetric Description of Dual-Pol Imagery
� Provides a Simple, Visual Analysis Technique
� Dual-Pol Decompositions:
� Alpha Angle – Not Just the Scattering Mechanism Any More
� Interpretation of Dual-Pol Alpha-Entropy Plots Depends Upon the Transmitted Polarization
Dual-Circular Mode vs. Quad-Pol
Dual-Circular Mode vs. Quad-Pol
Polarimetric Covariance Matrix
– Hermitian matrix, positive semi-definite
– Real positive eigenvalues
• Rearranging complex elements of the scattering matrix,
=
vv
vh
hv
hh
S
S
S
S
u
• The covariance matrix is formed by
[ ]
=⋅=
****
****
****
****
*
vvvvvvvvhvvvhhvv
vvvhvhvhhvvhhhvh
vvhvvvhvhvhvhhhv
vvhhvhhhhvhhhhhh
T
SSSSSSSS
SSSSSSSS
SSSSSSSS
SSSSSSSS
uuC
• For statistical analysis, speckle filtering and classification, the
covariance matrix is preferred.
Polarimetric Covariance Matrix
– Hermitian matrix, positive semi-definite
– Real positive eigenvalues
• Rearranging complex elements of the scattering matrix,
=
vv
vh
hv
hh
S
S
S
S
u
• The covariance matrix is formed by
[ ]
=⋅=
****
****
****
****
*
vvvvvvvvhvvvhhvv
vvvhvhvhhvvhhhvh
vvhvvvhvhvhvhhhv
vvhhvhhhhvhhhhhh
T
SSSSSSSS
SSSSSSSS
SSSSSSSS
SSSSSSSS
uuC
• For statistical analysis, speckle filtering and classification, the
covariance matrix is preferred.
Polarimetric Covariance Matrix
– Hermitian matrix, positive semi-definite
– Real positive eigenvalues
• Rearranging complex elements of the scattering matrix,
=
vv
vh
hv
hh
S
S
S
S
u
• The covariance matrix is formed by
[ ]
=⋅=
****
****
****
****
*
vvvvvvvvhvvvhhvv
vvvhvhvhhvvhhhvh
vvhvvvhvhvhvhhhv
vvhhvhhhhvhhhhhh
T
SSSSSSSS
SSSSSSSS
SSSSSSSS
SSSSSSSS
uuC
• For statistical analysis, speckle filtering and classification, the
covariance matrix is preferred.
Polarimetric Covariance Matrix
– Hermitian matrix, positive semi-definite
– Real positive eigenvalues
• Rearranging complex elements of the scattering matrix,
=
vv
vh
hv
hh
S
S
S
S
u
• The covariance matrix is formed by
[ ]
=⋅=
****
****
****
****
*
vvvvvvvvhvvvhhvv
vvvhvhvhhvvhhhvh
vvhvvvhvhvhvhhhv
vvhhvhhhhvhhhhhh
T
SSSSSSSS
SSSSSSSS
SSSSSSSS
SSSSSSSS
uuC
• For statistical analysis, speckle filtering and classification, the
covariance matrix is preferred.
Quad-Pol Entropy / Alpha Space
SURFACE
SCATTERING
MULTIPLE
SCATTERING
VOLUME
SCATTERING
Low Medium High
Linear Dual-Pol Decomposition
(VV, VH) Dual-Pol Imagery
Hue: α-angle
Sat.: Entropy
Value: Span
Linear Dual-Pol Decomposition
(VV, VH) Dual-Pol Imagery
Hue: |⟨VV·VH*⟩|
Sat.: Entropy
Value: Span
Linear Dual-Pol Decomposition
(HH, HV) Dual-Pol Imagery
Hue: |⟨HH·HV*⟩|
Sat.: Entropy
Value: Span