exploitation of temporary coherent scatterers in … · 2014. 6. 12. · bootstrap methods can...

Copyright - Tele-Rilevamento Europa - 2004 © TRE 2011treuropa.com

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

© TRE 2011treuropa.com 2

Outline

Background: the SqueeSAR approach

Limitations of SqueeSAR

Temporary Coherent Scatterers (TCS)

Challenges related to precision assessment for TCS

Examples on real data

Conclusions


SqueeSAR™: from PS to PS+DSSqueeSAR™: from PS to PS+DS

Rock BouldersBuildingsMan-Made Structures

Homogenous GroundScattered OutcropsShort Vegetation


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


Squeezing the coherence matrix

5

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


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

© TRE 2011treuropa.com 7PSInSAR™

Alpine area, Italy – 69 RSAT images

© TRE 2011treuropa.com 8SqueeSAR™

Alpine area, Italy – 69 RSAT images

PSInSAR™

SqueeSAR™


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.


“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


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


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


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


RESULTS ON REAL DATARESULTS ON REAL DATA


Test site: Etna VolcanoTest site: Etna Volcano


PSInSAR™PSInSAR™


SqueeSAR™SqueeSAR™


ML Estimation – Velocity (no THR) ML Estimation – Velocity (no THR)


Histogram of Estimated StDevHistogram of Estimated StDev

Unreliable values (

> 2 mm/yr )


ML Estimation – Velocity (THR)ML Estimation – Velocity (THR)


PSInSAR™ - DEM ErrorPSInSAR™ - DEM Error


SqueeSAR™ – DEM ErrorSqueeSAR™ – DEM Error


ML Estimation – Dem Error (no THR)ML Estimation – Dem Error (no THR)


ML Estimation – DEM Error (THR)ML Estimation – DEM Error (THR)


ML Estimation – Geocoded DEMML Estimation – Geocoded DEM


ML Estimation – Velocity FieldML Estimation – Velocity Field


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


Landslide MappingLandslide Mapping


33

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


Synergistic use of SqueeSAR and MLSynergistic use of SqueeSAR and ML

Tele-Rilevamento Europa

Ripa di Porta Ticinese 7920143 MilanoItaliawww.treuropa.com

TRE Canada Inc.

#550 – 409 Granville StreetVancouver, BC, V6C 1T2Canada www.trecanada.com

© TRE 2011treuropa.com

exploitation of temporary coherent scatterers in … · 2014. 6. 12. · bootstrap methods can...

Documents