WE3.L09 - EVALUATION OF SYSTEM POLARIZATION QUALITY FOR POLARIMETRIC SAR IMAGERY AND TARGET...

EVALUATION OF SYSTEM POLARIZATION QUALITY FOR POLARIMETRIC SAR IMAGERY

AND TARGET DECOMPOSITION

Yanting Wang, Thomas L. Ainsworth and Jong-Sen Lee

Naval Research Laboratory

April 12, 2023 IGARSS 2010, Hawaii 2

Objectives• PolSAR observations

– Subject to polarization distortions

• How good the polarization purity needs to be?– Evaluate the various effects of polarization distortions – Quantify the polarization quality of the PolSAR system

for polarimetric imagery

tvh

vh

vv

hh

r kg

g

g

g

k

1

cossin

sincos

cossin

sincos1

t

ttrm

S

XSXS

Faraday Rotation

Cross-talk

Channel Imbalance


Overview of Polarization Distortion

• The apparent errors on the measurements depend on the distortion type and the targets

k

1

1

1

sphere

20

01

k

Channel Imbalance

Cross-talk

bouncedouble

2

2

10

01

sphere

2

2

12

21

ObservationsSurface Channel

Double bounceChannel

2

12 k

2

1 2k

22

0

0

22

plane-di 45o0

0

k

k

0

00 )1(2 k

22

Cross-polChannel

0

To investigate the impact of polarization quality is not trivial task in a practical system.


Polarization Distortion Model

• Distortions act as a linear transformation over the target polarimetric response

• The measurement error vector

• Its norm can be used to evaluate the error budget on the observations

ttrm XSXS )()( trTtm SXXS vecvec

[D]:: The distortion matrix

)()( tSIDe vec

e We like to evaluate the error vector over the whole vector space {vec(St)}.


Polarization Quality Metric• Take its maximum to decouple the system

characteristics from targets

• Adjust for natural targets which are reciprocal.

[A4]:: “adapter” translates reciprocal scattering to general response

)(

1

0

0

0

0

21

21

0

0

0

0

1

)( tSIDe vec

444

t

t4

S

AIDIDAAID

S

SAID

t

)()()(

)(

)()(max

*max2

TT

vec

vecMNE

)(max

tS S

e

t vec MNE: Maximum Normalized Error


Polarization Quality Metric

• The MNE forms an appealing metric– Advantage: it is defined over the system polarization

distortions ( ) only– It caps the error budget in the whole target space

• The metric is polarization invariant– Induced matrix norm is invariant to unitary

transformation

rTt XX

))()(( ** UXUUSUUXUS tT

tT

rT

new

*

**

**

)()(

))()((

)()(

UUDUU

UUXXUU

UXUUXUD

T

rTt

TT

rTT

tT

new


Typical Distortion – channel imbalance

• Channel imbalance includes two parts: gain mismatch and phase mismatch

jaek

11


Typical Distortion – cross-talk

• Cross-talk also involves both the isolation level and the phase shifts.

1

1

1

12 v

h

j

j

v

v

h

h

e

e

g

e

g

e

Assume

dB20


Typical Distortion – Faraday rotation

• Low frequency spaceborne radar observations are also subject to propagation distortions

cossin

sincos


Polarimetric Decompositions• Normalized error for decompositions

• The maximum normalized error can be applied to evaluate the decomposition errors given a known set of decomposition bases

xBxbbbSt nvec ˆˆˆ)( 21 xDBS )( mvec

xBIDBxBIDBBBe )()()( 1 HorthonomalHH

k

kdk

kk SPAN

xxe

2)(2

In case of orthogonal decomposition bases, or effectively orthogonal polarization basis change, the maximum decomposition error is same as the MNE.

Pauli based decomposition falls into this category.


Example Scene

• E-SAR L-band Image

Applied with a known distortion:

dB20

528.0009.0470.0

009.0010.0009.0

470.0009.0462.0

5.713.0

5.714.52

3.04.52

oo

oo

oo

jj

jj

jj

ee

ee

ee

222.0023.0282.0

023.0022.0047.0

282.0047.0756.0

8.146.164

8.145.133

6.1645.133

oo

oo

oo

jj

jj

jj

ee

ee

ee

290.0010.0087.0

010.0250.0022.0

087.0022.0460.0

0.1026.15

0.1027.113

6.157.113

oo

oo

oo

jj

jj

jj

ee

ee

ee

1) Double bounce scattering

2) Volume scattering

3) Surface scattering


Pauli Based Decomposition

• The MNE is shown as a tight upper bound.


