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A small-baseline approach for investigating deformations on full-resolution differential SAR interferograms

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A small-baseline approach for investigating deformations on full-resolution differential SAR interferograms
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  IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 42, NO. 7, JULY 2004 1377 A Small-Baseline Approach for InvestigatingDeformations on Full-ResolutionDifferential SAR Interferograms Ricardo Lanari  , Senior Member, IEEE  , Oscar Mora  , Member, IEEE  , Michele Manunta,Jordi J. Mallorquí   , Member, IEEE  , Paolo Berardino, and Eugenio Sansosti  , Senior Member, IEEE   Abstract— This paper presents a differential synthetic apertureradar (SAR) interferometry (DIFSAR) approach for investigatingdeformation phenomena on full-resolution DIFSAR interfer-ograms. In particular, our algorithm extends the capabilityof the small-baseline subset (SBAS) technique that relies onsmall-baseline DIFSAR interferograms only and is mainly focusedon investigating large-scale deformations with spatial resolutionsof about 100 100 m. The proposed technique is implemented byusing two different sets of data generated at low (multilook data)and full (single-look data) spatial resolution, respectively. Theformer is used to identify and estimate, via the conventional SBAStechnique, large spatial scale deformation patterns, topographicerrors in the available digital elevation model, and possibleatmospheric phase artifacts; the latter allows us to detect, onthe full-resolution residual phase components, structures highlycoherent over time (buildings, rocks, lava, structures, etc.), as wellas their height and displacements. In particular, the estimation of the temporal evolution of these local deformations is easily imple-mented by applying the singular value decomposition technique.The proposed algorithm has been tested with data acquired by theEuropean Remote Sensing satellites relative to the Campania area(Italy) and validated by using geodetic measurements.  Index Terms— Ground deformations, synthetic aperture radar(SAR), SAR interferometry. I. I NTRODUCTION D IFFERENTIAL synthetic aperture radar (SAR) inter-ferometry (DIFSAR) is a remote sensing technique thatallows the investigaton of earth surface deformations withcentimeter to millimeter accuracy, by exploiting the round-tripphase components of SAR images relative to an investigatedarea [1], [2]. Due to its capability to produce spatially densedeformation maps with no environmental impact on the in-vestigated areas, this technique is becoming very important in Manuscript received July 8, 2003; revised January 9, 2004. This work wassupported in part by The European Community on Provision 3.16 under theproject of the Regional Center of Competence “Analysis and Monitoring of theEnvironmental Risk,” in part by the Italian Space Agency (ASI), the (Italian)National Group of Volcanology (GNV), the European Space Agency (ESA),and in part by the Spanish MCYT and FEDER funds under Project TIC 2002-04451-C02-01, and the Generalitat de Catalunya.R. Lanari, M. Manunta, P. Berardino, and E. Sansosti are with Istituto peril Rilevamento Elettromagnetico dell’Ambiente (IREA), National ResearchCouncil of Italy (CNR), 80124 Naples, Italy (e-mail: lanari.r@irea.cnr.it;manunta.m@irea.cnr.it; berardino.p@irea.cnr.it; sansosti.e@irea.cnr.it).O. Mora is with Unitat de Teledetecció, Institut Cartogràfic de Catalunya,08038 Barcelona, Spain (e-mail: omora@icc.es).J. J. Mallorquí is with Universitat Politècnica de Catalunya (UPC), SignalTheory and Communication Department (TSC), 08034 Barcelona, Spain(e-mail: mallorqui@tsc.upc.es).Digital Object Identifier 10.1109/TGRS.2004.828196 civil protection scenarios. Moreover, the possibility to studythe temporal evolution of the detected displacements is a keyissue with important implications in the understanding of the dynamics of the deformation phenomena. An effectiveway to study this temporal behavior is the generation of deformation time-series; to do this, the information availablefrom each interferometric data pair must be properly relatedto those included in the other acquisitions via the generationof an appropriate sequence of DIFSAR interferograms. In thiscontext, several approaches, based on different interferometriccombinations of the available SAR data relative to an investi-gated area, have been already proposed [3]–[9]. Among theseprocedures, the one referred to as the small-baseline subset(SBAS) approach [5] implements an ad hoc combination of the generated DIFSAR interferograms based on the followingstrategy. The data pairs used to produce the interferogramsare characterized by a small spatial separation between theorbits (baseline), in order to limit spatial decorrelation effects.Moreover, the number of data acquisition used for the analysisis increased by properly  linking  independent SAR datasetseparated by large baselines; this task is achieved by searchingfor the solution with a minimum kinetic energy, which is easilycomputed via the singular value