TOWARDS THE INTEGRATION OF SAR TOMOGRAPHY AND PSI FOR IMPROVEDDEFORMATION ASSESSMENT IN URBAN AREAS

Muhammad Adnan Siddique(1), Irena Hajnsek(1,3), Urs Wegmuller(2), and Othmar Frey(1,2)

(1)Earth Observation & Remote Sensing, ETH Zurich, Switzerland, Email: {siddique,hajnsek,frey}@ifu.baug.ethz.ch(2)Gamma Remote Sensing AG, Gumligen, Switzerland, Email: {wegmuller,frey}@gamma-rs.ch

(3)German Aersospace Center - DLR, Oberpfaffenhofen, Germany

ABSTRACT

Persistent scatterer interferometry (PSI) typically rejectsthe range-azimuth pixels containing multiple scatterers,such as in a layover scenario. Since layovers occur fre-quently in urban areas, a significant number of candidatesmay get rejected. SAR tomography allows for resolv-ing layover and has thus the potential to extend the spa-tial sampling of deformation measurements to layover-affected areas. Using extended phase models, also tak-ing into account temperature, an improved simultane-ous estimation of elevation, deformation velocity, andtemperature-induced scatterer displacement is possible.This paper explores the combined use of PSI and SAR to-mography for deformation analysis in urban areas, usinga multibaseline and multitemporal interferometric stackof stripmap TerraSAR-X images acquired over the cityof Barcelona.

Key words: SAR tomography; PSI; DIn-SAR; multi-baseline interferometry.

1. INTRODUCTION

Persistent scatterer interferometry (PSI) [1, 2] is an estab-lished tool for radar-based deformation assessment in ur-ban areas. Using an interferometric time-series of multi-baseline SAR images, PSI allows retrieval of radar line-of-sight (LOS) deformation parameters. PSI-based anal-ysis entails a preliminary identification of PS candidatesbased on methods such as spectral diversity and tempo-ral variability of the backscattering [2]. PSI relies onthe assumption of a single dominant scatterer in a range-azimuth pixel. Therefore, the pixels with multiple scatter-ers (such as in a ground-to-facade layover) are typicallyrejected. SAR tomography [3, 4, 5] has the potential toovercome this limitation. It has the ability to retrieve theelevation and deformation parameters for multiple scat-terers in the same resolution cell, as shown in differentcontributions such as [6, 7, 8, 9].

In continuation of our earlier work [10, 11, 12] towards

the integration of SAR tomography into the operational‘Interferometric Point Target Analysis (IPTA)’ [2] toolfor PSI processing, this paper presents our current inves-tigations. We report results on an interferometric stackof X-band stripmap SLCs acquired over an urban area.A PSI solution is first obtained using the IPTA frame-work. SAR tomographic inversion is applied next inde-pendently of the PSI solution, though keeping the samereference layer and reference point. We implement to-mography with three different phase models, and com-pare the simultaneously estimated deformation parame-ters with those obtained iteratively with the PSI solution.In this paper, we focus on a particular high-rise buildingwhere potentially deformation and thermal expansion areto be expected.

2. SAR TOMOGRAPHIC MODEL

Considering a stable point target source in a given range-azimuth resolution cell, the mathematical model for con-ventional SAR tomography (3D SAR imaging) can bewritten as [5, 13]:

yn =

∫4s

γ (s) exp [−jϕn (s)] ds (1)

where yn is the nth single-look-complex (SLC) valuefrom a coregistered stack containing N images, n =0, 1, . . . , N − 1, γ (s) is the reflectivity profile along theelevation s, and ϕn is the following interferometric phaseterm [5]:

ϕn (s) = 2k (rn (s)− r0 (s))

≈ 2k

s2

2(r0 − b‖n

) − b⊥n s

r0 − b‖n

(2)

where k is the central wavenumber, and rn is the rangedistance from sensor n to scatterer at elevation s. In thiscontext, elevation refers to the distance along the per-pendicular to line-of-sight (PLOS) direction. The ref-erence acquisition in the interferometric stack is repre-sented with n = 0. b⊥n and b‖n represent the orthogonal

_____________________________________ Proc. ‘Fringe 2015 Workshop’, Frascati, Italy 23–27 March 2015 (ESA SP-731, May 2015)

Figure 1. Left: SAR average backscatter image of the observed area. The high-rise building suffering from layover is theTorre Agbar tower. The red line marks the extent of an echo whose tomograhic inversion is presented afterwards. Right:Google Earth view of the corresponding neighborhood. The yellow line marks the approximate on-ground projection ofthe slant-range vector.

and parallel baseline components between the sensor nand the reference image, respectively.

