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PhaseQualityOptimizationinPolarimetricDifferentialSARInterferometry

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1

Phase Quality Optimization in PolarimetricDifferential SAR Interferometry

Rubén Iglesias, Student Member, IEEE, Dani Monells, Student Member, IEEE, Xavier Fabregas, Member, IEEE,Jordi J. Mallorquí, Senior Member, IEEE, Albert Aguasca, Member, IEEE, and

Carlos López-Martínez, Senior Member, IEEE

Abstract—In this paper, a study of polarimetric optimiza-tion techniques in the frame of differential synthetic apertureradar (SAR) interferometry (DInSAR) is considered. Historically,DInSAR techniques have been limited to the single-polarimetriccase, mainly due to the unavailability of fully polarimetricdata. Lately, the launch of satellites with polarimetric capabil-ities, such as the Advanced Land Observing Satellite (ALOS),RADARSAT-2, or TerraSAR-X, allowed merging polarimetric andinterferometric techniques to improve the pixels’ phase qualityand, thus, the density and the reliability of the final DInSARresults. The relationship between the polarimetrically optimizedcoherence or amplitude dispersion maps and the final DInSARresults is carefully analyzed, using both orbital and ground-basedSAR fully polarimetric data. DInSAR processing using polarimet-ric optimization techniques in the pixel selection process is com-pared with the classical single-polarimetric approach, achievingup to a threefold increase of the number of pixel candidates inthe coherence case and up to a factor of seven in the amplitudedispersion case.

Index Terms—Amplitude dispersion optimization, coherenceoptimization, differential synthetic aperture radar (SAR) in-terferometry (DInSAR), polarimetric DInSAR (PolDInSAR),polarimetry.

I. INTRODUCTION

D IFFERENTIAL synthetic aperture radar (SAR) interfer-ometry (DInSAR) algorithms have been developed during

the last decade, showing their feasibility and usefulness for themonitoring of deformation episodes in wide areas with milli-metric precision. Due to decorrelation, not all the pixels withinthe area under study present enough phase quality to makethem suitable to the DInSAR processing. Two main factorsrestrict the performance of any advanced DInSAR processing:the number of reliable pixels within the monitored area andtheir phase quality. For these reasons, prior to the use of any

Manuscript received July 17, 2012; revised January 25, 2013; acceptedMay 31, 2013. This work was supported in part by the Safeland project fundedby the Commission of the European Communities (Grant 226479), by the BigRisk project (Contract BIA2008-06614), and by Project TEC2011-28201-C02-01 and Grant BES-2009-015990 associated to Project TEC2008-06764-C02-01, both funded by the Spanish Ministerio de Ciencia e Innovación (MICINN)and Fondo Europeo de Desarrollo Regional (FEDER) funds. The Radarsat-2images were provided by MacDonald, Dettwiler and Associates (MDA) in theframework of the scientific project SOAR-EU 6779.

The authors are with the Department of Signal Theory and Communications,Technical University of Catalonia, 08034 Barcelona, Spain (e-mail: ruben.iglesias@tsc.upc.edu; dmonells@tsc.upc.edu).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2013.2267095

DInSAR technique, an adequate pixel selection over the areaunder study is mandatory.

Persistent scatter interferometry (PSI) is a development fromthe conventional DInSAR, based on the study of pixels whichremain stable over a sequence of interferograms. Two maincriteria are available in the literature for the estimation ofthe pixels’ phase stability or, in other words, of the pixels’phase quality: the coherence stability [1], [2] and the ampli-tude dispersion [3]. The first approach assumes ergodicity andspatial homogeneity of the scattering process and evaluates theaccuracy of the interferometric phase through the coherenceestimator applied to each interferometric pair of the data set. Inthe second approach, the quality of the phase information alongthe whole stack of images is associated to the amplitude-baseddispersion index (DA). Essentially, the higher the interferomet-ric coherence or the lower the amplitude dispersion, the betterthe phase quality. Better phase qualities entail more reliabledeformation maps.

Owning to the lack of long-time polarimetric SAR (PolSAR)data, the development of DInSAR techniques has been tra-ditionally limited to the single-polarimetric case. Over thelast years, several polarimetric satellites have been launched,such as the Advanced Land Observing Satellite (ALOS),RADARSAT-2, or Terra-SAR-X, allowing the extension ofDInSAR techniques to the fully polarimetric case. So far, someworks on polarimetric optimization for DInSAR purposes havebeen already presented. This concept was first introduced in[4] and [5] for its application to zero-baseline ground-basedSAR (GB-SAR) data. The objective was to improve the numberof reliable pixel candidates during the pixel selection step,taking advantage of the polarimetric capabilities of data. In [4],the polarimetric optimization of the interferometric coherenceswas performed using a simple approach, based on selectingthe polarimetric channel with the highest temporal averagedcoherence value. For the first time, the concept of polarimetricDInSAR (PolDInSAR) was presented. In [5], more sophis-ticated optimization methods available in the literature wereapplied to simulated and real GB-SAR fully polarimetric data,using again the coherence estimator during the pixel selectionapproach. One year later, in [6]–[8], polarimetric spacebornedata were used for the first time in the framework of PSI ap-plications, using both the coherence stability and the amplitudedispersion criteria.

In this paper, a study of the different polarimetric opti-mization techniques, applied to the coherence stability andamplitude dispersion criteria, is presented. This study is carried

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2 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

out using both zero-baseline and multibaseline PolSAR data,highlighting for each case its main particularities. The objectiveis the exploitation of the available polarimetric optimizationmethods, in the framework of DInSAR applications, to improvethe density and also the quality of the deformation processretrieval.

The different approaches available in the literature, referredto in this paper as Best [4], [5], equal scattering mechanism(ESM) [9], and multibaseline ESM (ESM-MB) [10], are an-alyzed in terms of the pixels’ density and final DInSAR de-formation maps, using first the coherence stability criterion.Then, its application to the amplitude dispersion pixel selectioncriterion [6]–[8] is also analyzed when fully polarimetric dataare available. Finally, with the aim to overcome some of thelimitations of the existing methods, for instance, when polari-metric stationarity does not apply, the application of the methodreferred to as suboptimum scattering mechanism (SOM) [11]is presented for both the coherence stability and the amplitudedispersion criteria.

This paper is organized as follows. Section II presents a briefreview of the classical single-polarimetric DInSAR processing.In Section III, general concepts of PolSAR are introduced inorder to ease the comprehension of the further sections of thispaper. Section IV presents the formulation for the applicationof the different polarimetric optimization techniques in theDInSAR framework. In Section V, the joint treatment of severalpolarimetric channels within the same DInSAR processing ispresented. Section VI describes the test sites and the availablefully polarimetric data sets for the validation of the algorithmsdescribed. In Section VII, the deformation maps obtained usingthe polarimetric optimization techniques are presented. Finally,the main conclusions are put forward.

II. DInSAR PROCESSING

PSI processing is based on the retrieval of deformationepisodes, together with the topographic error and atmosphericphase screens in a multibaseline configuration, from a stackof multitemporal differential interferograms. The techniqueemployed in this work is the coherent pixel technique(CPT) [12], [13], developed in the Universitat Politècnica deCatalunya (UPC).

The reliability of the final PSI products is directly related tothe phase quality of the interferograms. Thus, a preselection ofpixel candidates is mandatory in order to avoid the inclusion ofnoisy data in the processing. The most common phase qualityestimators employed are the interferometric coherence [1], [2]and the amplitude dispersion [3].

The interferometric coherence is expressed as [14]

γ = |γ| · ejφ =E {S1S

∗2}√

E {|S1|2}E {|S2|2}(1)

where S1 and S2 are the complex pixels of each SAR imageforming the interferogram, |.| is the modulus operator, and E{.}stands for the expectation operator. The modulus of the com-plex coherence |γ| indicates the quality of the interferometricphase φ. In practice, under the assumption of ergodicity and

for stationary processes, the expectation operator is replaced bya spatial average, i.e., the maximum likelihood estimator [15].In order to have temporal sensitivity, usually, the temporarilyaveraged coherence, referred to in the following as mean coher-ence, is used. The pixel candidates will be those presenting amean coherence value above a given threshold. This approachis, in principle, more suited for distributed scatterers, but it alsoworks for deterministic ones.

A more suitable approach for deterministic scatterers, such asthose in urban areas, is the DA estimator that allows the selec-tion of the so-called permanent scatterers (PSs) [3]. PSs behaveas pointlike scatterers in the whole stack of images, and theyare, in theory, not affected by spatial decorrelation. These pixelsare characterized by their temporal amplitude dispersion DA

DA =σA

mA=

1

〈|s|〉

√√√√ 1

N

N∑i=1

(|Si| − 〈|s|〉)2 (2)

where

〈|s|〉 = 1

N

N∑i=1

|Si|. (3)

σA stands for the amplitude standard deviation, mA stands forthe mean amplitude of the pixel time series, N is the number ofacquisitions, and s = [S1, S2, . . . , SN ] is the vector containingthe complex reflectivity of each acquisition Si. In fact, thephase standard deviation is approximately proportional to theamplitude dispersion value for high values of signal-to-noiseratio (SNR) [3]. Therefore, the amplitude dispersion indexDA may be employed as an estimation of the phase stabilityfor scatterers with high values of SNR. The so-called PSsare selected by evaluating their DA, considering only thosepixels under a certain threshold, typically DA < 0.25. Noticethat the estimation relies on the SAR images themselves,not on the interferograms, which is different to the case ofthe interferometric coherence estimator. Hence, the temporaldependence is inherent in the DA estimator.

The next step in the CPT algorithm is based on performinga Delaunay triangulation [16] of the pixel candidates found. Itis used to work with phase increments between pixels, insteadof absolute phases. The objective of this approach is twofold.On the one hand, the atmospheric artifacts are minimized sincethey change smoothly in space. On the other hand, assuminga high density of pixel candidates, the phase increments willbe, in most cases, lower than π radians, and therefore, anunwrapping process may not be necessary. The interferometricphase increment of each arc of the triangulation is defined as

Δφ =4π

λTΔv +

4π

λ

B

R sin θΔε+Δφres (4)

where Δv and Δε are the linear deformation rate in the lineof sight and the vertical topographic error increment, λ isthe wavelength, T and B are the temporal and perpendicularspatial baselines, R is the sensor to the target distance, θ isthe incidence angle, and Δφres accounts for the atmospheric,nonlinear, and noise components of the phase.

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 3

In order to estimate the linear deformation rate and theresidual topographic components of the interferometric phase,a linear model including only these elements is defined foreach arc of the triangulation. Then, the model is adjusted tothe data through the minimization of a cost function, addressedas the model adjustment function (MAF) [13]. With gooddistributions of temporal and spatial baselines, the model canbe correctly adjusted, even in the case that some of the phaseincrements were wrapped.

Once the linear deformation rate and the topographic errorincrements are obtained, the MAF is evaluated as a measureof the quality of each arc. The low quality arcs are truncated,removing, at the same time, those pixels that remain isolated.Another iteration of the minimization process is then performedwith the surviving pixels. This process allows removing thosepixels that do not fit the linear model, despite that they havefulfilled the pixel selection thresholds. This is mainly causedby strong nonlinear deformations. Finally, the absolute valuesof linear deformation and topographic error for each pixel arecalculated through an integration process, using one or multipleseeds with known behavior as tie points [13], leading to the finaldeformation results.

III. POLSAR INTERFEROMETRY

A. Polarimetric Scattering Matrix and Basis Transformation

The scattering matrix Shv describes the scattering processof a target when it is illuminated by an electromagnetic wave.It is a complex matrix, which is defined for a given imaginggeometry and an illuminating frequency by [17]

Shv =

[Shh Shv

Shv Svv

](5)

considering a monostatic configuration under the backscatter-ing alignment assumption, where the transmitting and receivingantennas are placed at the same location. Spq refers to thecomplex SAR images obtained from the receiving and transmit-ting electromagnetic waves with the polarization states p andq, respectively. Usually, p, q = (h, v) indicates the orthogonalhorizontal and vertical polarization states.

With the knowledge of Shv in the linear polarization basis{h, v}, it is possible to obtain the scattering matrix in anyelliptical orthogonal basis {a, b}, Sab, using the followingunitary transformation [17], [18]:

Sab =

[Saa Sab

Sab Sbb

]= UT

2 ShvU2 (6)

where T refers to the vector transposition, and the transforma-tion matrix U2 can be expressed through the orientation andellipticity angles (ψ, χ) of the polarization ellipse by

U2=

[cosψ −sinψsinψ cosψ

][cosχ j sinχj sinχ cosχ

][e+jφ0 00 e−jφ0

]. (7)

φ0 refers to the absolute phase term, which is irrelevant from aninterferometric point of view and is normally set to φ0 = 0.

B. Vector Interferometry

PolSAR interferometry (PolInSAR) is based on obtainingfully polarimetric data sets from slightly different points ofview. In the monostatic case, the scattering vector ki, for eachresolution element of each PolSAR data set, is obtained as avectorization of Shv [19], [20]

ki =1√2[Shh,i + Svv,i, Shh,i − Svv,i, 2Shv,i]

T (8)

where i = (1, 2) indicates two PolSAR acquisitions obtainedat different times. From the entire possible basis, the Pauli isusually used because it allows a direct interpretation of data inphysical terms. Then, the so-called PolInSAR vector betweentwo PolSAR acquisitions is defined as follows [19], [20]:

k =[kT1 ,k

T2

]T. (9)

Notice that, in the case of pointlike scatterers, (9) corre-sponds to a deterministic vector. However, for distributed scat-terers, (9) behaves as a random vector due to the complexity ofthe scattering process. In this case, under the hypotheses of spa-tial homogeneity and ergodicity, the 6 × 6 PolInSAR coherencycomplex matrix T6 is defined to completely characterize thescatterer behavior [19], [20]

T6 = E{kkH} =

[T11 Ω12

ΩH12 T22

](10)

where H refers to the conjugate transpose, T11 and T22 cor-respond to the individual coherency matrices of each PolSARdata set, and Ω12 is the polarimetric interferometric coherencymatrix.

