Polarimetric Differential SAR Interferometry: First ...

IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 6, NO. 1, JANUARY 2009

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Polarimetric Differential SAR Interferometry: First Results With Ground-Based Measurements Luca Pipia, Xavier Fabregas, Member, IEEE, Albert Aguasca, Member, IEEE, Carlos López-Martínez, Member, IEEE, Sergi Duque, Student Member, IEEE, Jordi J. Mallorquí, Member, IEEE, and Jordi Marturià

Abstract—The Remote Sensing Laboratory of the Universitat Politècnica de Catalunya carried out a one-year measuring campaign in the village of Sallent, northeastern Spain, using a polarimetric ground-based synthetic aperture radar (SAR) sensor. The objective was to study the subsidence phenomenon induced by the salt mining activity conducted in this area up to the middle of the last century. Zero-Baseline polarimetric SAR (PolSAR) data were gathered at X-band in nine different days, from June 2006 to March 2007. In this letter, the problem of extracting subsidence information from fully PolSAR acquisitions for the retrieval of high-quality deformation maps is addressed. After compensating for the atmospheric artifacts caused by troposphere changes, the linear component of the deformation process is estimated separately for each polarization channel with the Coherent Pixels Technique (CPT). Afterward, a novel polarimetric approach mixing the differential-phase information of each polarization channel is proposed. The results obtained in the two cases are quantitatively compared, and the advantages provided by the polarimetric acquisitions are finally stressed. Index Terms—Ground-based synthetic aperture radar (GBSAR) sensor, SAR differential interferometry (DInSAR), SAR polarimetry.

I. I NTRODUCTION

A

CHALLENGE of the remote-sensing synthetic aperture radar (SAR) community in the very next years is to exploit the high amount of information contained in the PolSAR data to improve the performance of already assessed singlepolarization techniques. This is the case of differential SAR interferometry (DInSAR), where complementary coherence- and amplitude-based approaches, like the coherent pixels technique (CPT) [1] and permanent scatterers [2], were demonstrated to be successful over different types of scenarios. In both cases, a critical issue is the selection of reliable pixels for an accurate estimate of the deformation process under observation. Up to now, the lack of spaceborne polarimetric sensors has not made it possible to extend the mathematical formulation of these advanced methods to multiple-polarization channels. From this

Manuscript received July 16, 2008; revised October 1, 2008. Current version published January 14, 2009. This work was supported by the Spanish MCYT under the Project TEC 2005-06863-C0201. L. Pipia, X. Fabregas, A. Aguasca, C. López-Martínez, S. Duque, and J. J. Mallorquí are with the Signal Theory and Communications Department, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain (e-mail: luca. [email protected]; [email protected]; [email protected]; carlos. [email protected]; [email protected]; [email protected]). J. Marturià is with the Institut Geologic de Catalunya, 08006 Barcelona, Spain (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2008.2009007

point of view, the recent development of ground-based SAR (GBSAR) systems [3], [4] gives the opportunity to overcome this issue. Despite the limitations of the terrestrial platform, like the small area that can be observed and the high sensitivity to positioning errors, these sensors are able to gather high-quality zero-baseline SAR data sets. The capability of terrestrial platforms to retrieve linear and nonlinear deformation maps has been shown in [4]. This letter demonstrates that the complete knowledge the scattering matrix [S] can be employed to improve the estimation of the deformation process with respect to the single-polarization analysis. For this purpose, the data acquired by the GBSAR sensor of the Universitat Politècnica de Catalunya (UPC) during a period of approximately one-year in the village of Sallent, northeastern Spain, are employed. The measuring campaign was carried out by the Remote Sensing Laboratory (RSLab) in collaboration with the Geological (IGC) and the Cartographic (ICC) Institutes of Catalonia and aimed at studying the subsidence phenomenon induced by the salt mining activity conducted in this area in the past century. PolSAR data were monthly gathered at X-band from June 2006 to March 2007 with exactly the same observation geometry. Before performing an advanced DInSAR analysis, the problem of the variation of the propagation properties due to changes of the troposphere during the same day (short time) and between different months (long time) is stressed. In order to cope with the resulting atmospheric-phase artifacts, two different strategies are described. Then, the CPT algorithm is employed to analyze the benefits provided by fully polarimetric data. First, the classical technique is applied to each channel of [S] separately. Second, a new criterion for the selection of reliable pixels using the whole polarimetric information is proposed to work out a polarimetric CPT. The results achieved with the classical and the new methods are quantitatively compared, and the advantages offered by the polarimetric approach are finally pointed out. II. S YSTEM AND T EST -S ITE D ESCRIPTION A new generation of GBSAR sensors conceived as standalone systems was projected and developed by the RSLab of UPC [3]. A base-band FM-CW signal is generated by a solidstate DDS chipset and transmitted after a proper modulation. The radar front-end is mounted on a sled which moves along a linear unit and performs the synthetic aperture. The system is modularly structured, and data can be acquired at different bands (X- and K-bands) by simply substituting the antennas’ block and modifying the setup parameters. The use of a DDS shortens sensitively the time required for the scanning process with respect to a vector-network-analyzer solution, even when

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 6, NO. 1, JANUARY 2009

to polarimetrically calibrate the data as proposed in [8]. Then, (2) reduces to [Sc ] = [S]ejφ(r,n) + [NT ]

(3)

where [Sc ] denotes the calibrated scattering matrix still affected by propagation-property changes. In order to compensate for the resulting phase variations, a specific analysis tailored to the ground-based observation geometry is instead required, as shown in the next section. III. A TMOSPHERIC P REPROCESSING Fig. 1. UPC sensor in the operating configuration.

