potentials of volumetric differential interferometry...

POTENTIALS OFPOTENTIALS OF

VOLUMETRIC DIFFERENTIAL INTERFEROMETRYVOLUMETRIC DIFFERENTIAL INTERFEROMETRY

AND ROBUST TOMOGRAPHYAND ROBUST TOMOGRAPHY

ESA Fringe 2007 Workshop, Frascati, Italy

Fabrizio LOMBARDINIFabrizio LOMBARDINI

UNIVERSITY OF PISA

Dept. of “Ingegneria dell’Informazione”

Pisa, Italy - [email protected]

v Recalls of Diff-Tomo, Space-time signatures

v Potentials for distributed, non-rigid, decorrelating scatterers:

Volumetric Differential Interferometry and Robust Tomography

v Simulated results

v Conclusions and future developments

Outline of the Presentation

Differential Tomography

Diff-Tomo exploits the multibaseline-multitemporal information content

to enter the SAR pixel and extract separated information on

elevation and velocity of multiple superimposed scatterers

Ideal 3D Tomo

acquisition

(time is nuisance)

Ideal Differential

acquisition

(space is nuisance)

Multibaseline-Multitemporal acquisitions

Practical

2D (curv. or sparse)

support in

Baseline-Time plane:

it is actually rich source

of information!

[Lombardini IGARSS’03, TGARS 2005]

Space-time signatures

4 /( )i iS nsr

h r! " #=

4 /i iT los

v! " #=

discrete space-time spectrum

Space-time spectral leakage from sparse sampling of 2D Baseline-Time support:

2D sidelobe-suppressing processing (e.g. adaptive nulling) important for 4D Diff-Tomo

spatial harmonic

temporal harmonicuniform motion:

i-th compact scatterer,

continuous space-time spectrum

spatial harmonic

distribution

temporal harmonic

distribution

range of velocities:

extended scatterer:

temporal harmonic

distribution !

temporal decorrelation

of a scattering

component:

(temporal frequencies code velocities)

(temporal frequencies code velocities)

2 /T

cB! " #=

velocities are now equivalent velocities !

(originated by amplitude/phase modulation)

More general case:

Other challenging potentials

May Diff-Tomo extract further information

in these more complex scenarios ?

In principle, Diff-Tomo has a continuous joint elevation-velocity/temp. freq. profiling

and separation capability of multiple scattering components:

“volumetric differential interferometry” or “full” 4D imaging !

Joint elevation-velocity continuous distributions:

Velocity profiling of moving volumetric scatterers ?

3D Tomo robust to internal motions ?

Misinterpretation avoided of time-signal histories with space-signal histories:

Velocity measurement of buried scatterers ?

Interference avoided among layover moving scatterers:

Preliminary exploration of potentials under controlled conditions

by simple simulated scenarios

Non-rigid sliding volume on ground (1)

single-track per pass

2D Beam. Diff-Tomo image

SNR=15 dB

g/v=1/7




SNR=15 dB

16 looksg/v=1/7




SNR=15 dB

Space-time signature of non-rigid volume !

16 looksg/v=1/7


multistatic

SNR=15 dB

16 looksg/v=1/7


velocity profile

multistatic

SNR=15 dB

Velocity profiling of non-rigid volume !

16 looksg/v=1/7

robust tomo profile

multistatic

SNR=15 dB


3D Tomo robust to internal motions !

16 looksg/v=1/7

robust tomo profile

multistatic

SNR=15 dB


conventional tomo profile

16 looksg/v=1/7

robust tomo profile

multistatic

SNR=15 dB


conventional comp. tomo profile

16 looksg/v=1/7

Moving subsurface scatterer (1)

SNR=15 dB

t c=11.2 (rev. time units):Bv los=0.25 (Fourier res. units)

b/v=1/1


SNR=15 dB



Buried scatterer separated !

16 looksb/v=1/1

multistatic


SNR=15 dB



16 looksb/v=1/1

SNR=15 dB

multistatic




16 looksb/v=1/1

Short- and long-term decorrelating volume over ground (1)

SNR=15 dB

t c=1.4 (rev. time units):Bv los=2 (Fourier res. units)

r 0=0.5

g/v=1/5


SNR=15 dB


r 0=0.5


16 looksg/v=1/5

multistatic


16 looks

SNR=15 dB


r 0=0.5


g/v=1/5

multistatic


SNR=15 dB


r 0=0.5


16 looksg/v=1/5

Conclusions

Future Work…

• Capability of Differential Tomography of operating with

distributed, non-rigid, buried, decorrelating scatterers

analyzed by simulation

• Encouraging results obtained for simple yet representative scenarios

• Indication of potential of velocity profiling;

• Indication of potential of robust Tomo; robust DEM generation

to be further investigated…

• Challenging potential of subsurface/sub-canopy scatterer monitoring

• Miscalibration effects analysys

• Extension of simulations (point scatterers model)

• Controlled experiments in order (microwave anechoic chamber)

• Live data experiments, algorithms optimization

Long-term decorrelating distributed scatterer

16 looks

SNR=15 dB


adaptive Diff-Tomo image

multistatic



robust tomo profile(DEM)

Temporal effects decoupled !