The interferometric coherence γ defined in the previous sec-tion can be generalized by taking into account its polarimetricdependence. The PolInSAR Pauli vector ki could be projectedonto an unitary vector to obtain a generic scattering coefficientSi = wH

i ki for i = 1, 2. Si is a complex value analogous toa new SAR image resolution element, obtained as a linearcombination of the elements of ki through the projection vectorwi. At this point, considering the interferogram formed bytwo different Si’s, the generalized polarimetric interferometriccoherence for different combinations of w1 and w2 can beobtained [19], [20]

γ(w1,w2) =wH

1 Ω12w2√wH

1 T11w1wH2 T22w2

. (11)

In PolDInSAR applications, w1 and w2 must be the samealong the whole stack of interferograms since the choice ofdifferent projection vectors between two acquisitions of theinterferogram may lead to an artificial change in the phasecenter of the scatterers. Under this restriction, (11) becomes

γ(w) =wHΩ12w√

wHT11wwHT22w. (12)

In the case of pointlike scatterers, the DA index relatedto phase accuracy was defined in (2). The generalized DA

4 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

index for each projection vector w is defined by replacing thescattering coefficient Si by wHki, yielding to [6]–[8]

DA(w)=σA

mA=

1

〈|wHk|〉

√√√√ 1

N

N∑i=1

(|wHki|−〈|wHk|〉)2 (13)

where

⟨|wHk|

⟩=

1

N

N∑i=1

|wHki|. (14)

Notice how the projection vector w must be preserved againalong the whole data set to avoid changes in the phase centers.

IV. POLARIMETRIC OPTIMIZATION

A. Coherence Stability Optimization

The objective of this section is to explore the application ofthe different polarimetric optimization methods available in theliterature to the coherence estimator. The aim is to enhance theinterferograms’ phase quality, using the available polarimetricinformation in PolSAR data.

In this framework, two different configurations, dependingon how the data are acquired, must be taken into account.

1) The zero-baseline configuration, such as in GB-SAR sen-sors, refers to the absence of a spatial baseline betweenthe different temporal acquisitions of the sensor. In thiscase, all the images are acquired with exactly the samepoint of view.

2) The multibaseline configuration, such as in spacebornesensors, refers to the presence of a spatial baseline be-tween different temporal acquisitions. In this case, thespatial baseline changes from acquisition to acquisitionsince the images are acquired with slightly differentpoints of view.

Hence, two different modi operandi should be considered inorder to correctly apply the polarimetric optimization methods.

1) In the zero-baseline case, owing to the lack of a topo-graphic component in the interferometric phase, a single-baseline optimization process can be performed for eachinterferogram independently. In this case, the projectionvectors can be optimized independently at the interfero-gram level with no risk of adding undesired phase termsdue to changes in the phase centers within the same pixel.Notice that the restriction seen in the previous section ofhaving identical projection vectors w1 and w2 for the twoimages of the interferogram is still mandatory.

2) In the multibaseline case, a topographic component in thedifferential phase of the interferograms appears. Selectingdifferent projection vectors for each interferogram or, inother words, optimizing them independently as in thezero-baseline configuration case would lead to changes inthe phase centers within the same pixel, corrupting the re-trieved deformation maps. Therefore, in the multibaselineconfiguration, the projection vector needs to be the samealong the whole stack of interferograms. In this case, the

single-baseline optimization methods need to be extendedto the multitemporal case.

For simplicity, the algorithms explained in this section areaddressed first to the single-baseline case, which can be appliedto zero-baseline configuration sensors, such as GB-SAR, andthen, they are extended to the multibaseline case, which can beapplied to spaceborne sensors.

1) Best: The first approach to improve the quality of thedifferential phase consists of selecting the polarimetric channelproviding the highest value of coherence for each interfero-gram. This method is referred to as Best. For this case, themodulus of the optimized coherence is given for each pixel by

|γBest| = max {|γhh|, |γhv|, |γvv|} (15)

and the optimized interferometric phase will be the phase of thatselected channel providing the highest coherence. In fact, thischoice corresponds to select the channel that is less affected bydecorrelation factors for each pair of images, and it is translatedinto a significant improvement of the coherence and, thus, of thenumber of pixel candidates in the later pixel selection step.

For the multibaseline case, the method is extended selectingthe polarimetric channel providing, in this case, the highesttemporally averaged mean coherence. This method will bereferred to in the following as Best-MB.

Despite producing a significant improvement in the finalDInSAR results, as we will see later, the so-called Best ap-proach does not completely exploit the potential of polarimetry.The following methods attempt to use PolSAR data in a moreefficient way.

2) ESM: The most common optimization strategy that canbe found in the literature is based on finding the projectionvector w that optimizes the generalized coherence defined in(12). Since this approach forces both projection vectors to beequal, it is referred to as ESM. There are different methods toobtain the optimum projection vector.

The simplest approach is based on the parameterization ofthe unitary projection vector w, in order to obtain all thepossible values of the generalized coherence [6]–[8].To ensurethe unitarity of the projection vector, the parameterization,presented in [20], can be used

w =

⎡⎣ cosαsinα cosβejδ

sinα sinβejγ

⎤⎦⎧⎪⎨⎪⎩

0 ≤ α ≤ π2

0 ≤ β ≤ π0 ≤ δ ≤ π−π ≤ γ < π.

(16)

In this case, the optimum projection vector will be the oneproviding the maximum coherence. The main drawback ofsolving the optimization problem by brute force methods is thehigh computational cost. Using a fine sampling of 1◦ to exploreall the space of possible w’s, ∼1010 operations per pixel arerequired. It is equivalent to spending 2 s per pixel using a PCwith a 3.16-GHz Intel Dual-Core CPU and 3.25 GB of RAM,running under Windows.

To overcome this time limitation, two efficient approachescan be found in the literature [9], [21]. The method presentedin [9] is the most commonly used one in this framework. Thisapproach uses an iterative solution based on the numerical

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 5

radius [22], assuming polarimetric stationarity or, in otherwords, that the two coherency matrices T11 and T22 are verysimilar. Under this condition, the estimated complex differentialcoherence is approximated by

γ(w) =wHΩ12w

wHTw(17)

where

T =T11 +T22

2. (18)

It is always accomplished that |γ| ≤ |γ|, while the samephase is preserved if the condition is fulfilled. With this iterativesolution, the computational cost can be reduced drastically upto three orders of magnitude. For this reason, this solution isconsidered in this paper to perform the ESM approach.

Despite these advantages, some restrictions must be com-mented since not all the pixels of the interferogram will besuited to be optimized for PolDInSAR applications. This al-gorithm is only valid under the assumption of polarimetricstationarity. When this hypothesis does not apply, the algorithmdoes not reach the maximum, and in addition, the optimizeddifferential phase may be affected by this difference of po-larimetric behavior. Hence, when polarimetric stationarity doesnot apply, the optimization process may have no sense. Thesepixels, where the condition is not fulfilled, will be referred toin the following as outliers of the polarimetric optimizationprocess. Despite this, when this algorithm is applied to mul-titemporal series in the framework of DInSAR applications,the lack of polarimetric stationarity will be normally reflectedin high temporal decorrelation phenomena, degrading thus thetemporally averaged mean coherence values of the outliers. Asa consequence, these pixels will generally not be selected forthe later DInSAR processing.

Once the optimum projection vector wopt,ESM is found,the coherence can be directly obtained through (12), and theinterferometric phase is given by

φESM = arg(wH

opt,ESMΩ12wopt,ESM

)(19)

where arg(.) refers to the argument of a complex.Notice how, under the multibaseline configuration, the use of

the same projection w vector in the whole temporal stack ofacquisitions is mandatory. Hence, an independent optimizationprocess for each interferogram, as seen in the zero-baselinecase, is no longer possible. In this case, the use of the methodpresented by Neumann et al. in [10], referred to in this paperas ESM-MB, is proposed. This method is an extension of theESM method proposed by Colin et al. in [9], which aims tooptimize the temporally averaged mean coherence instead ofthe coherence of each interferogram separately. The polarimet-ric stationarity hypothesis is assumed for all the acquisitionsjointly, so (18) is extended to the temporal averaging of all thecoherency matrices.

3) SOM: To avoid outliers in the ESM polarimetric opti-mization process described earlier, when polarimetric station-ary does not apply, the method described in [11] is proposed.As in the ESM case, it preserves the polarimetric signature

between the acquisitions that forms an interferogram, but itsolves the coherence optimization problem in a way closer to aphysical interpretation. The algorithm is based on sweeping allthe possible combinations of orientation and ellipticity angles(ψ, χ) at the scattering matrix level. If the original scatteringmatrix Shv is expressed in the linear polarization basis {h, v},which corresponds to ψ = 0 and χ = 0, it is possible to obtainthe scattering matrix in a new elliptical orthogonal basis Sab

through the unitary matrix transformation presented in (6). Allthe (ψ, χ) space is then explored in order to find the polarizationbasis transformation providing the highest coherence among allthe copolar γaa and cross-polar γab coherence values. Underthis approach, the polarimetric optimized absolute value of thecoherence is given by

|γSOM | = max(ψ,χ)

{|γaa(ψ, χ)| , |γab(ψ, χ)|} (20)

where γaa and γab can be expressed as

γaa =E{Saa,1Saa,2}√

E {|Saa,1|2}E {|Saa,2|2}

γab =E{Sab,1Sab,2}√

E {|Sab,1|2}E {|Sab,2|2}. (21)

Saa,i and Sab,i are the copolar and cross-polar channels in thenew (ψ, χ) polarization basis, for the first and the second imagei = 1, 2 of the interferogram, respectively. Consequently, theoptimized interferometric phase will be given by the argumentof the new channel providing the best value of coherence, eitherthe copolar arg(γaa) or the cross-polar arg(γab).

Notice that all the possible solutions generated by eachorientation and ellipticity angles (ψ, χ) are a subspace of theones in the ESM approach, and for this reason, this method isreferred as SOM. The main drawback of this technique is againits high computational cost since it is based on a numericalsolution that finds the optimum value of coherence by a bruteforce method. Using a 1◦ step in the (ψ, χ) sampling, ∼105operations are required per pixel, which is equivalent to 0.1 s.

With the objective to reduce the computational cost of theproposed algorithm, the shape of the coherence to optimize isexplored for different values of the orientation and the ellipticityangles. An interferogram obtained with the UPC’s GB-SAR inthe El Forn de Canillo campaign, presented in Section VI, hasbeen used to illustrate the process. Fig. 1 shows the modulusof the copolar coherence values |γaa(ψ, χ)| for all possibleorientation and ellipticity angles (ψ, χ) using four representa-tive pixels with different coherence values in the Best approach|γBest|. The cross-polar coherence functions |γab(ψ, χ)| showsimilar shapes, so only the copolar case is showed. Each pixelpresents a high dynamic range of coherences between thebest and the worst polarimetric basis transformation. At thesame time, the coherence to maximize is smooth enough toallow numerical methods based on the gradient computation toeasily converge to the maximum. For this reason, the conjugategradient method (CGM) [23] has been used to reduce thecomputational cost. Since this method finds the minimum ofa function, the coherence expression must be inverted, 1/|γ|.

6 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Fig. 1. Copolar coherence values as a function of (ψ, χ) for four representa-tive pixels, with different values of |γBest|. (a) |γBest| = 0.3. (b) |γBest| =0.5. (c) |γBest| = 0.7. (d) |γBest| = 0.9.

First, a coarse sampling (∼30◦) finds a point near the absolutemaximum of the coherence, and then, the CGM is applied toreach the optimum value with less function evaluations. Withthis approach, the number of operations has been reduced to∼102, three orders of magnitude less.

Finally, for the multibaseline case, which will be referredto in this paper as SOM-MB, the method is easily extended.It is based on sweeping all the possible combinations of ori-entation and ellipticity angles (ψ, χ), but now maintaining thesame combination along the whole set of images. The optimalpolarization basis transformation will be the one providing thehighest temporally averaged mean coherence. Once again, theapplication of the CGM largely reduces the computation time.

B. Amplitude Dispersion Optimization

In this section, the polarimetric optimization techniques seenfor the coherence case are applied to the DA estimator in theframe of PolDInSAR applications. Recent works have beendone in this context using the ESM method [6]–[8].

The objective now is to look for the best polarimetric channel(Best), the optimum scattering coefficient (ESM), or the appro-priate polarimetric basis transformation (SOM), applied alongthe whole PolSAR data set, providing the minimum DA. Since,for this case, the spatial baseline plays no role in the phasequality estimation, there are no differences in the formulationbetween working with zero-baseline or multibaseline data.

1) Best: The first way to improve the DA and, consequently,the quality of the differential phase consists of selecting theinterferometric phases of the polarimetric channel providingthe minimum DA along the PolSAR data set. This methodis referred to, as in the coherence case, as Best. The Bestoptimized amplitude dispersion is then given for each pixel by

DA,Best = min{DA,hh, DA,hv, DA,vv} (22)

and the interferometric phase is derived from the channelproviding the minimum DA value.

2) ESM: The ESM approach has been recently adapted in[6]–[8] in order to find the projection vector providing theoptimum value of DA. This approach consists of performinga search over the whole polarimetric space in order to obtainthe projection vector w that optimizes for each pixel the gen-eralized DA expression seen in (13). The optimization problemis solved parameterizing the projection vector w as describedin (16).

The problem is now reduced to look for the angles α, β, δ,and γ that minimize the generalized DA over the polarimetricspace of possible projection vectors w. Once the optimum pro-jection vector wopt,ESM is found, the optimized DA is directlygiven by (13) with the projection vector under consideration.The interferometric phase of a pixel could be expressed for eachpair of images i, j as follows:

φESM = arg{(

wHopt,ESMki

) (wH

opt,ESMkj

)∗}. (23)

As in the previous cases, the main drawback of this methodis its computational cost. Using a sampling step of 1◦ to exploreall the possible values of α, β, δ, and γ, ∼1010 operations perpixel are required. In this case, it is equivalent to 9.6 s, assuminga stack of 34 images. In order to optimize the process, a coarsesampling of 30◦ is done to roughly locate the position of theabsolute minimum, and then, the CGM is proposed to reach theoptimum value. The number of operations can be reduced to∼104 per pixel, six orders of magnitude less.