decomposition (SVD) method.The availability of both spatial and temporal information onthe processed data is used to identify and filter out atmosphericphaseartifacts;therefore,spatiallydensedeformationmapsand,at the same time, deformation time-series for each investigatedpixeloftheimagedscenecanbeproduced.TheSBAStechniquehas already been successfully applied to investigate volcanicand tectonic related deformations [10]–[12]; however, becauseit was srcinally designed to monitor deformations occurringat a relatively large spatial scale (pixel dimensions of the orderof 100 100 m are typical), it is not appropriate for analyzinglocal deformations that may affect, for example, single build-ings or structures. Accordingly, we present in this paper a newalgorithm that extends the monitoring capability of the SBAStechniquetolocalizedisplacementsbyinvestigatingfull-resolu-tionDIFSARinterferograms.Theproposedsolution,brieflyde-scribed in [13], still relies on small-baseline interferograms butis implemented by using two different dataset generated at low(multilook data) and full (single-look data) spatial resolution,respectively. The former is used to identify, via the SBAS ap-proach, large-scale deformation patterns, topographic errors intheavailabledigitalelevationmodel(DEM),andpossibleatmo-spheric phase artifacts; the latter is investigated after removingthe low-resolution signal components; indeed, structures highly 0196-2892/04$20.00 © 2004 IEEE  1378 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 42, NO. 7, JULY 2004 coherent over time (buildings, rocks, lava, structures, etc.) areidentified on the residual phase signals jointly with an estimateoftheirlocaltopographyandofthemeanvelocityoftheresidualdeformation. A final step, implemented via the SVD technique,leadstotheestimationofthetemporalevolutionofthenonlinearcomponents of the local displacement affecting these highly co-herent structures. The availability of both deformation and to-pography information, at the two different spatial scales, allowsus to exhaustively analyze the deformation behavior of the in-vestigated pixels and to correctly localize them in a geographic(or cartographic) reference system.We remark that the presented solution is easy to implementbecause it does not need any dedicated processing and can beused as a postprocessing step applied to a set of DIFSAR inter-ferograms generated via already available interferometric dataprocessing tools.The proposed approach has been tested with a SAR datasetrelative to the city of Naples, Italy, and surroundings, acquiredby the European Remote Sensing (ERS) satellites. A validationof the results, via a comparison with leveling and gloabal posi-tioning system (GPS) measurements, has been also carried out.II. DIFSAR D ATA  A NALYSIS  A. Lowpass Signals The presented approach relies on the availability of a set of SARimagesofthesameareaacquiredattheorderedtimes, from which a stack of single-look DIFSAR inter-ferograms is produced. We consider here only interferometricdata pairs with a small baseline, i.e., significantly smaller thanthe critical one [14].Let us now assume, similarly to [5], that the DIFSAR stack is composed of interferograms, with the following two indexvectors:(1)corresponding to the acquisition time-indexes associated withthe image pairs used for the interferograms generation; in par-ticular, we consider the master (IE) and slave (IS) images to bechronologically ordered, i.e., .Accordingly,thephaseexpressionforeachpixeloftheDIFSARinterferograms can be written as follows:(2)where and are the azimuth and range pixel coordinates,and represent the phase values forthe master and slave images, respectively, and .The first step of the procedure requires the evaluation of thespatially lowpass (LP) DIFSAR phase components, which mayinclude large spatial scale deformation patterns, topographic er-rors caused by inaccuracies in the considered DEM, and pos-sible contributions caused by atmospheric inhomogeneities be-tween the acquisitions (often referred to as atmospheric phaseartifacts). Because of the small-baseline characteristics of theinterferograms, a complex (spatial) multilook operation can beeasily applied to the DIFSAR data in order to get an estimate of the LP signal component whose expression, for the th inter-ferogram, is [5], [8](3)wherein and represent the LP componentsof the deformation signal and of the topographic errors, re-spectively, while the factoraccountsforpossibleatmosphericphaseartifactsandfor the noise contributions. Moreover, represents the trans-mitted signal wavelength, the perpendicular baselinecomponent, and the incidence angle. We further remark thatwe assume hereafter , beingthe investigated domain; therefore, it is natural to identifywith , as the LP deformationtime-series relevant to the pixel located at and computedwith respect to the reference acquisition time .Based on (3), the conventional SBAS approach can be ap-plied to single out, for each coherent pixel, the signal com-ponents and . Toachieve this task, possible atmospheric artifacts are identifiedand compensated for by applying the three-dimensional (space-time) filtering step described in [5], which is based on the anal-ysis shown in [3] and [15]; however, alternative filtering ap-proaches, such as the one discussed in [8] and [9], can be alsoincluded with no significant impact on the implementation of the processing chain.As a final remark, we underline that some concerns on thecorrectness of the solution provided by the SBAS technique [5]have been recently raised in [7]. We stress that these concernsare based on a single unrealistic example; therefore, we presentin the Appendix an error analysis based on a number of simu-lated experiments that demonstrate the effectiveness of the ap-proach in real scenarios.  