16 looks

SNR=15 dB


[Lombardini TGARS 2005]

E-SAR DLR data, 14 tracks

[Lombardini Int. Report 2007]

robust tomo profile

multistatic

16 looks

SNR=15 dB


3D Tomo robust to internal motions !

Differential Tomography

Diff-Tomo exploits the multibaseline-multitemporal information content

to extract joint elevation-velocity measures of multiple scatterers:

Ideal 3D Tomo

acquisition

(time is nuisance)

Ideal Differential

acquisition

(space is nuisance)

Multibaseline-Multitemporal acquisitions

Practical

2D (curv. or sparse)

support in

Baseline-Time plane:

it is actually rich source

of information!

2D

[ , ] ( , )S Tg b t ! " "# $F4 /( )

S nsrh r! " #=

4 /T los

v! " #=

cmplx amplitude space-

time spectrum

(discrete)

Space-time spectral leakage from sparse sampling of 2D Baseline-Time support:

2D sidelobe-suppressing processing (e.g. adaptive nulling) important for 4D Diff-Tomo

[Lombardini IGARSS’03, TGARS 2005]

Space-time signatures

2D

[ , ] ( , )S Tg b t ! " "# $F4 /( )

S nsrh r! " #=

4 /T los

v! " #=

Non-regular/random amplitude/motion temporal processes:

temporal spectral components originated by amplitude/phase modulation!

continuous space-time spectrum:

temporal frequencies code velocities

Signatures from spatial extension and motion

Signatures from temporal decorrelation

Analysis of concept and limits

First preliminary probing of potentials under controlled conditions

by simple simulated scenarios

Limits expected depending on:

• Pattern of Baseline-Time acquisition

• Extension (complexity) of continuous space-time spectra

• Processing adopted

Statistical simulators for random volume / distributed scatterers

with non-rigid motion / temporal decorrelation(comparison with point scatterers model simulation also made)

analysis by:

possible identifiability / accuracy problems

from sparse Baseline-Time sampling;

reduced 2D leakage suppression

if flexible non-model based adaptive processing is employed

(degrees of freedom problems in nulling)

Temporal decorrelation

Regular temporal motions of extended scatterer components:

2D

[ , ] ( , )S Tg b t ! " "# $F4 /( )

S nsrh r! " #=

4 /T los

v! " #=continuous space-time spectrum:


Non-regular/random amplitude/motion temporal processes:


2D

2[ , ] | ( , ) |g S Tr b t ! " "# $F

continuous space-time power spectrum:

velocities are “equivalent velocities”

temporal decorrelation phenomena

affects space-time autocorrelation

space-time spectral signatures expected

So far signatures from spatial extension and motion considered.

What about signatures from temporal decorrelation ?

Conclusions

Future Work…

• Capability of Differential Tomography of operating with

extended space-time spectra (distributed decorrelating scatterers)

analyzed by simulation

• Encouraging results obtained for simple yet representative scenarios

• Indication of potential of velocity profiling

• Indication of potential of robust Tomo; robust DEM generation

to be further investigated

• Other potentials investigated; applications searched;

may richly exploit SAR data archives and incoming satellite clusters

• Miscalibration effects analysys

• Extension of statistical and point scatterers model simulations

• Controlled experiments in microwave anechoic chamber in order

• Algorithms optimization

Proposal of New Crossed Mode

joint elevation-velocity

resolution of

multiple scatterers

System Capabilities in the New General Framework

“Tomo-Doppler” imaging !

“Differential Tomography”

D-InSAR concept

Tomo-SAR concept

conv. acquisition

new processing

+

2D Capon-based Differential Tomography

Differential Tomography framework formalized:

2D Capon filter applied, also for curvilinear baseline-time acquisition:

PN

CNpasses cmplx SAR images at each pass

( , )B u v!( )t v

C PN N! ( )nY

( , )S T

S ! ! 4 /( )S nsr

h r! " #=

4 /T los

V! " #=

[ (1, ) ( )]

( ,1) [ ( , ) ( )]

1 S P T P

S C S C P T P

j B N t N

j B N j B N N t N

e

e e

! !

