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EXPLOITATION OF TEMPORARY COHERENT
SCATTERERS IN SQUEESAR ANALYSES
EXPLOITATION OF TEMPORARY COHERENT
SCATTERERS IN SQUEESAR ANALYSES
A. Ferretti, A. Fumagalli, F. Novali, C. Prati, F. Rocca, A. Rucci
FRINGE 2011 – September 19-23 ESA-ESRIN, Frascati - Italy
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Outline
Background: the SqueeSAR approach
Limitations of SqueeSAR
Temporary Coherent Scatterers (TCS)
Challenges related to precision assessment for TCS
Examples on real data
Conclusions
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SqueeSAR™: from PS to PS+DSSqueeSAR™: from PS to PS+DS
Rock BouldersBuildingsMan-Made Structures
Homogenous GroundScattered OutcropsShort Vegetation
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Basic ideas
::
DSPS
We want to use both deterministic (point- wise) and stochastic (distributed) targets.
To detect DS, we adopt a statistical test to identify Statistically Homogeneous Pixels (SHP) in the neighborhood of each pixel ( DespecKS algorithm)
Whenever the number of SHP is high enough we have a DS and we can compute the sample coherence matrix, .
The coherence matrix
can fully characterize the target (CG variables)
DS
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Squeezing the coherence matrix
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For each DS, the sample covariance matrix can be easily computed:
A ML estimation is carried out to estimate the phase vector matching the phase values of the elements of the covariance (coherence) matrix corresponding to all possible interferograms ( PTA algorithm)
In SqueeSAR the optimum N phase values are estimated (1) before any phase unwrapping procedure and (2) using all interferograms.
N
H ddp
CCd
detexp)(
1 φφ ΓΓφφ
ii ee 1maxarg
jkijk
P
H ecPPP
)()(1)( ddC
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0 1 2 3 …. N-1 ]
DespecKS algo for each DS…
From N/(N-1)/2 itfgs…
..to N optimum phase values..
The SqueeSARTM approachThe SqueeSARTM approach
3D Phase Unwrapping
Displacement Estimation
via PTA…
Ferretti et al. “A New Algorithm for Processing Interferometric Data-Stacks: SqueeSAR” IEEE Trans. Geoscience And Rem. Sens., 49(9), September 2011
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Alpine area, Italy – 69 RSAT images
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Alpine area, Italy – 69 RSAT images
PSInSAR™
SqueeSAR™
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Limits of the SqueeSAR approachLimits of the SqueeSAR approach
In the current version of SqueeSAR, we require for each DS a good phase
stability in all SAR images, in order to retrieve a full time-series of displacement values for each measurement point.
Temporary Coherent Scatterers (TCS), i.e. targets whose SNR values can vary dramatically over time, are typically discarded.
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“First order” TCS analysis“First order” TCS analysis
Pros ConsPossible to extract information on DS exhibiting coherence only in a few interferograms
No time series available (if no prior information is available)
Significant increase in the density of measurement points
Precision of h and v values can be very different. Confidence intervals can be difficult to get
On TCS is still possible to extract useful information by adopting
a similar approach (ML estimation) in order to estimate, for each
DS: (1) the elevation; (2) the average displacement rate, after APS
estimation and removal:
),(1),(
,maxarg, vhivhiH
vheevh ff dΓd
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Precision AssessmentPrecision Assessment
PROBLEM: How to estimate error-bars for (h,v) ?
The Cramer-Rao Lower Bound (CRLB) can provide an estimate of the variance of our estimates, but:
The “true” covariance matrix is unknown (and the number of
SHP can be limited).
The CRLB is based on the coherence values of the
interferograms and do not take into account the presence of any atmospheric leakage.
Typically CRLB values are very optimistic.
Another option is the use of statistical bootstrap methods
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Statistical Bootstrap (1)Statistical Bootstrap (1)
• The bootstrap is a powerful technique for assessing the accuracy (confidence interval) of a parameter estimator when standard methods cannot be applied
• The bootstrap creates a large number of datasets by random sampling with replacement from the data we have and computes the parameter of interest using each of these datasets.
::
DS
),(1),(
,maxarg, vhivhiH
vheevh ff dΓd
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Statistical Bootstrap (2)Statistical Bootstrap (2)
In our case, data are M complex vectors associated to a DS
The computation of the histogram of the estimates of both h and v allows one to identify measurement points that should be considered unreliable.
The precision (i.e. the confidence intervals) of v and h for the same TCS can be very different.
Data-set of M camplex vectors (supposed i.i.d.)
D=[ d1 , d2 , d3 , …, dM ]
D=[ d1 , d1 , d2 , …, dM ]
D=[ d1 , d2 , d2 , …, dM ]
D=[ d1 , d2 , …, dM , dM ]
(h1 ,v1 )
(h2 ,v2 )
(hW ,vW )
h
v
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RESULTS ON REAL DATARESULTS ON REAL DATA
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Test site: Etna VolcanoTest site: Etna Volcano
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PSInSAR™PSInSAR™
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SqueeSAR™SqueeSAR™
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ML Estimation – Velocity (no THR) ML Estimation – Velocity (no THR)
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Histogram of Estimated StDevHistogram of Estimated StDev
Unreliable values (
> 2 mm/yr )
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ML Estimation – Velocity (THR)ML Estimation – Velocity (THR)
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PSInSAR™ - DEM ErrorPSInSAR™ - DEM Error
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SqueeSAR™ – DEM ErrorSqueeSAR™ – DEM Error
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ML Estimation – Dem Error (no THR)ML Estimation – Dem Error (no THR)
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ML Estimation – DEM Error (THR)ML Estimation – DEM Error (THR)
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ML Estimation – Geocoded DEMML Estimation – Geocoded DEM
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ML Estimation – Velocity FieldML Estimation – Velocity Field
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Confidence Intervals for v and hConfidence Intervals for v and h
Based on coherence matrix of the DS, confidence intervals (and ) of v and h can be very different
v
v
h
h
DS1
DS2
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Landslide MappingLandslide Mapping
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Conclusions Conclusions The SqueeSAR approach suggests a strategy for a synergistic use of PS and DS, providing for both kind of targets a time series of displacement
For TCS we can still provide useful information (e.g. average displacement rate and elevation), through a ML estimator
Bootstrap methods can provide a more effective estimation of reliable estimates, compared to CRLB
We suggest a joint use of the 2 algorithms to gain an enhanced insight into ground deformation phenomena
the ML approach makes it possible to better identify the footprint of unstable areas
the displacement time-series provided by SqueeSAR allows one to monitor the temporal evolution of the deformation field
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Synergistic use of SqueeSAR and MLSynergistic use of SqueeSAR and ML
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