B. Highpass Signals Let us now focus on the full-resolution DIFSAR data that areconsidered, in our approach, after the modulo- subtractionof the LP components; because of this phase removal step, theobtained residual phase pattern will be related to the highpass(HP) deformation and topographic phase signals, the formeralso referred in the following to as  residual deformations  (theHP contributions will be often referred in the following toas high-frequency or high-resolution signal components). Inparticular, the residual phase of each pixel within the thsingle-look interferogram can be expressed as follows:(4)wherein and represent the mean velocityand the nonlinear component of the residual displacement,  LANARI  et al. : INVESTIGATING DEFORMATIONS ON FULL-RESOLUTION DIFFERENTIAL SAR INTERFEROGRAMS 1379 respectively, the high-resolution topographic error,and the noise component.Some considerations on (4) are in order. First of all, we re-mark that the atmospheric phase artifacts are pertinent of theLP DIFSAR components only. This occurs because the LP fil-tering operation is carried out with a filter whose bandwidth ischosen, both in azimuth and range, significantly larger than thatoftheatmosphericphasesignal,whosespatialcorrelationlengthis typically of about 1 km [15]. Accordingly, the atmosphericphase artifacts do not affect the HP signal components.Moreover, we stress that only a wrapped measurement of thesignal [see(4)]isavailableaftertheabove-mentionedmodulo subtraction; accordingly, a signal decoupling into alinear and a nonlinear component has been considered in (4) inorder toimplement theresidual phase-unwrappingoperation. Inparticular, the following two-step unwrapping strategy is con-sidered; first, we estimate the terms and in(4) that maximize the temporal coherence factor(5)wherein represents the phase model assumed as(6)Note that the temporal coherence factor in (5) provides aquantitative measurement of the degree of similarity betweenthe HP deformation signal and the assumed model (6). Thesecond step consists (for pixels exhibiting a coherence valuelarger than a fixed threshold) of the determination of the non-linear deformation component in (4). To this end, weassumethat the deviationof the modelfrom thetrue HP compo-nent of the phase signal is within the interval. There-fore, we can obtain a relationship between the HP phase signaland the nonlinear component of the residual deformation bysimply subtracting, modulo- , the estimated model (6) fromthe signal in (4). This operation leads to the system (7), shownat the bottom of the page, where the symbol represents themodulo- operation. Clearly, the known term at the right-handside of (7) is an estimate of the unwrapped difference if thequoted hypothesis is verified.The components can be now achieved by invertingthe system (7) that, however, exhibits a smaller number of in-dependent equations than unknowns if more than one subset ispresent.Inthiscase,thesystemhasarankdeficiency;thus,eventheleastsquares(LS)solutionisnotunique,and additionalcon-straints are necessary. The use of the SVD method allows us tocompute, among all the LS solutions, the one with minimumlength (norm) [16]; in this case, the solution is robust with re-specttothenoiseeffectsandunwrappingerrorsandallowsustoeffectivelycombine the information available from the differentsubset. In analogy to [5], we rewrite the system (7) in terms of velocities, by replacing the unknowns with the com-ponents of the velocity vector in (8), shown at the bottom of thepage.Based on (8), we may now rewrite (7) as the system (9),shown at the bottom of the page, which can be solved via theSVD method to compute the velocity vector in (8). We remark that in this case the minimum norm constraint is relevant to thevector and allows us to avoid large discontinuitiesin the final solution, as discussed in [5]. Of course, in this caseanadditional,buttrivial,integrationoperation[see(9)]isneces-sary to recover from the computed signal....(7)(8)...