! ! !

"

" "

+

+

# $% &% &% &' (

L

MMMMM

L

( , ) [ ( , )], ( ) [ ( )]S T S T

vec n vec n! ! ! != =a A y Y

1ˆ ˆ( , ) 1/[ ( , ) ( , )]H

C S T S T y S TP ! ! ! ! ! !"= a R a

( ) ( )C P C PN N N N! " ! 1

1

ˆ ( ) ( )N H

y nN n n

!

== "R y y

acquisition times baselines with respect to master acquisition

N looks in each SAR image

calibrated baseline-time data matrix for given rg.-az. resolution cell

Problem: estimation of spatial-temporal spectrum

( )

( , )S T

! ! =A baseline-time steering matrixC PN N!

baseline-time steering and data vectors

Capon Tomo-Doppler image

baseline-time multilook covariance matrix estimate

…

…

…

… …

SommarioSommario

•• Introduzione alla tomografia differenzialeIntroduzione alla tomografia differenziale

•• Metodo Metodo CaponCapon 2D 2D

••Analisi di nuove potenzialitàAnalisi di nuove potenzialità

••Scenari simulati:Scenari simulati:

ØØretrodiffusoreretrodiffusore volumetrico in moto, volumetrico in moto,

ØØ retrodiffusore distribuito con retrodiffusore distribuito condecorrelazionedecorrelazione,,

ØØretrodiffusoreretrodiffusore volumetrico con volumetrico condecorrelazionedecorrelazione

••ConclusioniConclusioni

FiltroFiltro didi CaponCapon 2D 2D

Matrice dati sparsa-2D Analisi di Fourier 2D

Risente della forte presenza di

leakage

( )ly ˆ ( )CP !

steering

1

1

ˆ ( )

ˆ( ) ( )

Y

H

Y

!

! !

"

"=

R ah

a R a

%

%

1

1ˆ ( )ˆ( ) ( )

C H

Y

P !! !"

=a R a%

Vantaggi rispetto a Fourier 2D

•E’ adattivo (dipende dai dati)

•Riduce i lobi laterali

•Risoluzione migliore

•No informazioni a priori(modelli)

Filtro di Capon (1D)

ScenariScenari distribuiti con distribuiti con decorrelazionedecorrelazione (2) (2)

Simulatore Simulatore fisicofisico

Simulatore fisico Simulatore statisticoSimulatore statistico

Verificata

anche la

stazionarietà

••conferma i risultati del simulatore statistico,conferma i risultati del simulatore statistico,

••maggiore flessibilità per scenari futurimaggiore flessibilità per scenari futuri

Immagine

Tomo-Diff

(media)

Decorrelazione

temporale

ConclusioniConclusioni

••Simulazioni di Simulazioni di scatteratoriscatteratori volumetrici in moto: l volumetrici in moto: l’’immagineimmagine

tomograficatomografica differenziale è una buona ricostruzione dello differenziale è una buona ricostruzione dello

spettro 2D, così come lo sono il profilo di velocità e dispettro 2D, così come lo sono il profilo di velocità e di

riflettivitàriflettività stimati per basi multiple (nuova applicazione), stimati per basi multiple (nuova applicazione),

••Simulazioni di Simulazioni di retrodiffusoreretrodiffusore distribuito con distribuito con decorrelazionedecorrelazione

temporale: possono essere utilizzati per studiare gli algoritmitemporale: possono essere utilizzati per studiare gli algoritmi

più robusti,più robusti,

••Simulazioni per Simulazioni per scatteratorescatteratore volumetrico con volumetrico con decorrelazionedecorrelazione

temporale: misure con ragionevole precisione della velocità deltemporale: misure con ragionevole precisione della velocità del

retrodiffusoreretrodiffusore sottostante (nuova applicazione), sottostante (nuova applicazione),

••Il simulatore fisico potrà essere utilizzato per analizzare scenariIl simulatore fisico potrà essere utilizzato per analizzare scenari

ancora più complessi,ancora più complessi,

••PotenzialitPotenzialitàà ancheanche per per nuovenuove costellazionicostellazioni satellitarisatellitari SAR SAR

(COSMO-(COSMO-SkyMedSkyMed).).

Recent proposal of New Crossed Mode

joint elevation-velocity

resolution of

multiple scatterers !