3) SOM: Despite the significant reduction in time with theuse of the CGM, the computational cost increases significantlywith the number of acquisitions and the extent of the area understudy, due to the large number of pixels when working at fullresolution. For this reason, the SOM approach, which requiresthe optimization of a lower number of variables, is adapted tothe polarimetric DA optimization process.

As in the coherence case, it consists of sweeping all thepossible orientation and ellipticity angles (ψ, χ) at the level ofthe scattering matrix S, to achieve a scattering matrix Sab inthe new polarization basis, through the unitary matrix transfor-mation seen in (6). All the space of possible (ψ, χ) is exploredin order to find the polarization basis transform providing theminimum DA value among all the copolar and cross-polar DA

values (DA,aa, DA,ab) as follows:

DA,SOM = min(ψ,χ)

{DA,aa(ψ, χ), DA,ab(ψ, χ)} . (24)

The shape of the function to optimize, the DA, is exploredfor all the possible values of (ψ, χ) using as an example theRADARSAT-2 Barcelona data set presented in Section VI.Fig. 2 shows the results for four representative pixels withdifferent copolar DA,aa values in the Best approach DA,Best.As in the coherence case, the function to minimize presents asmooth behavior, being suitable for the application of the CGM,both for the copolar and cross-polar cases. Once again, its uselargely reduces the processing time.

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 7

Fig. 2. Copolar amplitude dispersion values as a function of (ψ, χ) for fourrepresentative pixels with different values of DA,Best. (a) DA,Best = 0.3.(b) DA,Best = 0.25. (c) DA,Best = 0.2. (d) DA,Best = 0.15.

V. POLARIMETRIC DINSAR PROCESSING

In classical DInSAR, a single-polarimetric channel is consid-ered in the processing, or in other words, all selected pixels aredefined with respect to the same polarimetric configuration. Theprevious section has shown different techniques able to find anoptimal polarimetric state that maximizes the coherence, whenmultilooked data are used, or minimizes the DA, when workingat full resolution. For both cases, the phase quality of the pixelin the optimal polarimetric state is better than those of the orig-inal polarimetric channels, as measured by the estimators. Eachselected pixel of the stack of interferograms has an optimumpolarimetric state that can be completely different from thatof the neighbors. At the same time, for a pair of acquisitions,the original three interferograms, one per polarimetric channel,have been reduced to a single one through the proper combi-nation in the optimization process. As it has been indicated,independently of the considered method, the temporal polari-metric stationarity must be accomplished for all interferograms.This means that the scattering mechanism characterizing a pixelmust remain constant from the two acquisitions generating aninterferogram, for the zero-baseline case, or constant from thewhole set of interferograms, in the multibaseline case.

At this stage, the classical DInSAR processing is appliedto this new stack of optimized interferograms. Notice thatthere is no difference with respect to the single-polarimetriccase as explained in Section II. The relative interferometricphase between two neighboring pixels will thus present termsassociated to the deformation in the line of sight, to the verticaltopographic error, and, finally, to the noise due to atmosphericvariation and decorrelation sources. Regarding the target’s po-larimetric behavior, notice that the residue Δφres of the linearestimation process includes an absolute phase term Δφpol,associated to the polarimetric changes induced by both thetemporal and the spatial baselines. A scatterer can change itspolarimetric behavior along time basically due to changes onthe scatterer itself, a kind of temporal decorrelation, or due to its

TABLE IUPC GB-SAR PARAMETERS

angular response, a kind of geometric decorrelation. The formerappears in all the cases, and the latter appears only in the multi-baseline case. As a consequence, the phase center of the opti-mized channel may change from image to image, which, in fact,will be considered as an additional nonlinear deformation term.It is important to highlight that this problem already existed inthe single-polarimetric case; therefore, no special treatment isrequired when working with fully polarimetric data.

Finally, when working with polarimetric optimization tech-niques, particularly with those that minimize the DA, it isimportant to highlight the role of the discarding process ofthe CPT, detailed in Section II. Since the proposed algorithmsoptimize the DA values not only for the stable pointlike scat-terers but also for the clutter, some points with “artificially”improved values of DA could be erroneously selected. In thiscase, low values of the MAF may be associated to strongnonlinear deformations, as in the single-polarimetric case, andalso to erroneously polarimetric optimized clutter. Such pixelswill behave as noisy ones, and they will be discarded as theydo not adjust to the linear model. The number of rejected pixelsdepends strongly on the linearity of the deformation process, onthe scenario, urban or rural, and on the optimization techniqueused. Typically, the number of discarded pixels ranges betweenthe 1% and the 5%, depending on the cases discussed earlier.

VI. TEST SITES AND DATA SETS

A. GB-SAR Over Canillo

The Remote Sensing Laboratory, in collaboration with theDepartment of Geotechnical Engineering and Geosciences ofthe UPC, carried out a one-year measuring campaign, fromOctober 2010 to October 2011, in the landslide of El Forn deCanillo, in Andorra (located between Spain and France), usingthe UPC’s X-band polarimetric GB-SAR (RISKSAR) [24]. Atotal of ten daily averaged images have been collected with atemporal baseline of approximately one month.

Unlike most of the other GB-SAR systems available in theremote sensing community, which are based on a vector net-work analyzer for the linear stepped frequency sweeping of thetransmitted signal bandwidth, the continuous-wave frequency-modulated radar used by the the RISKSAR system is based ona digital-direct-synthesizer chip set that generates a high-ratestepped linear frequency-modulated continuous-wave signal[24], [25]. This type of solution allows performing PolSARmeasurements without increasing the temporal decorrelation

8 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Fig. 3. (a) Mean amplitude corresponding to the ten daily averaged GB-SAR acquisition campaigns. (b) Mean coherence histograms using the hh polarimetricchannel or Best, SOM, and ESM coherence stability optimization methods. Average interferometric mean coherence using (c) the hh polarimetric channel or(d) Best, (e) SOM, and (f) ESM coherence stability optimization methods.

effects during a single scan. The range resolution is 1.25 m, andas in all GB-SARs, the cross-range resolution is not constant,ranging from 0.75 m at near range up to 6 m at the far rangeof 1600 m. Table I describes the sensor setting parameters usedduring the campaign.

The general landslide of El Forn de Canillo is an ancientlandslide with a complex movement that took place in morethan one episode. Nowadays, it has some residual movementon the order of some millimeters per year. Some geologicalstudies show that local slides may be produced by situations likebig excavations, undermining by erosion, or important ascentsof the groundwater level in extraordinary periods of rainfall.In the northeast extreme of the landslide of El Forn Canillo,there is the secondary landslide of Cal Borró-Cal Ponet thatstill presents activity coinciding with episodes of strong rainsand big increases of the piezometric conditions. It can reachlinear velocities up to 2–3 cm per year [26].

El Forn de Canillo is a partially vegetated area, whichdecorrelates fast at the X-band, containing some bare surfacesand few man-made structures. The potential density of coherentscatterers or PSs is consequently low. The scene is a perfecttest bed to check the benefits of the polarimetric optimizationmethods presented in the previous section.

Prior to the optimization process, data must be correctlycalibrated using a corner reflector located in near range and astrong cross-polar urban scatterer [27], [28]. In addition, theatmospheric artifacts must be correctly compensated [29], [30]before starting the DInSAR processing.

B. RADARSAT-2 Over Barcelona

The orbital PolSAR data set used in this study consists of34 Fine Quad-Pol RADARSAT-2 acquisitions, from January2010 to May 2012, over the metropolitan area of Barcelona,

northeastern Spain. This SAR sensor works at the C-band, witha resolution of 5 m in both range and azimuth directions and arevisit time of 24 days.

Barcelona is affected by the construction of new under-ground infrastructures. For instance, the tunnel that will connectBarcelona and France with high-speed trains passes very closeto the Sagrada Familia cathedral. Also, a new undergroundline, that will connect the city with the airport, generatessubsidence in different urban areas. Several hazards have beenrelated to these activities, such as the collapse of a block in theEl Carmel neighborhood in 2005 or damages on a building inthe south of the city. Therefore, there is a clear need of largescale monitoring of these works.

In this case, the monitored area is urbanized and character-ized by a high density of deterministic scatterers. Prior to thepolarimetric optimization process, some preprocessing must bedone to the data. This includes the generation of the differen-tial interferograms by removing the topographical componentwith an external digital elevation map and the generation ofthe polarimetric coherence matrices T and the polarimetricinterferometric coherence matrices Ω for each interferogram.In order to reduce the effects of the Doppler and geometricdecorrelation, the azimuth and the range spectral filtering [14]are applied to each component of the T and the Ω matrices.

VII. POLDINSAR RESULTS

This section shows the PolDInSAR results obtained using thedifferent polarization optimization techniques described before,for the two scenarios. Results are differentiated according tothe pixel selection criteria: coherence stability and amplitudedispersion.

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 9

TABLE IINUMBER OF RELIABLE PIXELS SELECTED. ZERO-BASELINE

APPROACH. COHERENCE STABILITY PIXEL SELECTION

A. Coherence Stability PolDInSAR Results

In this case, we will distinguish between the cases of zero-baseline data, using the GB-SAR data set, and the multibaselinedata, using RADARSAT-2 data set.

As mentioned in the previous section, the GB-SAR test site ismostly a vegetated area with few man-made structures along thehillside. Fig. 3(a) shows the mean amplitude of the whole dataset, in a range/cross-range representation. Fig. 3(b) shows themean coherence histogram for the hh polarimetric channel andthe mean coherence histograms after applying all the optimiza-tion methods. The comparison between them reveals that theESM and SOM techniques are producing the largest coherenceimprovement, with the ESM approach being slightly better.Fig. 3(c)–(f) shows the mean coherence maps with a multilookwindow of 9 × 9 pixels for each case, showing the rise ofcoherence owing to the polarimetric optimization. In this kindof vegetated areas, a 9 × 9 multilook window shows a goodtradeoff between the reliability of the coherence estimator andthe spatial resolution. Notice that there is a higher improvementin the coherence values over the bare surfaces and low vegetatedregions of the area under study. In the few existing urbanizedregions, which already present high coherences for the single-polarimetric case, the coherence values are slightly improved.Obviously, this overall improvement will translate into a higherdensity of useful pixels suited for DInSAR purposes. In or-der to illustrate this, the whole DInSAR processing has beencarried out for each case in order to obtain the linear velocitydeformation maps. Pixel candidates are those presenting a meancoherence above 0.7, which corresponds to a phase standarddeviation lower than 5◦ [31]. Table II summarizes the pixels’selection densities for each optimization method. Notice howthe number of pixel candidates in the ESM approach triples theones selected in the single-polarimetric case.

Fig. 4 shows the final deformation velocity maps for thedifferent polarimetric optimization methods geocoded over anortophoto of the area. Notice how the global behavior is similarfor all the methods, except for the increase of pixels’ densitythat shows the usefulness of the different polarimetric optimiza-tion approaches. As expected, the landslide still presents someresidual movement of the order of 1–1.5 cm per year. In thetop-left border of the main landslide, there is the secondarylandslide with a motion rate of 2–2.5 cm per year. Theseresults present a high agreement with the conclusions extractedfrom [26].

Fig. 4. Lineal velocity retrieved from the daily averaged acquisitions fromOctober 2010 to November 2011 GB-SAR campaigns, using (a) the hh po-larimetric channel or (b) Best, (c) SOM, and (d) ESM coherence stabilityoptimization approaches for the DInSAR processing.

Fig. 5. Mean amplitude corresponding to the 34 RDARARSAT-2 acquisitions.

The multibaseline coherence optimization techniques ex-plained in Section IV-A, Best-MB, ESM-MB, and SOM-MB,have been applied to the Barcelona RADARSAT-2 data set.The objective is to compare their performances with the re-sults obtained for the zero-baseline case. The processed areacorresponds to an urban region with some vegetated hills (seeFig. 5). For this case, a 9 × 5 (azimuth × range) multilook win-dow has been applied. Since we are more interested in the urbanarea of the image, the multilook window chosen is smaller thanthat in the previous case. The objective is to preserve betterthe spatial resolution and maximize the chances of detectingman-made structures. In addition, the multilook window is notsquare to take into account the different resolutions in groundrange and azimuth of RADARSAT-2 data.

Fig. 6(a) shows the histograms of the mean coherence forthe different optimization methods, and Fig. 6(b) focuses on

10 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Fig. 6. (a) Mean coherence histograms using the hh polarimetric channelor the Best-MB, SOM-MB, and ESM-MB coherence stability optimizationmethods. (b) Detail of the coherence values from 0.4 to 1.

TABLE IIINUMBER OF RELIABLE PIXELS SELECTED. MULTIBASELINE

APPROACH. COHERENCE STABILITY PIXEL SELECTION

the higher coherence values, where the threshold for pixelselection shall be established. Peaks around 0.25 coherencevalues belong to pixels located in rural and sea areas severelyaffected by decorrelation. On the contrary, small peaks towardthe higher coherences belong to pixels located in urban areas.

Notice how, in the rural regions, the multibaseline optimiza-tion methods produce a lower improvement on the coherencehistograms than in the zero-baseline ones. This behavior canbe justified by the restriction of using an identical projectionvector for all images or, in other words, that polarimetricstationarity is assumed along the whole temporal span. Forthe zero-baseline case, this restriction was forced only at theinterferogram level, performing a single-baseline optimization.As the number of acquisitions increases, it is more likely tofind polarimetric instabilities induced by temporal, geometric,and volumetric decorrelation. In addition, the ensemble ofdifferent polarimetric mechanisms which may be mixed withinthe multilooked pixels makes the polarimetric optimization lesseffective. Despite this, in urban areas, which are, in general,more stable in time than the rural ones, a similar improvementas in the zero-baseline case can be observed.

