potentials of volumetric differential interferometry …
TRANSCRIPT
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
Non-rigid sliding volume on ground (1)
single-track per pass
2D Beam. Diff-Tomo image
SNR=15 dB
16 looksg/v=1/7
Non-rigid sliding volume on ground (1)
single-track per pass
2D Beam. Diff-Tomo image
SNR=15 dB
Space-time signature of non-rigid volume !
16 looksg/v=1/7
Non-rigid sliding volume on ground (2)
multistatic
SNR=15 dB
16 looksg/v=1/7
Non-rigid sliding volume on ground (2)
velocity profile
multistatic
SNR=15 dB
Velocity profiling of non-rigid volume !
16 looksg/v=1/7
robust tomo profile
multistatic
SNR=15 dB
Non-rigid sliding volume on ground (3)
3D Tomo robust to internal motions !
16 looksg/v=1/7
robust tomo profile
multistatic
SNR=15 dB
Non-rigid sliding volume on ground (3)
conventional tomo profile
16 looksg/v=1/7
robust tomo profile
multistatic
SNR=15 dB
Non-rigid sliding volume on ground (3)
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
single-track per pass
SNR=15 dB
t c=11.2 (rev. time units):Bv los=0.25 (Fourier res. units)
Moving subsurface scatterer (1)
Buried scatterer separated !
16 looksb/v=1/1
multistatic
single-track per pass
SNR=15 dB
t c=11.2 (rev. time units):Bv los=0.25 (Fourier res. units)
Moving subsurface scatterer (2)
16 looksb/v=1/1
SNR=15 dB
multistatic
single-track per pass
Moving subsurface scatterer (2)
t c=11.2 (rev. time units):Bv los=0.25 (Fourier res. units)
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
single-track per pass
SNR=15 dB
t c=1.4 (rev. time units):Bv los=2 (Fourier res. units)
r 0=0.5
Short- and long-term decorrelating volume over ground (1)
16 looksg/v=1/5
multistatic
single-track per pass
16 looks
SNR=15 dB
t c=1.4 (rev. time units):Bv los=2 (Fourier res. units)
r 0=0.5
Short- and long-term decorrelating volume over ground (2)
g/v=1/5
multistatic
single-track per pass
SNR=15 dB
t c=1.4 (rev. time units):Bv los=2 (Fourier res. units)
r 0=0.5
Short- and long-term decorrelating volume over ground (2)
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
t c=1.4 (rev. time units):Bv los=2 (Fourier res. units)
adaptive Diff-Tomo image
multistatic
single-track per pass
Long-term decorrelating distributed scatterer
robust tomo profile(DEM)
Temporal effects decoupled !
16 looks
SNR=15 dB
t c=1.4 (rev. time units):Bv los=2 (Fourier res. units)
[Lombardini TGARS 2005]
E-SAR DLR data, 14 tracks
[Lombardini Int. Report 2007]
robust tomo profile
multistatic
16 looks
SNR=15 dB
Non-rigid sliding volume on ground (3)
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:
temporal frequencies code velocities
Non-regular/random amplitude/motion temporal processes:
temporal spectral components originated by amplitude/phase modulation!
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
Long-term decorrelating distributed scatterer
adaptive Diff-Tomo 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:
temporal frequencies code velocities
Non-regular (random) temporal (amplitude/motion) processes:
temporal spectral components originated by amplitude/phase modulation!
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
adaptive Diff-Tomo image
multistatic
single-track per pass
Short- and long-term decorrelating volume over ground
adaptive Diff-Tomo image
16 looks
SNR=15 dB
t c=1.4 (rev. time units):Bv los=2 (Fourier res. units)
r 0=0.5