System Potentials in the New General Framework

“Doppler Tomography”

D-InSAR concept

Tomo-SAR concept

conv. acquisition

new processing

+

[Lombardini ‘03]

Doppler Tomography is an extension of

D-InSAR two-scatterer separation concept

from Politecnico di Milano ‘02

New imaging products:

Improved existing imaging products:

Joint information on elevation-velocity distributions: which velocities for each height…

Misinterpretation avoided of time-phase histories with baseline-phase histories…

Interference avoided among layover moving scatterers…

Conclusions

Future Work

• Doppler Tomography concept proved with spaceborne data

• Joint elevation-velocity resolution of two layover scatterers achieved

• Adaptive processor produces superresolution Tomo-Doppler image

• Robustness to miscalibration should be improved

• The new framework is promising

• Performance characterization with complex elevation-Doppler spectra

• Improvements of adaptive processor

• Further experimental activities and ground validation…

The Challenge of Spaceborne SAR Tomography

Trade-off ambiguity height/h-resolution

Limited h-resolution, many tracks required !

Typically irregular track distribution

Anomalous sidelobes in the h-PSF !

1) General problems of 3D SAR tomography:

2) Spaceborne tomography problems:

Atmospheric phase errors

Defocusing !

Deformation phase errors

Motion induced blurring !

Temporal decorrelationDefocusing

Rationale: satellite archives, next satellite clusters and constellations

enhanced (3D) imaging + synoptic view !

Two Goals:

New Two-stage Processing Approach:

2) Curing sidelobe problems

State of the art of spaceborne tomography:

Imaging of corner reflector [Homer-Longstaff-She ’97, She-Gray-Bogner-Homer-Longstaff ’02];

Experiments for extended scenes are lacking

Adaptive Spectral Estimation ! (adaptive imaging)

First experiments of Capon spaceborne MB SAR tomography

Space-varying Phase Compensation ! (pre-filtering)

1) Curing atmospheric and motion blurring

[Lombardini-Reigber ’03]

[Fornaro ’03]

ScenariScenari volumetrici in moto (2)volumetrici in moto (2)

Immagine Tomo-Diff

Profilo di velocità stimato Profilo di riflettività stimato

Base

singola

Ghiacciaio

con profilo

v. cubico

Profilo quota- velocità vero

ScenariScenari volumetrici in motovolumetrici in motoProfilo quota-velocità vero

Immagine Tomo-Diff

Profilo di velocità stimato Profilo di riflettività stimato

BasiBasi

multiplemultiple

Post-processing

Ghiacciaio

con profilo

v. cubico

ScenariScenari distribuiti con distribuiti con decorrelazionedecorrelazione

Basi multiple

Immagine

Tomo-Diff

! di quota al

variare di Bv

Post-processing

RetrodiffusoreRetrodiffusore distribuito affetto da distribuito affetto da decorrelazionedecorrelazione

temporale (moti temporale (moti brownianibrowniani))

Base singola

(Primi confronti con dei metodi classici)

ScenariScenari volumetrici con volumetrici con decorrelazionedecorrelazione

Foresta

TerrenoBase singolaBase singola Basi multipleBasi multiple

••SingolaSingola

realizzazionerealizzazione

••RealizzazioneRealizzazione

media media

Immagine

Tomo-Diff

Simulated Results

Capon Tomo-Doppler imageFourier Tomo-Doppler image

6PN =

1CN =

N=32 looks

( , )S T

! ! = (0, 0) (1.5,1)

SNR=15, 12 dB

2D fluctuating line spectrum

Rayleigh/Fourier resolution units

,(single-channel

airborne, spaceborne)

Simulated Results (2)

Capon Tomo-Doppler image

same elevation-Doppler spectrum

Np=5

Fourier Tomo-Doppler image



multistaticsingle-track per pass

Temporal decorrelation

Regular temporal motions of extended scatterer components:

2D

[ , ] ( , )S Tg b t ! " "# $F4 /( )

S nsrh r! " #=

4 /T los

v! " #=continuous space-time spectrum:


Non-regular (random) temporal (amplitude/motion) processes:


2D

2[ , ] | ( , ) |g S Tr b t ! " "# $F

continuous space-time power spectrum:

temporal frequencies code “equivalent velocities”

temporal decorrelation phenomena

affects space-time autocorrelation

space-time spectral signatures expected


multistatic


Short- and long-term decorrelating volume over ground


16 looks

SNR=15 dB


r 0=0.5

potentials of volumetric differential interferometry...

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