A selection of pixel candidates considering an optimizedmean coherence threshold of 0.75 has been performed, whichcorresponds to the same phase standard deviation of 5◦ [31]used in the GB-SAR case, for the new multilook used. Asit was expected, the selected pixels are mainly located inthe urban areas. Table III shows the pixel density achievedfor each method. In this case, the pixels’ density increaseis slightly lower than that in the zero-baseline approach,reaching an increase of 2.7 factor compared with the single-polarimetric case.

Fig. 7. Lineal velocity retrieved from the 34 RADARSAT-2 acquisitions overBarcelona, from January 2010 to May 2012, using (a) the hh polarimetricchannel or (b) Best-MB, (c) SOM-MB, and (d) ESM-MB mean coherenceoptimization approaches for the DInSAR processing.

Fig. 7 shows the deformation maps obtained using the hhpolarimetric channel data and the ones obtained with the differ-ent polarimetric optimization methods. The overall deformationpatterns are similar in all cases, and the only difference is foundin pixel densities shown in Table III. Different deformationbowls can be observed, with the most severe ones in the airportand harbor areas. Patterns of weaker deformations are observedin the city. An interesting case is located in the northeast partof the image, which follows a track of a metro line underconstruction. In fact, the affected area is quite narrow, whichcan make its detection difficult when the density of pixels is low.The increase of density provided by the polarimetric optimiza-tion methods contributes significantly to increase the precisionon determining the extension of the deformation bowl. Theamplitude dispersion results presented in the following sectionwill be focused on this particular area.

B. Amplitude Dispersion PolDInSAR Results

Since the reduced number of acquisitions for the GB-SARdata set prevents the application of the DA estimator [3], theresults in this section focus on the Barcelona RADARSAT-2data set.

Fig. 8(a) shows the mean amplitude of all the acquisitionsprocessed. This area corresponds to the northeast part of thecity, as commented in the previous section. Fig. 8(b) shows thehistograms of the DA for each method used. Fig. 8(c)–(f) showsthe DA maps for each polarimetric optimization method. Noticehow it is easy to distinguish between the urban areas and thevegetated ones from the values of the distribution. Looking atthe details, the streets can be perfectly seen. As expected, theESM produces the best results.

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 11

Fig. 8. (a) Mean amplitude detail corresponding to the 34 RADARSAT-2 acquisitions. (b) Amplitude dispersion histograms using the hh polarimetric channelor the Best, SOM, and ESM amplitude-based polarimetric optimization methods. Amplitude dispersion map using (c) the hh polarimetric channel or (d) Best,(e) SOM, and (f) ESM polarimetric amplitude-based optimization approaches.

TABLE IVNUMBER OF RELIABLE PIXELS SELECTED.AMPLITUDE DISPERSION PIXEL SELECTION

The DInSAR processing has been applied for all cases inorder to demonstrate the pixel’s density improvement achievedin the optimization process. A DA threshold of 0.25 has beenused for all cases, which corresponds to a phase standarddeviation of 15◦ [31]. Table IV summarizes the number of pixelcandidates selected for each approach.

As it can be seen, the differences among the different meth-ods are more substantial than for the coherence approach. Com-pared with the single-polarimetric channels, the Best methodprovides an increase in the selected pixels of roughly a factorof two. From Best to SOM, the number of selected pixels isalmost doubled again. Finally, ESM increases the number ofpixels by 80% with respect to SOM. This enrichment in pixels’density and quality in results clearly justifies the usefulness ofPolSAR data in the DInSAR framework.

Finally, the linear deformation maps for each approach areshown in Fig. 9(a)–(d), in order to demonstrate how the phaseinformation of the optimized pixels is reliable. Notice how the

overall deformation patterns are identical in the four cases whilethe pixels’ density is largely increased using the polarimetricoptimization techniques, as it has been commented before.This improvement in terms of pixels’ density helps to betterdetermine and characterize the extension of the areas affectedby subsidence. The different deformation bowls caused by theunderground tunnel construction (represented with an orangeline in Fig. 9) can be perfectly identified. Notice how theyperfectly match the path followed by the tunnel and the locationof the new station constructed, which corresponds to the largestdeformation bowl in the center of the images.

VIII. CONCLUSION

In this paper, general polarimetric optimization methods forits application to DInSAR processing have been evaluated.The objective has been to enhance the phase quality of theinterferograms to be processed by the DInSAR algorithms withthe proper combination of the available polarimetric channels.The optimized stack of interferograms allows the selection ofa larger number of pixels. Hence, the overall phase quality ofthe pixels is improved, and as a consequence, denser and moreprecise deformation maps are obtained.

The different polarimetric optimization methods available inthe literature have been tested and adapted to the particularcharacteristics of the data, zero baseline or multibaseline, andthe pixel selection criteria, coherence stability or amplitudedispersion. The simplest method described in this paper hasbeen the so-called Best. In this approach, for each pixel ofthe image, the polarimetric channel with the best value inthe estimator is selected. Despite the significant improvement

12 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Fig. 9. Lineal velocity retrieved from the RADARSAT-2 PolSAR acquisitions over Barcelona, from January 2010 to May 2012, using (a) the hh polarimetricchannel or (b) Best, (c) SOM, and (d) ESM amplitude-based optimization approaches for the DInSAR processing. The orange line indicates the undergroundtunnel construction.

achieved, this method does not completely exploit the potentialsof polarimetry.

More advanced methods have been studied. On the one hand,the ESM approach is able to reach the best optimized valuessince it explores the complete space of possible solutions, butwith a high computational cost. On the other hand, the SOMtechnique requires the optimization of a lower number of vari-ables, which makes the optimization less costly, but the space ofsolutions is a subspace of the ESM approach. As a consequence,SOM performance is usually lower compared with that ofESM in terms of phase improvement and, consequently, in thenumber of pixels selected.

On the one hand, working with the coherence estimator,the optimum projection vector may be optimized at the in-terferogram level for the zero-baseline case. On the contrary,for the multibaseline case, the optimum projection vector isforced to be identical for all interferograms. On the other hand,when working at full resolution with the amplitude dispersionapproach, the projection vector is forced to be the same in thewhole stack of SAR images, regardless of the spatial baselineconfiguration.

Generally, the main drawback of using ESM and SOM istheir computational cost. In this sense, this limitation has beenlargely improved with the combination of a coarse search of theglobal minimum and the CGM algorithm. The optimum projec-tion vectors have been found much faster with identical results.

Once the optimized interferograms are obtained, the DInSARprocessing is straightforward as there are no differences withrespect to the single-polarimetric case.

The different methods have been tested with two differentdata sets. The GB-SAR campaign in El Forn de Canillo hasprovided the zero-baseline data set while the RADARSAT ac-quisitions over Barcelona have provided the multibaseline one.

For all cases, results show a large improvement in the num-ber of pixel candidates selected with respect to the single-polarimetric case. Depending on the selection criteria, thespatial baseline configuration, and the scenario, some ap-proaches perform better than the others. The coherence sta-bility approach shows a better performance with zero-baselinedata since the optimization process can be applied to eachinterferogram separately. On the contrary, the multibaselinerestriction, which forces a single mechanism for the wholedata set, reduces the chances of improvement. In the amplitudedispersion approach, using orbital data over urban areas, theimprovement is even better, reaching an increase up to a factorof seven of the pixel candidates for the ESM approach, withrespect to the traditional single-polarimetric processing. For allscenarios, DInSAR results reveal deformations where expected.The differences between the deformation maps obtained withthe different polarimetric optimization techniques are onlyin the pixels’ density terms, but not on the deformation values,showing the goodness of the methods proposed.

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 13

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[30] X. Fabregas, R. Iglesias, and A. Aguasca, “A new approach for atmo-spheric phase screen compensation in ground-based SAR over areas withsteep topography,” in Proc. 9th EUSAR, Apr. 23–26, 2012, pp. 12–15.

[31] R. Touzi, A. Lopes, J. Bruniquel, and P. W. Vachon, “Coherence estima-tion for SAR imagery,” IEEE Trans. Geosci. Remote Sens., vol. 37, no. 1,pp. 135–149, Jan. 1999.

Rubén Iglesias (S’12) was born in Barcelona, Spain,in 1982. He received the B.Sc. degree in telecom-munication engineering from the Technical Univer-sity of Catalonia (UPC), Barcelona, in 2008, wherehe is currently working toward the Ph.D. degree,focused on the development of advanced differen-tial synthetic aperture radar (SAR) interferometry(DInSAR) and polarimetric DInSAR techniquesfor the detection, monitoring, and characterizationof slow-moving landslides with both orbital andground-based SAR (GB-SAR) data.

From June 2009 to June 2010, he was with the Active Remote Sensing Unitat the Institute of Geomatics, Barcelona, working in several projects relatedwith the application of DInSAR to terrain-deformation monitoring with orbitaland GB-SAR data. In 2010, he joined the Signal Theory and CommunicationsDepartment at UPC, working as a Research Assistant in the framework ofDInSAR applications.

Dani Monells (S’11) was born in Sant Joan de lesAbadesses, Spain, in 1981. He received the B.Sc.degree in telecommunication engineering from theTechnical University of Catalonia, Barcelona, Spain,in 2008, where he is currently working toward thePh.D. degree, focused on differential synthetic aper-ture radar (SAR) interferometry in orbital platforms,focusing on the exploitation of polarimetric SAR ac-quisitions, at the Signal Theory and CommunicationsDepartment (TSC).

From 2007, he has been working in severalprojects for the monitoring of terrain displacements and developing the TSCinterferometric chain and processor, in order to give support to the new-generation SAR satellites, including TerraSAR-X, Radarsat-2, Advanced LandObserving Satellite, and COnstellation of small Satellites for Mediterraneanbasin Observation.

14 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Xavier Fabregas (S’89–M’93) received the B.S.degree in physics from Barcelona University,Barcelona, Spain, in 1988 and the Ph.D. degree inapplied sciences from the Universitat Politecnica deCatalunya (UPC), Barcelona, in 1995.

In 1990, he joined the Photonic and Electromag-netic Engineering Group, Signal Theory and Com-munications Department, UPC. Since 1996, he hasbeen an Associate Professor with UPC. In 2001, hespent an eight-month sabbatical with the Microwavesand Radar Institute (HR) of the German Aerospace

Agency (DLR), Oberpfaffenhofen, Germany. He has published 26 internationaljournal papers and more than 106 conference proceedings and is the holder ofa patent. He is a reviewer in several international journals. His current researchinterests include polarimetric-retrieval algorithms, polarimetric calibration andspeckle models, ground-based synthetic aperture radar (SAR) sensors and theirapplications, and time series for multidimensional SAR data applications forurban and terrain deformation monitoring.

Jordi J. Mallorquí (S’93–M’96–SM’13) was bornin Tarragona, Spain, in 1966. He received the Inge-niero degree in telecommunications engineering andthe Doctor Ingeniero degree in telecommunicationsengineering for his research on microwave tomog-raphy for biomedical applications in the Departmentof Signal Theory and Communications from the Uni-versitat Politècnica de Catalunya (UPC), Barcelona,Spain, in 1990 and 1995, respectively.

Since 1993, he has been teaching at the Schoolof Telecommunications Engineering of Barcelona,

UPC, first as an Assistant Professor, later in 1997 as an Associate Professor,and since 2011 as a Full Professor. His teaching activity involves micro-waves, radionavigation systems, and remote sensing. He spent a sabbatical yearwith the Jet Propulsion Laboratory, Pasadena, CA, USA, in 1999, workingon interferometric airborne synthetic aperture radar (SAR) calibration algo-rithms. He is currently working on the application of SAR interferometry toterrain-deformation monitoring with orbital, airborne, and ground data; vesseldetection and classification from SAR images; and 3-D electromagnetic (EM)simulation of SAR systems. He is also collaborating in the design and construc-tion of a ground-based SAR interferometer for landslide control. Finally, he iscurrently developing the hardware and software of a bistatic opportunistic SARfor interferometric applications using European Remote Sensing, Environmen-tal Satellite, and TerraSAR-X as sensors of opportunity. He has published morethan 100 papers on microwave tomography, EM numerical simulation, SARprocessing, interferometry, and differential interferometry in refereed journalsand international symposia.

Albert Aguasca (S’90–M’94) was born in Barcelona,Spain, in 1964. He received the M.Sc. and Ph.D.degrees in telecommunication engineering fromthe Universitat Politècnica de Catalunya (UPC),Barcelona, in 1989 and 1993, respectively.

Since 1995, he has been an Associate Professorwith the School of Telecommunications Engineer-ing, UPC. His teaching activities involve RF andmicrowave circuits for communications and radio-navigation systems. His main research activitiesinvolve the design and development of synthetic

aperture radar (SAR) and microwave radiometer systems for unmanned aerialvehicle platforms. He also collaborates in the design and development of smartantennas and scavenging circuitry. He has published more than 40 papers onmicrowave SAR, radiometer systems, and microwave circuits.

Carlos López-Martínez (S’97–M’04–SM’11) re-ceived the M.Sc. degree in electrical engineering andthe Ph.D. degree from the Universitat Politècnicade Catalunya (UPC), Barcelona, Spain, in 1999 and2003, respectively.

From October 2000 to March 2002, he was withthe Frequency and Radar Systems Department (HR),German Aerospace Center (DLR), Oberpfaffenhofen,Germany. From June 2003 to December 2005, hewas with the Image and Remote Sensing Group—SAR Polarimetry Holography Interferometry Radar-

grammetry Team in the Institute of Electronics and Telecommunications ofRennes, Rennes, France. In January 2006, he joined the UPC as a Ramón-y-Cajal Researcher, where he is currently an Associate Professor in the areaof remote sensing and microwave technology. His research interests includesynthetic aperture radar (SAR) and multidimensional SAR, radar polarimetry,physical parameter inversion, digital signal processing, estimation theory, andharmonic analysis.

Dr. Lopez-Martinez is an Associate Editor of the IEEE JOURNAL OF

SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE

SENSING, and he served as a Guest Editor of the European Associationfor Signal Processing Journal on Advances in Signal Processing. He hasorganized different invited sessions in international conferences on radar andSAR polarimetry. He has presented advanced courses and seminars on radarpolarimetry to a wide range of organizations and events. He was the recipientof the Student Prize Paper Award at the European Conference on SyntheticAperture Radar (EUSAR) 2002 Conference and coauthored the paper awardedwith the First Place Student Paper Award at the EUSAR 2012 Conference.

