3D SAR Tomography of the Paracou Forest: Methods and Results

Mauro Mariotti d’AlessandroAnd

Stefano Tebaldini

Politecnico di MilanoDipartimento di elettronica e informazione

ESA Fringe 2011

IntroductionGoal: exploring the vegetation layer above the ground surface

biomass estimation

carbonium cycle

Tool: P-band SAR tomographygood coverage in short time

good resolution along the three dimensions

polarimetric measurements

suitable wavelength for penetrating the forest

Processing: model free polarimetric SAR tomographyproviding resolution along the vertical direction

not relying on any particular assumption about the observed scene

not having any issue related to the fitting of the model

exploiting the relationship (a Fourier transform) linking together reflectivity and multi-baseline signal

letting the natural phenomenon to be observed directly

polarimetry can further characterize the scattering mechanisms

Preliminary issues

total

basel

ine ap

erture

sample

d reg

ularly

✕

✕✕✕

✕

✕✕

cross

range

()

PSF

elev

atio

n

ground range

✕✕✕✕✕

✕✕

cross

range

()

PSF

same b

aselin

e ape

rture

sample

d irre

gular

ly

ground rangeel

evat

ion

Radar deviation from the ideal trajectory.

Non regular sampling of the total baseline aperture.

Undesired sidelobes in the Point Spread Function (PSF) along the cross-range

direction.

elev

atio

n

ground range

reference height

desi

red

heig

ht

desi

red

heig

ht

heig

ht a

ccor

ding

to

a fi

xed

refe

renc

e

heig

ht a

ccor

ding

to

a fi

xed

refe

renc

e

Common reference height to every range-azimuth couple

Height specifications are affected by local topography.

Goal: study the vegetation layer regardless of the local topography.

Ground phases removal (1)

W

k

kkk CRW ˆSKPD

AS

222111ˆ CRCRW

2 contributions

b

Rc

, Cc

Rg

, Cg

a 21 1 RaaRRg 211 aCCaCc

211 bCCbCg 21 1 RbbRRc

ground canopy

pola

rim

etry

stru

ctur

e Rg Rc

Cg Cc

Contribution coming from the ground levelContribution coming from the canopy level

Polarimetric covariance(polarimetry)

Interferometric covariance(structure)

Rg

Rc

Cg

Cc

Estimation of the multi-pol multi-baseline covariance matrix.

SKPD (Sum of Kronecker Product Decomposition)

2121 ,,:, RRspanRRRR gc 2121 ,,:, CCspanCCCC gc

Algebraic Synthesis (AS)

Rg

and Rc

are obtained by linearly combining R1

and R2

. Same for Cg

, Cc

.

By varying a couple of real parameters {a, b}, every possible solution may be explored.

S. Tebaldini and F. Rocca, “On the impact of propagation disturbanceson SAR tomography: Analysis and compensation,”

in Radar Conference,

2009 IEEE, 4-8 2009, pp. 1 –6.

S. Tebaldini and F. Rocca, “On the impact of propagation disturbanceson SAR tomography: Analysis and compensation,”

in Radar Conference,

2009 IEEE, 4-8 2009, pp. 1 –6.

Ground phases removal (1)

W

k

kkk CRW ˆSKPD

AS

222111ˆ CRCRW

2 contributions

b

Rc

, Cc

Rg

, Cg

a 21 1 RaaRRg 211 aCCaCc

211 bCCbCg 21 1 RbbRRc

ground canopy

pola

rim

etry

stru

ctur

e Rg Rc

Cg Cc

Contribution coming from the ground levelContribution coming from the canopy level

Polarimetric covariance(polarimetry)

Interferometric covariance(structure)

Rg

Rc

Cg

Cc

Estimation of the multi-pol multi-baseline covariance matrix.

SKPD (Sum of Kronecker Product Decomposition)

2121 ,,:, RRspanRRRR gc 2121 ,,:, CCspanCCCC gc

Algebraic Synthesis (AS)

Rg

and Rc

are obtained by linearly combining R1

and R2

. Same for Cg

, Cc

.

By varying a couple of real parameters {a, b}, every possible solution may be explored.

Ground phases removal (2)

0 1

entropy (H)

alph

a (

)By varying a different estimations of Rg

and Cc

can be obtained.Estimated matrices have to be positive definite (a{amin , amax }) .

Some criterion to pick up a unique estimation must be chosen.

Canopy polarimetry

elev

atio

n [m

]

0

40

20

Cc =(a-1)C1 +aC2

aminamax

Ground structure

Rg =aR1 +(1-a)R2

a

amin

amax

Phase Linking: ground phases (). from Rg

.

elev

atio

n

ground range

space-varying reference height

heig

ht w

.r.t.

the

grou

nd heig

ht w

.r.t.

the

grou

nd

Removal of the phases associated with the ground level.

0 m specification at the ground level for each (r,a) position.

reflectivity profile

(original signal)

Baseline interpolationelevation

[m]

0

40

reflectivity profile

(original signal)

0

40

0

40

elevation [m]

0

40

✕

spectra multiplication(interpolation)

resulting profile

(interpolated signal)

0

40

profileshift

(signal demodulation)

0

40

✕

spectra multiplication(interpolation)

0

40

resultingprofile

(interpolated baseband signal)

0

40

profile shifted back(interpolated

signal)

Fourier domain

(original domain)

Fourier domain

(original domain)

→

→

→

→

Linear interpolation involves a distortion of the measured

reflectivity profile.