Krogager Based Decomposition

• The decomposition is more affected by this distortion configuration– Helix scattering and double bounce scattering are not

orthogonal.– It is sensitive to the cross-talk phase terms.

Decomposition Error: -8.4 dB


Krogager Based Decomposition

• Individual decomposition channels


Freeman-Durden Decomposition

• High polarization distortions more likely violate the model assumption

Flip of surface scattering and double bounce scattering after the random volume component removed


Freeman-Durden Decomposition

• Individual decomposition channels


Eigen-based Decomposition

• Eigen-based decomposition is more resilient to this distortion configuration


MNE as Evaluation Baseline

• Simulation Settings

DISTORTION CONFIGURATION ON THE NATURAL TARGETS OF CANONICAL SCATTERING MECHANISMS

Distortion Range

Channel Imbalance Differential Gain: uniform in [-1, 1] dB

Differential Phase: uniform in [-20, 20] degrees

Cross-talk Isolation: uniform in [-50, -10] dB

Phase h: uniform in [-180, 180] degrees

Phase v: uniform in [-180, 180] degrees

Faraday Rotation Faraday angle: uniform in [0, 10] degrees


MNE as Evaluation Baseline• Decomposition errors versus MNE over the

selected canonical scattering mechanism


MNE as Evaluation Baseline

• The metric provides a convenient tool to connect PolSAR image quality with interacting polarization distortions.

• Reference table for the MNE metric as evaluated at various polarization distortions

Faraday Angles 0o 1o 2o 3o 5o 10o 20o Channel Imbalance – Amplitude 0.1 dB -32.7 -28.1 -22.8 -19.4 -15.1 -9.1 -3.2 0.3 dB -22.9 -22.4 -20.7 -18.4 -14.7 -9.0 -3.1 0.5 dB -18.3 -18.1 -17.5 -16.5 -13.9 -8.7 -3.0 Channel Imbalance – Phase 1o -29.1 -26.8 -22.6 -19.4 -15.1 -9.2 -3.3 3o -19.6 -19.4 -18.6 -17.3 -14.3 -9.0 -3.3 5o -15.2 -15.1 -14.8 -14.3 -12.9 -8.6 -3.2 Cross-talk – Isolation Level -30 dB -24.0 -22.8 -20.5 -18.3 -14.7 -9.1 -3.3 -20 dB -14.1 -13.9 -13.6 -13.1 -11.7 -8.2 -3.2 -15 dB -9.2 -9.2 -9.1 -8.9 -8.4 -6.7 -3.0


Questions and Comments?


Generalize to Arbitrary Polarization Mode

• The MNE definition can be further generalized to other polarization modes such as dual-pol mode

)(2

1

2

1

2

1

2

1

22

11

mrv

tv

rv

tv

rh

tv

rh

tv

rv

th

rv

th

rh

th

rh

th

tv

th

mrv

rh

rv

rh

vecpp

pp

pp

pp

pp

pp

pp

pp

p

p

pp

pp

S

SV

22

1

2

1

2

1

2

1 )( 4AID

rv

tv

rv

tv

rh

tv

rh

tv

rv

th

rv

th

rh

th

rh

th

pp

pp

pp

pp

pp

pp

pp

ppMNE

2

)(0

0

0

04AID

t

v

tv

th

th

p

p

p

pMNE

Dual-pol modeObservations

Dual-pol modeMNE

Receiving at H/V


Decomposition Error Profiles

WE3.L09 - EVALUATION OF SYSTEM POLARIZATION QUALITY FOR POLARIMETRIC SAR IMAGERY AND TARGET...

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Transcript of WE3.L09 - EVALUATION OF SYSTEM POLARIZATION QUALITY FOR POLARIMETRIC SAR IMAGERY AND TARGET...