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1

Phase Quality Optimization in PolarimetricDifferential SAR Interferometry

Rubén Iglesias, Student Member, IEEE, Dani Monells, Student Member, IEEE, Xavier Fabregas, Member, IEEE,Jordi J. Mallorquí, Senior Member, IEEE, Albert Aguasca, Member, IEEE, and

Carlos López-Martínez, Senior Member, IEEE

Abstract—In this paper, a study of polarimetric optimiza-tion techniques in the frame of differential synthetic apertureradar (SAR) interferometry (DInSAR) is considered. Historically,DInSAR techniques have been limited to the single-polarimetriccase, mainly due to the unavailability of fully polarimetricdata. Lately, the launch of satellites with polarimetric capabil-ities, such as the Advanced Land Observing Satellite (ALOS),RADARSAT-2, or TerraSAR-X, allowed merging polarimetric andinterferometric techniques to improve the pixels’ phase qualityand, thus, the density and the reliability of the final DInSARresults. The relationship between the polarimetrically optimizedcoherence or amplitude dispersion maps and the final DInSARresults is carefully analyzed, using both orbital and ground-basedSAR fully polarimetric data. DInSAR processing using polarimet-ric optimization techniques in the pixel selection process is com-pared with the classical single-polarimetric approach, achievingup to a threefold increase of the number of pixel candidates inthe coherence case and up to a factor of seven in the amplitudedispersion case.

Index Terms—Amplitude dispersion optimization, coherenceoptimization, differential synthetic aperture radar (SAR) in-terferometry (DInSAR), polarimetric DInSAR (PolDInSAR),polarimetry.

I. INTRODUCTION

D IFFERENTIAL synthetic aperture radar (SAR) interfer-ometry (DInSAR) algorithms have been developed during

the last decade, showing their feasibility and usefulness for themonitoring of deformation episodes in wide areas with milli-metric precision. Due to decorrelation, not all the pixels withinthe area under study present enough phase quality to makethem suitable to the DInSAR processing. Two main factorsrestrict the performance of any advanced DInSAR processing:the number of reliable pixels within the monitored area andtheir phase quality. For these reasons, prior to the use of any

Manuscript received July 17, 2012; revised January 25, 2013; acceptedMay 31, 2013. This work was supported in part by the Safeland project fundedby the Commission of the European Communities (Grant 226479), by the BigRisk project (Contract BIA2008-06614), and by Project TEC2011-28201-C02-01 and Grant BES-2009-015990 associated to Project TEC2008-06764-C02-01, both funded by the Spanish Ministerio de Ciencia e Innovación (MICINN)and Fondo Europeo de Desarrollo Regional (FEDER) funds. The Radarsat-2images were provided by MacDonald, Dettwiler and Associates (MDA) in theframework of the scientific project SOAR-EU 6779.

The authors are with the Department of Signal Theory and Communications,Technical University of Catalonia, 08034 Barcelona, Spain (e-mail: ruben.iglesias@tsc.upc.edu; dmonells@tsc.upc.edu).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2013.2267095

DInSAR technique, an adequate pixel selection over the areaunder study is mandatory.

Persistent scatter interferometry (PSI) is a development fromthe conventional DInSAR, based on the study of pixels whichremain stable over a sequence of interferograms. Two maincriteria are available in the literature for the estimation ofthe pixels’ phase stability or, in other words, of the pixels’phase quality: the coherence stability [1], [2] and the ampli-tude dispersion [3]. The first approach assumes ergodicity andspatial homogeneity of the scattering process and evaluates theaccuracy of the interferometric phase through the coherenceestimator applied to each interferometric pair of the data set. Inthe second approach, the quality of the phase information alongthe whole stack of images is associated to the amplitude-baseddispersion index (DA). Essentially, the higher the interferomet-ric coherence or the lower the amplitude dispersion, the betterthe phase quality. Better phase qualities entail more reliabledeformation maps.

Owning to the lack of long-time polarimetric SAR (PolSAR)data, the development of DInSAR techniques has been tra-ditionally limited to the single-polarimetric case. Over thelast years, several polarimetric satellites have been launched,such as the Advanced Land Observing Satellite (ALOS),RADARSAT-2, or Terra-SAR-X, allowing the extension ofDInSAR techniques to the fully polarimetric case. So far, someworks on polarimetric optimization for DInSAR purposes havebeen already presented. This concept was first introduced in[4] and [5] for its application to zero-baseline ground-basedSAR (GB-SAR) data. The objective was to improve the numberof reliable pixel candidates during the pixel selection step,taking advantage of the polarimetric capabilities of data. In [4],the polarimetric optimization of the interferometric coherenceswas performed using a simple approach, based on selectingthe polarimetric channel with the highest temporal averagedcoherence value. For the first time, the concept of polarimetricDInSAR (PolDInSAR) was presented. In [5], more sophis-ticated optimization methods available in the literature wereapplied to simulated and real GB-SAR fully polarimetric data,using again the coherence estimator during the pixel selectionapproach. One year later, in [6]–[8], polarimetric spacebornedata were used for the first time in the framework of PSI ap-plications, using both the coherence stability and the amplitudedispersion criteria.

In this paper, a study of the different polarimetric opti-mization techniques, applied to the coherence stability andamplitude dispersion criteria, is presented. This study is carried

0196-2892/$31.00 © 2013 IEEE

2 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

out using both zero-baseline and multibaseline PolSAR data,highlighting for each case its main particularities. The objectiveis the exploitation of the available polarimetric optimizationmethods, in the framework of DInSAR applications, to improvethe density and also the quality of the deformation processretrieval.

The different approaches available in the literature, referredto in this paper as Best [4], [5], equal scattering mechanism(ESM) [9], and multibaseline ESM (ESM-MB) [10], are an-alyzed in terms of the pixels’ density and final DInSAR de-formation maps, using first the coherence stability criterion.Then, its application to the amplitude dispersion pixel selectioncriterion [6]–[8] is also analyzed when fully polarimetric dataare available. Finally, with the aim to overcome some of thelimitations of the existing methods, for instance, when polari-metric stationarity does not apply, the application of the methodreferred to as suboptimum scattering mechanism (SOM) [11]is presented for both the coherence stability and the amplitudedispersion criteria.

This paper is organized as follows. Section II presents a briefreview of the classical single-polarimetric DInSAR processing.In Section III, general concepts of PolSAR are introduced inorder to ease the comprehension of the further sections of thispaper. Section IV presents the formulation for the applicationof the different polarimetric optimization techniques in theDInSAR framework. In Section V, the joint treatment of severalpolarimetric channels within the same DInSAR processing ispresented. Section VI describes the test sites and the availablefully polarimetric data sets for the validation of the algorithmsdescribed. In Section VII, the deformation maps obtained usingthe polarimetric optimization techniques are presented. Finally,the main conclusions are put forward.

II. DInSAR PROCESSING

PSI processing is based on the retrieval of deformationepisodes, together with the topographic error and atmosphericphase screens in a multibaseline configuration, from a stackof multitemporal differential interferograms. The techniqueemployed in this work is the coherent pixel technique(CPT) [12], [13], developed in the Universitat Politècnica deCatalunya (UPC).

The reliability of the final PSI products is directly related tothe phase quality of the interferograms. Thus, a preselection ofpixel candidates is mandatory in order to avoid the inclusion ofnoisy data in the processing. The most common phase qualityestimators employed are the interferometric coherence [1], [2]and the amplitude dispersion [3].

The interferometric coherence is expressed as [14]

γ = |γ| · ejφ =E {S1S

∗2}√

E {|S1|2}E {|S2|2}(1)

where S1 and S2 are the complex pixels of each SAR imageforming the interferogram, |.| is the modulus operator, and E{.}stands for the expectation operator. The modulus of the com-plex coherence |γ| indicates the quality of the interferometricphase φ. In practice, under the assumption of ergodicity and

for stationary processes, the expectation operator is replaced bya spatial average, i.e., the maximum likelihood estimator [15].In order to have temporal sensitivity, usually, the temporarilyaveraged coherence, referred to in the following as mean coher-ence, is used. The pixel candidates will be those presenting amean coherence value above a given threshold. This approachis, in principle, more suited for distributed scatterers, but it alsoworks for deterministic ones.

A more suitable approach for deterministic scatterers, such asthose in urban areas, is the DA estimator that allows the selec-tion of the so-called permanent scatterers (PSs) [3]. PSs behaveas pointlike scatterers in the whole stack of images, and theyare, in theory, not affected by spatial decorrelation. These pixelsare characterized by their temporal amplitude dispersion DA

DA =σA

mA=

1

〈|s|〉

√√√√ 1

N

N∑i=1

(|Si| − 〈|s|〉)2 (2)

where

〈|s|〉 = 1

N

N∑i=1

|Si|. (3)

σA stands for the amplitude standard deviation, mA stands forthe mean amplitude of the pixel time series, N is the number ofacquisitions, and s = [S1, S2, . . . , SN ] is the vector containingthe complex reflectivity of each acquisition Si. In fact, thephase standard deviation is approximately proportional to theamplitude dispersion value for high values of signal-to-noiseratio (SNR) [3]. Therefore, the amplitude dispersion indexDA may be employed as an estimation of the phase stabilityfor scatterers with high values of SNR. The so-called PSsare selected by evaluating their DA, considering only thosepixels under a certain threshold, typically DA < 0.25. Noticethat the estimation relies on the SAR images themselves,not on the interferograms, which is different to the case ofthe interferometric coherence estimator. Hence, the temporaldependence is inherent in the DA estimator.

The next step in the CPT algorithm is based on performinga Delaunay triangulation [16] of the pixel candidates found. Itis used to work with phase increments between pixels, insteadof absolute phases. The objective of this approach is twofold.On the one hand, the atmospheric artifacts are minimized sincethey change smoothly in space. On the other hand, assuminga high density of pixel candidates, the phase increments willbe, in most cases, lower than π radians, and therefore, anunwrapping process may not be necessary. The interferometricphase increment of each arc of the triangulation is defined as

Δφ =4π

λTΔv +

4π

λ

B

R sin θΔε+Δφres (4)

where Δv and Δε are the linear deformation rate in the lineof sight and the vertical topographic error increment, λ isthe wavelength, T and B are the temporal and perpendicularspatial baselines, R is the sensor to the target distance, θ isthe incidence angle, and Δφres accounts for the atmospheric,nonlinear, and noise components of the phase.

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 3

In order to estimate the linear deformation rate and theresidual topographic components of the interferometric phase,a linear model including only these elements is defined foreach arc of the triangulation. Then, the model is adjusted tothe data through the minimization of a cost function, addressedas the model adjustment function (MAF) [13]. With gooddistributions of temporal and spatial baselines, the model canbe correctly adjusted, even in the case that some of the phaseincrements were wrapped.

Once the linear deformation rate and the topographic errorincrements are obtained, the MAF is evaluated as a measureof the quality of each arc. The low quality arcs are truncated,removing, at the same time, those pixels that remain isolated.Another iteration of the minimization process is then performedwith the surviving pixels. This process allows removing thosepixels that do not fit the linear model, despite that they havefulfilled the pixel selection thresholds. This is mainly causedby strong nonlinear deformations. Finally, the absolute valuesof linear deformation and topographic error for each pixel arecalculated through an integration process, using one or multipleseeds with known behavior as tie points [13], leading to the finaldeformation results.

III. POLSAR INTERFEROMETRY

A. Polarimetric Scattering Matrix and Basis Transformation

The scattering matrix Shv describes the scattering processof a target when it is illuminated by an electromagnetic wave.It is a complex matrix, which is defined for a given imaginggeometry and an illuminating frequency by [17]

Shv =

[Shh Shv

Shv Svv

](5)

considering a monostatic configuration under the backscatter-ing alignment assumption, where the transmitting and receivingantennas are placed at the same location. Spq refers to thecomplex SAR images obtained from the receiving and transmit-ting electromagnetic waves with the polarization states p andq, respectively. Usually, p, q = (h, v) indicates the orthogonalhorizontal and vertical polarization states.

With the knowledge of Shv in the linear polarization basis{h, v}, it is possible to obtain the scattering matrix in anyelliptical orthogonal basis {a, b}, Sab, using the followingunitary transformation [17], [18]:

Sab =

[Saa Sab

Sab Sbb

]= UT

2 ShvU2 (6)

where T refers to the vector transposition, and the transforma-tion matrix U2 can be expressed through the orientation andellipticity angles (ψ, χ) of the polarization ellipse by

U2=

[cosψ −sinψsinψ cosψ

][cosχ j sinχj sinχ cosχ

][e+jφ0 00 e−jφ0

]. (7)

φ0 refers to the absolute phase term, which is irrelevant from aninterferometric point of view and is normally set to φ0 = 0.

B. Vector Interferometry

PolSAR interferometry (PolInSAR) is based on obtainingfully polarimetric data sets from slightly different points ofview. In the monostatic case, the scattering vector ki, for eachresolution element of each PolSAR data set, is obtained as avectorization of Shv [19], [20]

ki =1√2[Shh,i + Svv,i, Shh,i − Svv,i, 2Shv,i]

T (8)

where i = (1, 2) indicates two PolSAR acquisitions obtainedat different times. From the entire possible basis, the Pauli isusually used because it allows a direct interpretation of data inphysical terms. Then, the so-called PolInSAR vector betweentwo PolSAR acquisitions is defined as follows [19], [20]:

k =[kT1 ,k

T2

]T. (9)

Notice that, in the case of pointlike scatterers, (9) corre-sponds to a deterministic vector. However, for distributed scat-terers, (9) behaves as a random vector due to the complexity ofthe scattering process. In this case, under the hypotheses of spa-tial homogeneity and ergodicity, the 6 × 6 PolInSAR coherencycomplex matrix T6 is defined to completely characterize thescatterer behavior [19], [20]

T6 = E{kkH} =

[T11 Ω12

ΩH12 T22

](10)

where H refers to the conjugate transpose, T11 and T22 cor-respond to the individual coherency matrices of each PolSARdata set, and Ω12 is the polarimetric interferometric coherencymatrix.

