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