The interferometric phase in eq. (2) depends only on thesensor-to-target geometry, and assumes a stationary scat-terer. The scatterer may, however, be subject to displace-ment over time, which would incur an additional phasevariation. Assuming a linear deformation model overtime, the extended phase model yields:

ϕn (s, ν) = 2k [4rn (s) + νtn] (3)

where ν is then the average deformation velocity. TheSLC value of the nth sensor can now be written as:

yn =

∫∫4s,4ν

γ (s, ν) exp [−jϕn (s, ν)] dsdν (4)

This tomographic model is generally known as differen-tial tomography [14, 15, 16].

As reported in different PSI studies (such as [17][18]),scatterers may also be subject to an additional phase vari-ation due to thermal expansion of buildings. In this case,the model can be further extended to:

ϕn (s, ν, κ) = 2k

[4rn (s) + νtn +

1

2kκτn

](5)

where τn is the local temperature corresponding to thetime of the nth image acquisition, and κ represents thephase-to-temperature sensitivity. A more general tomo-graphic model can now be concisely written as:

yn =

∫4p

γ (p) exp [−jϕn (p)] dp (6)

where γ (p) and p = [s, ν, κ] are the unknown scattererreflectivity and parameter vector, respectively. Variousinversion methods have been proposed (such as [19, 12, 4,3]) for estimating γ (p) and p. In this work, we performsingle-look conventional beamforming (which is used as

the objective function for the maximisation applied forthe retrieval of the unknown parameters). The estimatedreflectivity is given by,

γ (p) = aH (p)y (7)

where y is the column vector containing the SLC values,and a is the steering vector:

a (p) =[1 e−jϕ1(p) . . . e−jϕN−1(p)

]T(8)

The unknown parameter vector is estimated using the fol-lowing maximization:

p = argmaxp

(γ (p)

‖a (p) ‖ ‖y‖

)(9)

In practice, the SLC vector y generally suffers fromnoise, especially in areas of low-backscatter or shadowregions. The noise component may lead to poor tomo-graphic inversion. A given resolution cell may not evencontain a temporally coherent scatterer. Ignoring anyphase miscalibration, we formulate the detection problemas a decision between two hypotheses, H0 and H1.

H0 : y = w

H1 : y = γ (p1)a (p1) +w(10)

where w represents the noise term, generally modelledas an additive N-dimensional circular Gaussian randomvector. Using a threshold T , we use the Generalized Like-hood Ratio Test (GLRT) [20][6] for this detection prob-lem, as follows:

argmaxp

(γ (p)

‖a (p) ‖ ‖y‖

)H0

≶H1

T (11)

It can be noted here that equations 9 and 11 require max-imisation of the same objective function. Therefore, onlya single maximisation needs to be carried out for eachresolution cell. A scatterer is considered ‘detected’ onlywhen the hypothesis H1 is accepted, i.e. when the max-imum value of the objective function exceeds the thresh-old. The elevation and deformation parameters for the

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Figure 2. Tomograms obtained with the maximization of the objective function based on tomographic inversion withbeamforming (see eq. 9). The elevation axis is perpendicular to line-of-sight (PLOS). Top: Only the sensor-to-targetgeometry dependent phase is modelled (P1). Middle: The phase model additionally provides for a linear deformationterm (P2). Bottom: The phase model is further extended to include a thermal expansion induced phase term (P3). Thecolor scale represents the reflectivity: γ(p)/‖a(p)‖‖y‖.

Elevation (m)

-50 0 50 100 150 200 250 300

Refl

ecit

ivit

y

0.1

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Figure 3. The estimated elevation profiles, correspondingto each phase model (P1, P2, and P3), for the transectshown in white dashed line in Fig. 2.

detected scatterer (DS) are simultaneously estimated (asthe elements of the parameter vector corresponding to themaximum of the objective function).

The detection threshold impacts the probabilities of de-tection and false alarm. It is not within the scope of thispaper to discuss the choice of the threshold; interestedreaders are referred to [20] for further details and a com-parison with other detection schemes.

3. PHASE CALIBRATION

The interferometric data stack needs to be precisely phasecalibrated. Atmospheric phase screen (APS) has to be es-timated and compensated for each layer in the stack priorto tomographic inversion. An accurate estimation of theAPS is restricted by the presence of various sources ofphase noise, such as temporal and geometric decorrela-tion, orbital errors, etc. This preprocessing step entailsa preliminary PSI analysis. In our work, we use the In-terferometric Point Target Analysis (IPTA) [2] to obtainan initial PSI solution. A set of PS candidates is selectedbased on their low spectral diversity and high temporalstability of the backscatter. The orbital and topographicphases are simulated and subtracted from the complex-valued point interferograms. SRTM DEM is used forthe simulation of topography, as an estimate of the initialheights (although it is not necessary in principle). Thepoint differential interferograms are analysed next. Theatmospheric phase exhibits low-frequency behaviour inthe spatial domain, but high-frequency in temporal do-main (as the acquisitions are repeat-pass). Once an ac-ceptable PSI solution is obtained, the low-frequency spa-tial behaviour of the atmospheric phase allows extrapo-lation of the point-wise estimations to the surroundingnon-PS as well. Further details on the IPTA framework