The interferometric coherence γ defined in the previous sec-tion can be generalized by taking into account its polarimetricdependence. The PolInSAR Pauli vector ki could be projectedonto an unitary vector to obtain a generic scattering coefficientSi = wH

i ki for i = 1, 2. Si is a complex value analogous toa new SAR image resolution element, obtained as a linearcombination of the elements of ki through the projection vectorwi. At this point, considering the interferogram formed bytwo different Si’s, the generalized polarimetric interferometriccoherence for different combinations of w1 and w2 can beobtained [19], [20]

γ(w1,w2) =wH

1 Ω12w2√wH

1 T11w1wH2 T22w2

. (11)

In PolDInSAR applications, w1 and w2 must be the samealong the whole stack of interferograms since the choice ofdifferent projection vectors between two acquisitions of theinterferogram may lead to an artificial change in the phasecenter of the scatterers. Under this restriction, (11) becomes

γ(w) =wHΩ12w√

wHT11wwHT22w. (12)

In the case of pointlike scatterers, the DA index relatedto phase accuracy was defined in (2). The generalized DA

4 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

index for each projection vector w is defined by replacing thescattering coefficient Si by wHki, yielding to [6]–[8]

DA(w)=σA

mA=

1

〈|wHk|〉

√√√√ 1

N

N∑i=1

(|wHki|−〈|wHk|〉)2 (13)

where

⟨|wHk|

⟩=

1

N

N∑i=1

|wHki|. (14)

Notice how the projection vector w must be preserved againalong the whole data set to avoid changes in the phase centers.

IV. POLARIMETRIC OPTIMIZATION

A. Coherence Stability Optimization

The objective of this section is to explore the application ofthe different polarimetric optimization methods available in theliterature to the coherence estimator. The aim is to enhance theinterferograms’ phase quality, using the available polarimetricinformation in PolSAR data.

In this framework, two different configurations, dependingon how the data are acquired, must be taken into account.

1) The zero-baseline configuration, such as in GB-SAR sen-sors, refers to the absence of a spatial baseline betweenthe different temporal acquisitions of the sensor. In thiscase, all the images are acquired with exactly the samepoint of view.

2) The multibaseline configuration, such as in spacebornesensors, refers to the presence of a spatial baseline be-tween different temporal acquisitions. In this case, thespatial baseline changes from acquisition to acquisitionsince the images are acquired with slightly differentpoints of view.

Hence, two different modi operandi should be considered inorder to correctly apply the polarimetric optimization methods.

1) In the zero-baseline case, owing to the lack of a topo-graphic component in the interferometric phase, a single-baseline optimization process can be performed for eachinterferogram independently. In this case, the projectionvectors can be optimized independently at the interfero-gram level with no risk of adding undesired phase termsdue to changes in the phase centers within the same pixel.Notice that the restriction seen in the previous section ofhaving identical projection vectors w1 and w2 for the twoimages of the interferogram is still mandatory.

2) In the multibaseline case, a topographic component in thedifferential phase of the interferograms appears. Selectingdifferent projection vectors for each interferogram or, inother words, optimizing them independently as in thezero-baseline configuration case would lead to changes inthe phase centers within the same pixel, corrupting the re-trieved deformation maps. Therefore, in the multibaselineconfiguration, the projection vector needs to be the samealong the whole stack of interferograms. In this case, the

single-baseline optimization methods need to be extendedto the multitemporal case.

For simplicity, the algorithms explained in this section areaddressed first to the single-baseline case, which can be appliedto zero-baseline configuration sensors, such as GB-SAR, andthen, they are extended to the multibaseline case, which can beapplied to spaceborne sensors.

1) Best: The first approach to improve the quality of thedifferential phase consists of selecting the polarimetric channelproviding the highest value of coherence for each interfero-gram. This method is referred to as Best. For this case, themodulus of the optimized coherence is given for each pixel by

|γBest| = max {|γhh|, |γhv|, |γvv|} (15)

and the optimized interferometric phase will be the phase of thatselected channel providing the highest coherence. In fact, thischoice corresponds to select the channel that is less affected bydecorrelation factors for each pair of images, and it is translatedinto a significant improvement of the coherence and, thus, of thenumber of pixel candidates in the later pixel selection step.

For the multibaseline case, the method is extended selectingthe polarimetric channel providing, in this case, the highesttemporally averaged mean coherence. This method will bereferred to in the following as Best-MB.

Despite producing a significant improvement in the finalDInSAR results, as we will see later, the so-called Best ap-proach does not completely exploit the potential of polarimetry.The following methods attempt to use PolSAR data in a moreefficient way.

2) ESM: The most common optimization strategy that canbe found in the literature is based on finding the projectionvector w that optimizes the generalized coherence defined in(12). Since this approach forces both projection vectors to beequal, it is referred to as ESM. There are different methods toobtain the optimum projection vector.

The simplest approach is based on the parameterization ofthe unitary projection vector w, in order to obtain all thepossible values of the generalized coherence [6]–[8].To ensurethe unitarity of the projection vector, the parameterization,presented in [20], can be used

w =

⎡⎣ cosαsinα cosβejδ

sinα sinβejγ

⎤⎦⎧⎪⎨⎪⎩

0 ≤ α ≤ π2

0 ≤ β ≤ π0 ≤ δ ≤ π−π ≤ γ < π.

(16)

In this case, the optimum projection vector will be the oneproviding the maximum coherence. The main drawback ofsolving the optimization problem by brute force methods is thehigh computational cost. Using a fine sampling of 1◦ to exploreall the space of possible w’s, ∼1010 operations per pixel arerequired. It is equivalent to spending 2 s per pixel using a PCwith a 3.16-GHz Intel Dual-Core CPU and 3.25 GB of RAM,running under Windows.

To overcome this time limitation, two efficient approachescan be found in the literature [9], [21]. The method presentedin [9] is the most commonly used one in this framework. Thisapproach uses an iterative solution based on the numerical

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 5

radius [22], assuming polarimetric stationarity or, in otherwords, that the two coherency matrices T11 and T22 are verysimilar. Under this condition, the estimated complex differentialcoherence is approximated by

γ(w) =wHΩ12w

wHTw(17)

where

T =T11 +T22

2. (18)

It is always accomplished that |γ| ≤ |γ|, while the samephase is preserved if the condition is fulfilled. With this iterativesolution, the computational cost can be reduced drastically upto three orders of magnitude. For this reason, this solution isconsidered in this paper to perform the ESM approach.

Despite these advantages, some restrictions must be com-mented since not all the pixels of the interferogram will besuited to be optimized for PolDInSAR applications. This al-gorithm is only valid under the assumption of polarimetricstationarity. When this hypothesis does not apply, the algorithmdoes not reach the maximum, and in addition, the optimizeddifferential phase may be affected by this difference of po-larimetric behavior. Hence, when polarimetric stationarity doesnot apply, the optimization process may have no sense. Thesepixels, where the condition is not fulfilled, will be referred toin the following as outliers of the polarimetric optimizationprocess. Despite this, when this algorithm is applied to mul-titemporal series in the framework of DInSAR applications,the lack of polarimetric stationarity will be normally reflectedin high temporal decorrelation phenomena, degrading thus thetemporally averaged mean coherence values of the outliers. Asa consequence, these pixels will generally not be selected forthe later DInSAR processing.

Once the optimum projection vector wopt,ESM is found,the coherence can be directly obtained through (12), and theinterferometric phase is given by

φESM = arg(wH

opt,ESMΩ12wopt,ESM

)(19)

where arg(.) refers to the argument of a complex.Notice how, under the multibaseline configuration, the use of

the same projection w vector in the whole temporal stack ofacquisitions is mandatory. Hence, an independent optimizationprocess for each interferogram, as seen in the zero-baselinecase, is no longer possible. In this case, the use of the methodpresented by Neumann et al. in [10], referred to in this paperas ESM-MB, is proposed. This method is an extension of theESM method proposed by Colin et al. in [9], which aims tooptimize the temporally averaged mean coherence instead ofthe coherence of each interferogram separately. The polarimet-ric stationarity hypothesis is assumed for all the acquisitionsjointly, so (18) is extended to the temporal averaging of all thecoherency matrices.

3) SOM: To avoid outliers in the ESM polarimetric opti-mization process described earlier, when polarimetric station-ary does not apply, the method described in [11] is proposed.As in the ESM case, it preserves the polarimetric signature

between the acquisitions that forms an interferogram, but itsolves the coherence optimization problem in a way closer to aphysical interpretation. The algorithm is based on sweeping allthe possible combinations of orientation and ellipticity angles(ψ, χ) at the scattering matrix level. If the original scatteringmatrix Shv is expressed in the linear polarization basis {h, v},which corresponds to ψ = 0 and χ = 0, it is possible to obtainthe scattering matrix in a new elliptical orthogonal basis Sab

through the unitary matrix transformation presented in (6). Allthe (ψ, χ) space is then explored in order to find the polarizationbasis transformation providing the highest coherence among allthe copolar γaa and cross-polar γab coherence values. Underthis approach, the polarimetric optimized absolute value of thecoherence is given by

|γSOM | = max(ψ,χ)

{|γaa(ψ, χ)| , |γab(ψ, χ)|} (20)

where γaa and γab can be expressed as

γaa =E{Saa,1Saa,2}√

E {|Saa,1|2}E {|Saa,2|2}

γab =E{Sab,1Sab,2}√

E {|Sab,1|2}E {|Sab,2|2}. (21)

Saa,i and Sab,i are the copolar and cross-polar channels in thenew (ψ, χ) polarization basis, for the first and the second imagei = 1, 2 of the interferogram, respectively. Consequently, theoptimized interferometric phase will be given by the argumentof the new channel providing the best value of coherence, eitherthe copolar arg(γaa) or the cross-polar arg(γab).

Notice that all the possible solutions generated by eachorientation and ellipticity angles (ψ, χ) are a subspace of theones in the ESM approach, and for this reason, this method isreferred as SOM. The main drawback of this technique is againits high computational cost since it is based on a numericalsolution that finds the optimum value of coherence by a bruteforce method. Using a 1◦ step in the (ψ, χ) sampling, ∼105operations are required per pixel, which is equivalent to 0.1 s.

With the objective to reduce the computational cost of theproposed algorithm, the shape of the coherence to optimize isexplored for different values of the orientation and the ellipticityangles. An interferogram obtained with the UPC’s GB-SAR inthe El Forn de Canillo campaign, presented in Section VI, hasbeen used to illustrate the process. Fig. 1 shows the modulusof the copolar coherence values |γaa(ψ, χ)| for all possibleorientation and ellipticity angles (ψ, χ) using four representa-tive pixels with different coherence values in the Best approach|γBest|. The cross-polar coherence functions |γab(ψ, χ)| showsimilar shapes, so only the copolar case is showed. Each pixelpresents a high dynamic range of coherences between thebest and the worst polarimetric basis transformation. At thesame time, the coherence to maximize is smooth enough toallow numerical methods based on the gradient computation toeasily converge to the maximum. For this reason, the conjugategradient method (CGM) [23] has been used to reduce thecomputational cost. Since this method finds the minimum ofa function, the coherence expression must be inverted, 1/|γ|.

6 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Fig. 1. Copolar coherence values as a function of (ψ, χ) for four representa-tive pixels, with different values of |γBest|. (a) |γBest| = 0.3. (b) |γBest| =0.5. (c) |γBest| = 0.7. (d) |γBest| = 0.9.

First, a coarse sampling (∼30◦) finds a point near the absolutemaximum of the coherence, and then, the CGM is applied toreach the optimum value with less function evaluations. Withthis approach, the number of operations has been reduced to∼102, three orders of magnitude less.

Finally, for the multibaseline case, which will be referredto in this paper as SOM-MB, the method is easily extended.It is based on sweeping all the possible combinations of ori-entation and ellipticity angles (ψ, χ), but now maintaining thesame combination along the whole set of images. The optimalpolarization basis transformation will be the one providing thehighest temporally averaged mean coherence. Once again, theapplication of the CGM largely reduces the computation time.

B. Amplitude Dispersion Optimization

In this section, the polarimetric optimization techniques seenfor the coherence case are applied to the DA estimator in theframe of PolDInSAR applications. Recent works have beendone in this context using the ESM method [6]–[8].

The objective now is to look for the best polarimetric channel(Best), the optimum scattering coefficient (ESM), or the appro-priate polarimetric basis transformation (SOM), applied alongthe whole PolSAR data set, providing the minimum DA. Since,for this case, the spatial baseline plays no role in the phasequality estimation, there are no differences in the formulationbetween working with zero-baseline or multibaseline data.

1) Best: The first way to improve the DA and, consequently,the quality of the differential phase consists of selecting theinterferometric phases of the polarimetric channel providingthe minimum DA along the PolSAR data set. This methodis referred to, as in the coherence case, as Best. The Bestoptimized amplitude dispersion is then given for each pixel by

DA,Best = min{DA,hh, DA,hv, DA,vv} (22)

and the interferometric phase is derived from the channelproviding the minimum DA value.

2) ESM: The ESM approach has been recently adapted in[6]–[8] in order to find the projection vector providing theoptimum value of DA. This approach consists of performinga search over the whole polarimetric space in order to obtainthe projection vector w that optimizes for each pixel the gen-eralized DA expression seen in (13). The optimization problemis solved parameterizing the projection vector w as describedin (16).

The problem is now reduced to look for the angles α, β, δ,and γ that minimize the generalized DA over the polarimetricspace of possible projection vectors w. Once the optimum pro-jection vector wopt,ESM is found, the optimized DA is directlygiven by (13) with the projection vector under consideration.The interferometric phase of a pixel could be expressed for eachpair of images i, j as follows:

φESM = arg{(

wHopt,ESMki

) (wH

opt,ESMkj

)∗}. (23)

As in the previous cases, the main drawback of this methodis its computational cost. Using a sampling step of 1◦ to exploreall the possible values of α, β, δ, and γ, ∼1010 operations perpixel are required. In this case, it is equivalent to 9.6 s, assuminga stack of 34 images. In order to optimize the process, a coarsesampling of 30◦ is done to roughly locate the position of theabsolute minimum, and then, the CGM is proposed to reach theoptimum value. The number of operations can be reduced to∼104 per pixel, six orders of magnitude less.