Shifting the reflectivity profile before interpolating leads to a

smaller distortion.

From multi‐baseline to multi‐height

ground range

elev

atio

n

0

1

2

n

imag

e ind

ex… b1

b2

…

dbr

jxrPxry nn4exp,,,

sin2 maxb

rz

Complex reflectivity along cross-range () direction and signal along image index are related by a Fourier transform.

Baseline distribution fixes resolution along the vertical direction.

Coherent focussing along the vertical direction can produce a new stack of images, each one associated with a specific elevation inside the forest.

z

Goal

The guyaflux tower (optical)

The guyaflux tower(SAR tomography)

elev

atio

n [m

]

rangeazimuth

0

45

15 m slice [dB]

Backscattered power at different heights

slc power is correlated with

0.04

45

40

35

30

25

20

15

10

5

0.08 0.12 0.16 0.2

elev

atio

n [m

]

correlation: power and

hhhvvv

sliceslctop and bottom slices

show a higher correlation

middle slice shows a low correlation with

physical interpretation

ground slope ( [°])15

10

5

0

-5

-10

-15

400

1400

86420

-2-4-6-8

15

10

5

0

-5

-10

-15

6002600 6002600

original image [dB]

0 m slice [dB]15

10

5

0

-5

-10

-15

400

1400

6002600 600260045 m slice [dB]30 m slice [dB]

15

10

5

0

-5

-10

-15

15

10

5

0

-5

-10

-15

400

1400

6002600 6002600

rang

era

nge

rang

e

azimuth azimuth

Characterizing the scattering mechanisms

slc - copolar phase [rad]400

1400

6002600

rang

e

azimuth

0m slice - copolar phase [rad]400

1400

6002600

rang

e

azimuth

0 →

-→

or

copolar phase: difference between hh phase and vv phase.It provides significant information about the target.

-10 dB

10 dB

0 dB

5 dB

-5 dB

back

scat

tere

d po

wer

copolar phasecopolar phase

slc - histogram 0m slice - histogram

Dihedral-like backscattering is characterized by a stronger power.

Dihedral-like backscattering is masked in the single look complex image.

The role of the ground slope

-10 dB

10 dB

0 dB

5 dB

-5 dB

back

scat

tere

d po

wer

ground slope [°]-8 86-6 ground slope [°]-8 86-6

slc - histogram 0m slice - histogram

-

0

copo

lar p

hase

[rad

]

ground slope [°]-8 86-6 ground slope [°]-8 86-6

slc - histogram 0m slice - histogram0m

pow

er

slop

e

0m c

op. p

hase

Backscattered power

Copolar phase

Strong backscattering is coming from the ground level.

Dihedral-like backscattering prevails on flat terrain only.As the ground slope drives away from zero the double-bounce vanishes.0m analysis allows to quantify how fast the phase returns to zero.

The dependence on the ground slope is emphasized in the 0m slice.

The peak of power is associated with the double bounce.

By measuring the width of the lobe and knowing

an effective H can be retrieved.

Analyzing the lobe of the copolar phase

dheI

H hj

0

cos2cos2

cos2cos2 hrrrhd ba

cos2cos22

cos2cos2sin

H

I

elev

atio

n

ground range

✕ rA

rB

h

image source

H

A simple model for double bounce

Length of the optical path

Summing contributions along the trunk

-

0

ground slope [°]-8 86-6

0m slice - histogram

copo

lar p

hase

[rad

]

-8 86-6 0 2 104-10 -4 -2ground slope [°]

model I(); H=7, =40°

Similar asymmetry

slow

er d

ecay

ing

fast

er d

ecay

ing

Double bounce as a function of 

-8 -6 -4 -2 0 2 4 6 8

-

0

-

0

-

0

-

0

slope [°]

0m – copolar phase

33°→38°

Look angle range:

38°→42°

Look angle range:

42°→45°

Look angle range:

45°→48°

Look angle range:

=36°=39°=42°=45°

model I(); H=7

-8 86-6 0 2 104-10 -4 -2ground slope [°]

Relating model and observations

The enlargement of the lobe cannot be explained with the dependence of I on

alone.

A dependence of the effective height H on

could still fit the model.

Physically H=H() could mean a limited ground region around the trunk in which the double bounce is made possible.

8 10-8 6-6 0 2 4-10 -4 -2ground slope [°]

0m – copolar phase [rad]

-4

0

:33°→38°:38°→42°:42°→45°:45°→48°

no double bounce

double bounce

1

2 H(1

)

H(2

)

Conclusions

• Particular baseline distributions allow a model free tomography.• It does not rely on any a priori assumption about the observed scene.• By means of a Fourier transform it is possible to associate a complex reflectivity

measurement to a particular height above the ground.• A new stack of images can be obtained, each one referred to a particular elevation

inside the vegetation layer.• Each image can be processed by means of standard SAR algorithm to retrieve the

desired information.

Model free polarimetric SAR tomography

Experimental results

• Slices associated with the extremes of the vegetation layer exhibit a strong correlation with topography. The intermediate one presents a lower correlation than the slc.

• The 0m slice shows the double bounce contribution very clearly. It is more powerful than the other backscattered signal.

• By relating the 0m slice with the ground slope it is possible to

appreciate how fast the double bounce contribution vanishes on tilted surfaces.

Thanks for your attention