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ν(m

m/yr)

-6

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-2

0

2

4

6Average deformation velocity

Tomo-DS

IPTA-PS

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K)

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)‖a(p

)‖‖y‖

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1Reflectivity (normalized) at the peak location

Tomo-DS

Figure 4. A comparison between the deformation parameters estimated using two different approaches: 1) an iterativePSI approach (IPTA), and 2) SAR tomography. In both cases, we have used the extended phase model (P3) i.e. modellingscatterer elevation, deformation and thermal expansion induced phase variation. PSI estimates are obtained iterativelyusing the IPTA framework. For the case of tomographic inversions, the estimates are obtained simultaneously with themaximisation of the beamforming function (eq. 9). Top: The estimated deformation velocity. Middle: The estimatedphase-to-temperature sensitivity. Bottom: The reflectivity at the peak location. A threshold is set at 0.65 for the detectionof a scatterer in each resolution cell.

are referred to [2, 21, 22].

4. DATA STACK

The interferometric data stack used in this work com-prises of 50 repeat-pass TerraSAR-X stripmap acqui-sitions. The images were acquired over the city ofBarcelona over a time span of approximately 5 years. Thetotal orthogonal baseline is 503.2 m. The distribution ofboth the temporal and spatial baselines are highly non-uniform.

5. RESULTS

Fig. 1 shows the Torre Agbar tower; the layover cast bythe tower is clearly visible in the SAR image. The tomo-grams in Fig. 2 show the focusing performance obtainedfor the three phase models (P1: elevation only, P2: eleva-tion and linear deformation, P3: elevation, linear defor-mation, and thermal expansion). The elevation profiles

for the transect marked in white dashed line in the tomo-grams are shown in Fig. 3. We obtained estimates ofthe elevation, deformation velocity and thermal expan-sion using the IPTA framework as well. A comparisonof the estimates of the deformation parameters obtainedwith IPTA for the PSs, and those obtained with tomo-graphic inversion on the DSs, is given in Fig. 4.

6. DISCUSSION

We performed inversions for each of the three tomo-graphic models presented in section 2: P1: elevationonly (p = [s]), P2: elevation and linear deformation(p = [s, ν]), P3: elevation, linear deformation, and ther-mal expansion (p = [s, ν, κ]). Fig. 2 shows the tomo-grams obtained individually with each model. The topand middle tomograms, corresponding to P1 and P2 re-spectively, clearly show that the upper part of the build-ing is not properly reconstructed. It implies that these twomodels (which consider only the sensor-to-target geom-etry and linear deformation induced phase changes) arenot well-suited for this building. The tomogram corre-sponding to P3, which additionally models a thermal ex-

pansion induced phase change, shows a marked improve-ment. The facade of the building, from the top to bottom,has been nicely focused in elevation. We closely observethe transect marked in white dashed line, and comparethe elevation profiles for each model in Fig. 3. A well-focused elevation profile is estimated only for P3.

With tomograhic inversion, the unknown parameter vec-tor is estimated at the peak of γ (p). We use the GLRT(eq. 11) for the detection of the scatterers. The detec-tion threshold can be empirically selected between 0 and1. We set the threshold at T = 0.65. A comparisonamong the deformation parameters’ estimates obtainedwith IPTA on the selected PSs, and with tomographic in-version on DSs, is presented in Fig. 4. The estimatesare mostly consistent. The PSI solution obtained with theIPTA framework involves an ‘iterative’ regression analy-sis for the thermal expansion term and the combined el-evation and deformation term, respectively; tomographicinversion, on the other hand, provides a ‘simultaneous’estimation. Moreover, there is a higher density of DSsthan PSs, i.e. higher deformation sampling. There are afew resolution cells getting detected as PS but not as DS,which raises a point of inquiry whether the threshold forthe detection should be relaxed.

7. CONCLUSION

This paper provides an analysis of three different phasemodels for tomographic inversion of an interferometricstack of TerraSAR-X data acquired over Barcelona. Theresults show that in case of high-rise buildings, it maybe necessary to model thermal expansion induced phasechanges. Insufficient phase modelling leads to improperfocusing and hence missed detection. We have comparedthe velocity and elevation parameters estimated from botha tomographic model and an iteratively obtained PSI so-lution using an extended phase model. The results areconsistent. A detailed assessment of the detection ofdouble-scatterers using a more appropriate layover sce-nario, and simultaneous retrieval of their individual de-formation parameters, will be part of our future work.

ACKNOWLEDGMENTS

This research project has been funded by the Swiss SpaceOffice, State Secretariat for Education and Research ofthe Swiss Confederation (SER/SSO), under the MdP2012initiative. TerraSAR-X SAR data used in this project wasobtained courtesy of the German Aerospace Center DLRunder proposal MTH1717. SRTM is copyright USGS.

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