(9)  1380 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 42, NO. 7, JULY 2004 Fig. 1. Block diagram of the implemented procedure.Fig. 2. Pictorial example of the lowpass/highpass DIFSAR signal decoupling. At this stage, the overall deformation signal can be finallycomputed by combining the linear and nonlinear HP displace-ments computed from the residual DIFSAR phase [see (4)] andthe large spatial scale displacements estimated from the mul-tilook signals [see (3)]; accordingly, the overall deformationsignal expression is represented by(10), while the estimated topographic contributioncan be equivalently recovered as(11)Few final remarks on the presented analysis are in order. Firstof all, we want to stress that the deformation signal decouplingintoalinearandanonlinearcomponent[see(4)]issimilartowhathasbeenimplementedinthepermanentscatterers(PS)approach[3],[4];however,wealsounderlinethat,unlikethePStechnique,thediscussedinversionprocedureisappliedtotheresidualphasesignal components only because an LP signal removal step,which includes the atmospheric phase components, has beenpreviously applied; for this reason the overall analysis is carriedout on the phase signal relevant to single pixels instead of thephase differences between neighboring pixels. In this context,the quasi-linear model assumption (6) is certainly meaningful.III. A LGORITHM  D ESCRIPTION The overall processing procedure is implemented accordingto the block diagram of Fig. 1, wherein the input data consistsofa stackof single-lookcomplexDIFSAR interferograms com-puted from small-baseline SAR data pairs. The starting pointof the procedure is represented by the DIFSAR signal decou-pling into LP and HP components. The former are obtainedby implementing a complex multilook operation, the latterby subtracting, modulo- the obtained LP signals from thehigh-resolution data; a pictorial example of the LP/HP signaldecoupling is shown in Fig. 2. We remark that the LP filteringstep is carried out via an average operation with a data window  LANARI  et al. : INVESTIGATING DEFORMATIONS ON FULL-RESOLUTION DIFFERENTIAL SAR INTERFEROGRAMS 1381 of length of about 100 m in both azimuth and range directions,thus certainly smaller than the spatial correlation of the atmo-spheric phase artifacts [15]. The LP data processing is finalizedby the application of the conventional SBAS technique [5] thatallows us to recover the deformation signal and the errors inthe available DEM and, at the same time, to detect and filterout possible atmospheric phase artifacts.Regarding the HP signal estimation, the data processing im-plementation follows the lines of the analysis presented in theprevious section. In particular, we first compute the high-reso-lution terms and in (6) via the maximiza-tion of the coherence factor ; then, on the pixels with acoherence value larger than a chosen threshold, we recover thenonlinear HP signal component via the SVD-based inversionof (9), followed by the integration of the estimatedvector[see(8)].Atthisprocessingstage,bothlow-andhigh-res-olution topography and deformation information are available;the former are essential to correctly geolocate the detected co-herent pixels, i.e., to estimate their positions in a selected ref-erence system; the latter allow us to fully analyze the observeddeformation behavior.As a final remark, we note that the considered processingstrategy requires the investigated areas to be coherent both atlow and high resolution. This may be not the case in presenceof isolated structures or for areas at the edge of low-reso-lution coherent zones, where no LP information is available.Accordingly, a further operation is required in order to detectand analyze these targets. In this case, pixels with a tem-poral coherence value significantly lower than the selectedthreshold, and located in incoherent zones of the multilook interferograms, are reconsidered. In particular, we investigatepixels with a temporal coherence value larger than 0.35 buthighly correlated with targets located in the surrounding areas,where the overall processing has been already successfullycarried out. In this case, the data processing is identical tothe one carried out in previous HP data processing step, withthe only difference that the residual phase of the investigatedpixel is computed by subtracting the HP and LP signal com-ponents relative to the adjacent coherent pixels detected inthe surrounding areas. Following this operation, not reportedin Fig. 1 for sake of simplicity, only those pixels with anachieved high temporal coherence value will be assumed reli-able and considered in the final output.IV. E XPERIMENTAL  R ESULTS The validation of the proposed approach has been carried outby processing a dataset of 55 ERS-1/ERS-2 images acquiredon descending orbits and spanning the time interval from June1992 to September 2001 (see Table I). Based on this dataset,138DIFSARinterferograms,withamaximumbaselineofabout130 m, have been computed. The investigated area is centeredon the city of Naples (see Fig. 3) and includes the Campi Fle-grei caldera (left) and the Somma-Vesuvius volcanic complex(right). In order to provide an overall picture of the detectedlarge-scale deformations, we present in Fig. 3 the false-colormap showing the cumulative deformation measured, for eachinvestigated pixel, in the considered time interval. Fig. 3 clearly TABLE IERS-1/2 D ATASET . D IFFERENT  S UBSETS  A RE H IGHLIGHTED IN THE  L AST  C OLUMN shows that a very significant deformation phenomenon is af-fecting the Campi Flegrei caldera area with displacements ex-ceeding, in some zones, 20 cm [11]; moreover, a deformation
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