3) SOM: Despite the significant reduction in time with theuse of the CGM, the computational cost increases significantlywith the number of acquisitions and the extent of the area understudy, due to the large number of pixels when working at fullresolution. For this reason, the SOM approach, which requiresthe optimization of a lower number of variables, is adapted tothe polarimetric DA optimization process.

As in the coherence case, it consists of sweeping all thepossible orientation and ellipticity angles (ψ, χ) at the level ofthe scattering matrix S, to achieve a scattering matrix Sab inthe new polarization basis, through the unitary matrix transfor-mation seen in (6). All the space of possible (ψ, χ) is exploredin order to find the polarization basis transform providing theminimum DA value among all the copolar and cross-polar DA

values (DA,aa, DA,ab) as follows:

DA,SOM = min(ψ,χ)

{DA,aa(ψ, χ), DA,ab(ψ, χ)} . (24)

The shape of the function to optimize, the DA, is exploredfor all the possible values of (ψ, χ) using as an example theRADARSAT-2 Barcelona data set presented in Section VI.Fig. 2 shows the results for four representative pixels withdifferent copolar DA,aa values in the Best approach DA,Best.As in the coherence case, the function to minimize presents asmooth behavior, being suitable for the application of the CGM,both for the copolar and cross-polar cases. Once again, its uselargely reduces the processing time.

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 7

Fig. 2. Copolar amplitude dispersion values as a function of (ψ, χ) for fourrepresentative pixels with different values of DA,Best. (a) DA,Best = 0.3.(b) DA,Best = 0.25. (c) DA,Best = 0.2. (d) DA,Best = 0.15.

V. POLARIMETRIC DINSAR PROCESSING

In classical DInSAR, a single-polarimetric channel is consid-ered in the processing, or in other words, all selected pixels aredefined with respect to the same polarimetric configuration. Theprevious section has shown different techniques able to find anoptimal polarimetric state that maximizes the coherence, whenmultilooked data are used, or minimizes the DA, when workingat full resolution. For both cases, the phase quality of the pixelin the optimal polarimetric state is better than those of the orig-inal polarimetric channels, as measured by the estimators. Eachselected pixel of the stack of interferograms has an optimumpolarimetric state that can be completely different from thatof the neighbors. At the same time, for a pair of acquisitions,the original three interferograms, one per polarimetric channel,have been reduced to a single one through the proper combi-nation in the optimization process. As it has been indicated,independently of the considered method, the temporal polari-metric stationarity must be accomplished for all interferograms.This means that the scattering mechanism characterizing a pixelmust remain constant from the two acquisitions generating aninterferogram, for the zero-baseline case, or constant from thewhole set of interferograms, in the multibaseline case.

At this stage, the classical DInSAR processing is appliedto this new stack of optimized interferograms. Notice thatthere is no difference with respect to the single-polarimetriccase as explained in Section II. The relative interferometricphase between two neighboring pixels will thus present termsassociated to the deformation in the line of sight, to the verticaltopographic error, and, finally, to the noise due to atmosphericvariation and decorrelation sources. Regarding the target’s po-larimetric behavior, notice that the residue Δφres of the linearestimation process includes an absolute phase term Δφpol,associated to the polarimetric changes induced by both thetemporal and the spatial baselines. A scatterer can change itspolarimetric behavior along time basically due to changes onthe scatterer itself, a kind of temporal decorrelation, or due to its

TABLE IUPC GB-SAR PARAMETERS

angular response, a kind of geometric decorrelation. The formerappears in all the cases, and the latter appears only in the multi-baseline case. As a consequence, the phase center of the opti-mized channel may change from image to image, which, in fact,will be considered as an additional nonlinear deformation term.It is important to highlight that this problem already existed inthe single-polarimetric case; therefore, no special treatment isrequired when working with fully polarimetric data.

Finally, when working with polarimetric optimization tech-niques, particularly with those that minimize the DA, it isimportant to highlight the role of the discarding process ofthe CPT, detailed in Section II. Since the proposed algorithmsoptimize the DA values not only for the stable pointlike scat-terers but also for the clutter, some points with “artificially”improved values of DA could be erroneously selected. In thiscase, low values of the MAF may be associated to strongnonlinear deformations, as in the single-polarimetric case, andalso to erroneously polarimetric optimized clutter. Such pixelswill behave as noisy ones, and they will be discarded as theydo not adjust to the linear model. The number of rejected pixelsdepends strongly on the linearity of the deformation process, onthe scenario, urban or rural, and on the optimization techniqueused. Typically, the number of discarded pixels ranges betweenthe 1% and the 5%, depending on the cases discussed earlier.

VI. TEST SITES AND DATA SETS

A. GB-SAR Over Canillo

The Remote Sensing Laboratory, in collaboration with theDepartment of Geotechnical Engineering and Geosciences ofthe UPC, carried out a one-year measuring campaign, fromOctober 2010 to October 2011, in the landslide of El Forn deCanillo, in Andorra (located between Spain and France), usingthe UPC’s X-band polarimetric GB-SAR (RISKSAR) [24]. Atotal of ten daily averaged images have been collected with atemporal baseline of approximately one month.

Unlike most of the other GB-SAR systems available in theremote sensing community, which are based on a vector net-work analyzer for the linear stepped frequency sweeping of thetransmitted signal bandwidth, the continuous-wave frequency-modulated radar used by the the RISKSAR system is based ona digital-direct-synthesizer chip set that generates a high-ratestepped linear frequency-modulated continuous-wave signal[24], [25]. This type of solution allows performing PolSARmeasurements without increasing the temporal decorrelation

8 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Fig. 3. (a) Mean amplitude corresponding to the ten daily averaged GB-SAR acquisition campaigns. (b) Mean coherence histograms using the hh polarimetricchannel or Best, SOM, and ESM coherence stability optimization methods. Average interferometric mean coherence using (c) the hh polarimetric channel or(d) Best, (e) SOM, and (f) ESM coherence stability optimization methods.

effects during a single scan. The range resolution is 1.25 m, andas in all GB-SARs, the cross-range resolution is not constant,ranging from 0.75 m at near range up to 6 m at the far rangeof 1600 m. Table I describes the sensor setting parameters usedduring the campaign.

The general landslide of El Forn de Canillo is an ancientlandslide with a complex movement that took place in morethan one episode. Nowadays, it has some residual movementon the order of some millimeters per year. Some geologicalstudies show that local slides may be produced by situations likebig excavations, undermining by erosion, or important ascentsof the groundwater level in extraordinary periods of rainfall.In the northeast extreme of the landslide of El Forn Canillo,there is the secondary landslide of Cal Borró-Cal Ponet thatstill presents activity coinciding with episodes of strong rainsand big increases of the piezometric conditions. It can reachlinear velocities up to 2–3 cm per year [26].

El Forn de Canillo is a partially vegetated area, whichdecorrelates fast at the X-band, containing some bare surfacesand few man-made structures. The potential density of coherentscatterers or PSs is consequently low. The scene is a perfecttest bed to check the benefits of the polarimetric optimizationmethods presented in the previous section.

Prior to the optimization process, data must be correctlycalibrated using a corner reflector located in near range and astrong cross-polar urban scatterer [27], [28]. In addition, theatmospheric artifacts must be correctly compensated [29], [30]before starting the DInSAR processing.

B. RADARSAT-2 Over Barcelona

The orbital PolSAR data set used in this study consists of34 Fine Quad-Pol RADARSAT-2 acquisitions, from January2010 to May 2012, over the metropolitan area of Barcelona,

northeastern Spain. This SAR sensor works at the C-band, witha resolution of 5 m in both range and azimuth directions and arevisit time of 24 days.

Barcelona is affected by the construction of new under-ground infrastructures. For instance, the tunnel that will connectBarcelona and France with high-speed trains passes very closeto the Sagrada Familia cathedral. Also, a new undergroundline, that will connect the city with the airport, generatessubsidence in different urban areas. Several hazards have beenrelated to these activities, such as the collapse of a block in theEl Carmel neighborhood in 2005 or damages on a building inthe south of the city. Therefore, there is a clear need of largescale monitoring of these works.

In this case, the monitored area is urbanized and character-ized by a high density of deterministic scatterers. Prior to thepolarimetric optimization process, some preprocessing must bedone to the data. This includes the generation of the differen-tial interferograms by removing the topographical componentwith an external digital elevation map and the generation ofthe polarimetric coherence matrices T and the polarimetricinterferometric coherence matrices Ω for each interferogram.In order to reduce the effects of the Doppler and geometricdecorrelation, the azimuth and the range spectral filtering [14]are applied to each component of the T and the Ω matrices.

VII. POLDINSAR RESULTS

This section shows the PolDInSAR results obtained using thedifferent polarization optimization techniques described before,for the two scenarios. Results are differentiated according tothe pixel selection criteria: coherence stability and amplitudedispersion.

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 9

TABLE IINUMBER OF RELIABLE PIXELS SELECTED. ZERO-BASELINE

APPROACH. COHERENCE STABILITY PIXEL SELECTION

A. Coherence Stability PolDInSAR Results

In this case, we will distinguish between the cases of zero-baseline data, using the GB-SAR data set, and the multibaselinedata, using RADARSAT-2 data set.

As mentioned in the previous section, the GB-SAR test site ismostly a vegetated area with few man-made structures along thehillside. Fig. 3(a) shows the mean amplitude of the whole dataset, in a range/cross-range representation. Fig. 3(b) shows themean coherence histogram for the hh polarimetric channel andthe mean coherence histograms after applying all the optimiza-tion methods. The comparison between them reveals that theESM and SOM techniques are producing the largest coherenceimprovement, with the ESM approach being slightly better.Fig. 3(c)–(f) shows the mean coherence maps with a multilookwindow of 9 × 9 pixels for each case, showing the rise ofcoherence owing to the polarimetric optimization. In this kindof vegetated areas, a 9 × 9 multilook window shows a goodtradeoff between the reliability of the coherence estimator andthe spatial resolution. Notice that there is a higher improvementin the coherence values over the bare surfaces and low vegetatedregions of the area under study. In the few existing urbanizedregions, which already present high coherences for the single-polarimetric case, the coherence values are slightly improved.Obviously, this overall improvement will translate into a higherdensity of useful pixels suited for DInSAR purposes. In or-der to illustrate this, the whole DInSAR processing has beencarried out for each case in order to obtain the linear velocitydeformation maps. Pixel candidates are those presenting a meancoherence above 0.7, which corresponds to a phase standarddeviation lower than 5◦ [31]. Table II summarizes the pixels’selection densities for each optimization method. Notice howthe number of pixel candidates in the ESM approach triples theones selected in the single-polarimetric case.

Fig. 4 shows the final deformation velocity maps for thedifferent polarimetric optimization methods geocoded over anortophoto of the area. Notice how the global behavior is similarfor all the methods, except for the increase of pixels’ densitythat shows the usefulness of the different polarimetric optimiza-tion approaches. As expected, the landslide still presents someresidual movement of the order of 1–1.5 cm per year. In thetop-left border of the main landslide, there is the secondarylandslide with a motion rate of 2–2.5 cm per year. Theseresults present a high agreement with the conclusions extractedfrom [26].

Fig. 4. Lineal velocity retrieved from the daily averaged acquisitions fromOctober 2010 to November 2011 GB-SAR campaigns, using (a) the hh po-larimetric channel or (b) Best, (c) SOM, and (d) ESM coherence stabilityoptimization approaches for the DInSAR processing.

Fig. 5. Mean amplitude corresponding to the 34 RDARARSAT-2 acquisitions.

The multibaseline coherence optimization techniques ex-plained in Section IV-A, Best-MB, ESM-MB, and SOM-MB,have been applied to the Barcelona RADARSAT-2 data set.The objective is to compare their performances with the re-sults obtained for the zero-baseline case. The processed areacorresponds to an urban region with some vegetated hills (seeFig. 5). For this case, a 9 × 5 (azimuth × range) multilook win-dow has been applied. Since we are more interested in the urbanarea of the image, the multilook window chosen is smaller thanthat in the previous case. The objective is to preserve betterthe spatial resolution and maximize the chances of detectingman-made structures. In addition, the multilook window is notsquare to take into account the different resolutions in groundrange and azimuth of RADARSAT-2 data.

Fig. 6(a) shows the histograms of the mean coherence forthe different optimization methods, and Fig. 6(b) focuses on

10 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Fig. 6. (a) Mean coherence histograms using the hh polarimetric channelor the Best-MB, SOM-MB, and ESM-MB coherence stability optimizationmethods. (b) Detail of the coherence values from 0.4 to 1.

TABLE IIINUMBER OF RELIABLE PIXELS SELECTED. MULTIBASELINE

APPROACH. COHERENCE STABILITY PIXEL SELECTION

the higher coherence values, where the threshold for pixelselection shall be established. Peaks around 0.25 coherencevalues belong to pixels located in rural and sea areas severelyaffected by decorrelation. On the contrary, small peaks towardthe higher coherences belong to pixels located in urban areas.

Notice how, in the rural regions, the multibaseline optimiza-tion methods produce a lower improvement on the coherencehistograms than in the zero-baseline ones. This behavior canbe justified by the restriction of using an identical projectionvector for all images or, in other words, that polarimetricstationarity is assumed along the whole temporal span. Forthe zero-baseline case, this restriction was forced only at theinterferogram level, performing a single-baseline optimization.As the number of acquisitions increases, it is more likely tofind polarimetric instabilities induced by temporal, geometric,and volumetric decorrelation. In addition, the ensemble ofdifferent polarimetric mechanisms which may be mixed withinthe multilooked pixels makes the polarimetric optimization lesseffective. Despite this, in urban areas, which are, in general,more stable in time than the rural ones, a similar improvementas in the zero-baseline case can be observed.

A selection of pixel candidates considering an optimizedmean coherence threshold of 0.75 has been performed, whichcorresponds to the same phase standard deviation of 5◦ [31]used in the GB-SAR case, for the new multilook used. Asit was expected, the selected pixels are mainly located inthe urban areas. Table III shows the pixel density achievedfor each method. In this case, the pixels’ density increaseis slightly lower than that in the zero-baseline approach,reaching an increase of 2.7 factor compared with the single-polarimetric case.

Fig. 7. Lineal velocity retrieved from the 34 RADARSAT-2 acquisitions overBarcelona, from January 2010 to May 2012, using (a) the hh polarimetricchannel or (b) Best-MB, (c) SOM-MB, and (d) ESM-MB mean coherenceoptimization approaches for the DInSAR processing.

Fig. 7 shows the deformation maps obtained using the hhpolarimetric channel data and the ones obtained with the differ-ent polarimetric optimization methods. The overall deformationpatterns are similar in all cases, and the only difference is foundin pixel densities shown in Table III. Different deformationbowls can be observed, with the most severe ones in the airportand harbor areas. Patterns of weaker deformations are observedin the city. An interesting case is located in the northeast partof the image, which follows a track of a metro line underconstruction. In fact, the affected area is quite narrow, whichcan make its detection difficult when the density of pixels is low.The increase of density provided by the polarimetric optimiza-tion methods contributes significantly to increase the precisionon determining the extension of the deformation bowl. Theamplitude dispersion results presented in the following sectionwill be focused on this particular area.

B. Amplitude Dispersion PolDInSAR Results

Since the reduced number of acquisitions for the GB-SARdata set prevents the application of the DA estimator [3], theresults in this section focus on the Barcelona RADARSAT-2data set.

Fig. 8(a) shows the mean amplitude of all the acquisitionsprocessed. This area corresponds to the northeast part of thecity, as commented in the previous section. Fig. 8(b) shows thehistograms of the DA for each method used. Fig. 8(c)–(f) showsthe DA maps for each polarimetric optimization method. Noticehow it is easy to distinguish between the urban areas and thevegetated ones from the values of the distribution. Looking atthe details, the streets can be perfectly seen. As expected, theESM produces the best results.

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 11

Fig. 8. (a) Mean amplitude detail corresponding to the 34 RADARSAT-2 acquisitions. (b) Amplitude dispersion histograms using the hh polarimetric channelor the Best, SOM, and ESM amplitude-based polarimetric optimization methods. Amplitude dispersion map using (c) the hh polarimetric channel or (d) Best,(e) SOM, and (f) ESM polarimetric amplitude-based optimization approaches.

TABLE IVNUMBER OF RELIABLE PIXELS SELECTED.AMPLITUDE DISPERSION PIXEL SELECTION

The DInSAR processing has been applied for all cases inorder to demonstrate the pixel’s density improvement achievedin the optimization process. A DA threshold of 0.25 has beenused for all cases, which corresponds to a phase standarddeviation of 15◦ [31]. Table IV summarizes the number of pixelcandidates selected for each approach.

As it can be seen, the differences among the different meth-ods are more substantial than for the coherence approach. Com-pared with the single-polarimetric channels, the Best methodprovides an increase in the selected pixels of roughly a factorof two. From Best to SOM, the number of selected pixels isalmost doubled again. Finally, ESM increases the number ofpixels by 80% with respect to SOM. This enrichment in pixels’density and quality in results clearly justifies the usefulness ofPolSAR data in the DInSAR framework.

Finally, the linear deformation maps for each approach areshown in Fig. 9(a)–(d), in order to demonstrate how the phaseinformation of the optimized pixels is reliable. Notice how the

overall deformation patterns are identical in the four cases whilethe pixels’ density is largely increased using the polarimetricoptimization techniques, as it has been commented before.This improvement in terms of pixels’ density helps to betterdetermine and characterize the extension of the areas affectedby subsidence. The different deformation bowls caused by theunderground tunnel construction (represented with an orangeline in Fig. 9) can be perfectly identified. Notice how theyperfectly match the path followed by the tunnel and the locationof the new station constructed, which corresponds to the largestdeformation bowl in the center of the images.

VIII. CONCLUSION

In this paper, general polarimetric optimization methods forits application to DInSAR processing have been evaluated.The objective has been to enhance the phase quality of theinterferograms to be processed by the DInSAR algorithms withthe proper combination of the available polarimetric channels.The optimized stack of interferograms allows the selection ofa larger number of pixels. Hence, the overall phase quality ofthe pixels is improved, and as a consequence, denser and moreprecise deformation maps are obtained.

The different polarimetric optimization methods available inthe literature have been tested and adapted to the particularcharacteristics of the data, zero baseline or multibaseline, andthe pixel selection criteria, coherence stability or amplitudedispersion. The simplest method described in this paper hasbeen the so-called Best. In this approach, for each pixel ofthe image, the polarimetric channel with the best value inthe estimator is selected. Despite the significant improvement

12 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Fig. 9. Lineal velocity retrieved from the RADARSAT-2 PolSAR acquisitions over Barcelona, from January 2010 to May 2012, using (a) the hh polarimetricchannel or (b) Best, (c) SOM, and (d) ESM amplitude-based optimization approaches for the DInSAR processing. The orange line indicates the undergroundtunnel construction.

achieved, this method does not completely exploit the potentialsof polarimetry.

More advanced methods have been studied. On the one hand,the ESM approach is able to reach the best optimized valuessince it explores the complete space of possible solutions, butwith a high computational cost. On the other hand, the SOMtechnique requires the optimization of a lower number of vari-ables, which makes the optimization less costly, but the space ofsolutions is a subspace of the ESM approach. As a consequence,SOM performance is usually lower compared with that ofESM in terms of phase improvement and, consequently, in thenumber of pixels selected.

On the one hand, working with the coherence estimator,the optimum projection vector may be optimized at the in-terferogram level for the zero-baseline case. On the contrary,for the multibaseline case, the optimum projection vector isforced to be identical for all interferograms. On the other hand,when working at full resolution with the amplitude dispersionapproach, the projection vector is forced to be the same in thewhole stack of SAR images, regardless of the spatial baselineconfiguration.

Generally, the main drawback of using ESM and SOM istheir computational cost. In this sense, this limitation has beenlargely improved with the combination of a coarse search of theglobal minimum and the CGM algorithm. The optimum projec-tion vectors have been found much faster with identical results.

Once the optimized interferograms are obtained, the DInSARprocessing is straightforward as there are no differences withrespect to the single-polarimetric case.

The different methods have been tested with two differentdata sets. The GB-SAR campaign in El Forn de Canillo hasprovided the zero-baseline data set while the RADARSAT ac-quisitions over Barcelona have provided the multibaseline one.

For all cases, results show a large improvement in the num-ber of pixel candidates selected with respect to the single-polarimetric case. Depending on the selection criteria, thespatial baseline configuration, and the scenario, some ap-proaches perform better than the others. The coherence sta-bility approach shows a better performance with zero-baselinedata since the optimization process can be applied to eachinterferogram separately. On the contrary, the multibaselinerestriction, which forces a single mechanism for the wholedata set, reduces the chances of improvement. In the amplitudedispersion approach, using orbital data over urban areas, theimprovement is even better, reaching an increase up to a factorof seven of the pixel candidates for the ESM approach, withrespect to the traditional single-polarimetric processing. For allscenarios, DInSAR results reveal deformations where expected.The differences between the deformation maps obtained withthe different polarimetric optimization techniques are onlyin the pixels’ density terms, but not on the deformation values,showing the goodness of the methods proposed.

IGLESIAS et al.: PHASE QUALITY OPTIMIZATION IN POLARIMETRIC DIFFERENTIAL SAR INTERFEROMETRY 13

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Rubén Iglesias (S’12) was born in Barcelona, Spain,in 1982. He received the B.Sc. degree in telecom-munication engineering from the Technical Univer-sity of Catalonia (UPC), Barcelona, in 2008, wherehe is currently working toward the Ph.D. degree,focused on the development of advanced differen-tial synthetic aperture radar (SAR) interferometry(DInSAR) and polarimetric DInSAR techniquesfor the detection, monitoring, and characterizationof slow-moving landslides with both orbital andground-based SAR (GB-SAR) data.

From June 2009 to June 2010, he was with the Active Remote Sensing Unitat the Institute of Geomatics, Barcelona, working in several projects relatedwith the application of DInSAR to terrain-deformation monitoring with orbitaland GB-SAR data. In 2010, he joined the Signal Theory and CommunicationsDepartment at UPC, working as a Research Assistant in the framework ofDInSAR applications.

Dani Monells (S’11) was born in Sant Joan de lesAbadesses, Spain, in 1981. He received the B.Sc.degree in telecommunication engineering from theTechnical University of Catalonia, Barcelona, Spain,in 2008, where he is currently working toward thePh.D. degree, focused on differential synthetic aper-ture radar (SAR) interferometry in orbital platforms,focusing on the exploitation of polarimetric SAR ac-quisitions, at the Signal Theory and CommunicationsDepartment (TSC).

From 2007, he has been working in severalprojects for the monitoring of terrain displacements and developing the TSCinterferometric chain and processor, in order to give support to the new-generation SAR satellites, including TerraSAR-X, Radarsat-2, Advanced LandObserving Satellite, and COnstellation of small Satellites for Mediterraneanbasin Observation.

14 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Xavier Fabregas (S’89–M’93) received the B.S.degree in physics from Barcelona University,Barcelona, Spain, in 1988 and the Ph.D. degree inapplied sciences from the Universitat Politecnica deCatalunya (UPC), Barcelona, in 1995.

In 1990, he joined the Photonic and Electromag-netic Engineering Group, Signal Theory and Com-munications Department, UPC. Since 1996, he hasbeen an Associate Professor with UPC. In 2001, hespent an eight-month sabbatical with the Microwavesand Radar Institute (HR) of the German Aerospace

Agency (DLR), Oberpfaffenhofen, Germany. He has published 26 internationaljournal papers and more than 106 conference proceedings and is the holder ofa patent. He is a reviewer in several international journals. His current researchinterests include polarimetric-retrieval algorithms, polarimetric calibration andspeckle models, ground-based synthetic aperture radar (SAR) sensors and theirapplications, and time series for multidimensional SAR data applications forurban and terrain deformation monitoring.

Jordi J. Mallorquí (S’93–M’96–SM’13) was bornin Tarragona, Spain, in 1966. He received the Inge-niero degree in telecommunications engineering andthe Doctor Ingeniero degree in telecommunicationsengineering for his research on microwave tomog-raphy for biomedical applications in the Departmentof Signal Theory and Communications from the Uni-versitat Politècnica de Catalunya (UPC), Barcelona,Spain, in 1990 and 1995, respectively.

Since 1993, he has been teaching at the Schoolof Telecommunications Engineering of Barcelona,

UPC, first as an Assistant Professor, later in 1997 as an Associate Professor,and since 2011 as a Full Professor. His teaching activity involves micro-waves, radionavigation systems, and remote sensing. He spent a sabbatical yearwith the Jet Propulsion Laboratory, Pasadena, CA, USA, in 1999, workingon interferometric airborne synthetic aperture radar (SAR) calibration algo-rithms. He is currently working on the application of SAR interferometry toterrain-deformation monitoring with orbital, airborne, and ground data; vesseldetection and classification from SAR images; and 3-D electromagnetic (EM)simulation of SAR systems. He is also collaborating in the design and construc-tion of a ground-based SAR interferometer for landslide control. Finally, he iscurrently developing the hardware and software of a bistatic opportunistic SARfor interferometric applications using European Remote Sensing, Environmen-tal Satellite, and TerraSAR-X as sensors of opportunity. He has published morethan 100 papers on microwave tomography, EM numerical simulation, SARprocessing, interferometry, and differential interferometry in refereed journalsand international symposia.

Albert Aguasca (S’90–M’94) was born in Barcelona,Spain, in 1964. He received the M.Sc. and Ph.D.degrees in telecommunication engineering fromthe Universitat Politècnica de Catalunya (UPC),Barcelona, in 1989 and 1993, respectively.

Since 1995, he has been an Associate Professorwith the School of Telecommunications Engineer-ing, UPC. His teaching activities involve RF andmicrowave circuits for communications and radio-navigation systems. His main research activitiesinvolve the design and development of synthetic

aperture radar (SAR) and microwave radiometer systems for unmanned aerialvehicle platforms. He also collaborates in the design and development of smartantennas and scavenging circuitry. He has published more than 40 papers onmicrowave SAR, radiometer systems, and microwave circuits.

Carlos López-Martínez (S’97–M’04–SM’11) re-ceived the M.Sc. degree in electrical engineering andthe Ph.D. degree from the Universitat Politècnicade Catalunya (UPC), Barcelona, Spain, in 1999 and2003, respectively.

From October 2000 to March 2002, he was withthe Frequency and Radar Systems Department (HR),German Aerospace Center (DLR), Oberpfaffenhofen,Germany. From June 2003 to December 2005, hewas with the Image and Remote Sensing Group—SAR Polarimetry Holography Interferometry Radar-

grammetry Team in the Institute of Electronics and Telecommunications ofRennes, Rennes, France. In January 2006, he joined the UPC as a Ramón-y-Cajal Researcher, where he is currently an Associate Professor in the areaof remote sensing and microwave technology. His research interests includesynthetic aperture radar (SAR) and multidimensional SAR, radar polarimetry,physical parameter inversion, digital signal processing, estimation theory, andharmonic analysis.

Dr. Lopez-Martinez is an Associate Editor of the IEEE JOURNAL OF

SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE

SENSING, and he served as a Guest Editor of the European Associationfor Signal Processing Journal on Advances in Signal Processing. He hasorganized different invited sessions in international conferences on radar andSAR polarimetry. He has presented advanced courses and seminars on radarpolarimetry to a wide range of organizations and events. He was the recipientof the Student Prize Paper Award at the European Conference on SyntheticAperture Radar (EUSAR) 2002 Conference and coauthored the paper awardedwith the First Place Student Paper Award at the EUSAR 2012 Conference.