Fig. 2. Photo of the Station district affected by subsidence phenomena in Sallent from the UPC GBSAR location.

multipolarization data are collected. The decorrelation effects introduced by atmospheric changes during the aperture synthesis are, hence, reduced. Even in quite turbulent conditions, the troposphere layer through which the transmitted and scattered waves propagate may be assumed to be still homogeneous [5]. Concerning the monitoring campaign in Sallent, a 2-m-long linear unit was used. The entire rail was covered in about 2.5 min with an azimuth sampling of 1 cm. The UPC sensor in the operating configuration and the urban test-site are shown in Figs. 1 and 2, respectively. Data acquisitions were carried out on nine days from June 2006 to March 2007, as reported in Table I. During each day, a minimum of 40 data sets was gathered with a time delay of 20 min. The polarimetric capability of the sensor has allowed us to measure the complete scattering matrix. The antennas mounted on the front-end of the sensor horizontally (h) and vertically (v) polarized. Then, the backscattering matrix [S] describing a target may be defined as   Shh Shv (1) [S] = Shv Svv where the left and right subscripts identify the received and transmitted polarization, respectively. Owing to the nonideality of the system, the matrix [M ] measured by the sensor is related to [S] by jφ(r,n)

[M ] = [R][S][T ]e

+ [NT ]

(2)

where [R] and [T ] are the transmitter and receiver, respectively, 2 × 2 complex distortion matrices [6], φ(r, n) is the propagation phase term, which is a function of the sensor-to-target range distance r and of the refractive index n [7], and, finally, [NT ] is the additive noise contribution. The polarization purity of the system, about 30 dB in the central lobe, makes it possible

The subsidence phenomenon to be studied was shown in [9] to follow a linear behavior with vertical displacement meanrate equal to 2 cm/year. This result was carried out using CPT with a collection of ERS1-2 acquisitions from 1993 to 2005 and confirmed by topographic-leveling techniques. A ground-truth contour map describing the subsidence phenomena provided by the IGC is shown in Fig. 3. Therefore, it is reasonable to assume a timescale of the deformation process on the order of few centimeters per year also during the UPC’s measurement campaign. It follows that the set of daily acquisitions is not able to directly describe the deformation process. Nevertheless, they give the opportunity to improve the signal-to-noise ratio (SNR) without reducing the image spatial resolution by properly timefiltering the whole daily collection. Let Nw be the number of calibrated scattering matrices measured by the sensor during the day w. Under the hypothesis of propagation through a homogeneous atmosphere [5], the ith term of the sequence may be expressed as [Sc ]i,w = [S]w e−j2k0 ni,w r + [NT ], i = 1, . . . , Nw ,

w = 1, . . . , N

(4)

where k0 is the wavenumber in the vacuum and ni,w is the refractive index describing the troposphere layer during the ith acquisition process. If the first data set of the daily collection is fixed as master, (4) may be rewritten as [Sc ]i,w = [S]w e−j2k(n1,w +Δni,w )r + [NT ]

(5)

where n1,w describes the atmosphere of the master image and Δni,w the refractive-index variation between the two scans. In order to improve the SNR, the atmospheric-phase artifact introduced by Δni,w must be first compensated for. To do this, the coherence-based technique proposed in [5] is employed. The differential-phase ϕ of pixels within the scenario fulfilling a minimum coherence constraint, usually 0.97, is projected onto a single-range cut, and the distribution is fitted to the linear model  i,w . ϕ(r)  = 2k Δn

(6)

Then, high-coherence pixels whose differential phase diverges from the expected artifact are filtered out by checking the condition  p )| ≤ 3σ mod |ϕp − ϕ(r

(7)

where the subscript p denotes the generic coherent pixel and σ mod is the linear-model standard deviation. Finally, the description of the atmospheric artifact is obtained by fitting the differential-phase distribution of the pixels fulfilling (7) to

PIPIA et al.: POLARIMETRIC DInSAR: FIRST RESULTS WITH GROUND-BASED MEASUREMENTS

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TABLE I TIMETABLE OF THE MEASUREMENT CAMPAIGN

Fig. 3. Deformation velocity contour map obtained through topographic leveling techniques.

the linear model in (6). For each of the Nw − 1 slave data sets, the corresponding correction function f is obtained as ni,w r fi = ej2kΔ

(8)

 i,w is the value of Δni,w given by the second where Δn estimation. The time-averaged scattering matrix may be finally expressed as Nw    Sc w = [Sc ]i,w fi = [S]w e−j2kn1,w r .

two consecutive PolSAR data sets. As the trihedral employed to perform the data polarimetric calibration was removed after each day of measurement, a new phase with respect to (6) must be introduced in the long-term linear model to take into account the calibrator different range position [8]. At this point, the timescale of the subsidence allows us to neglect the contribution of the deformation process and to describe the one-month differential phase in terms of the propagation property changes. All the coherent pixels within the scenario can be, hence, employed to estimate the onemonth atmospheric artifact. It is worth pointing out that pixels characterized by a stronger deformation, which might bias the artifact description, are automatically filtered out by the twostep procedure described earlier. Therefore, a set of one-month compensation functions defined as nw,w+1 r+ϕ0,i , Fw = ej2kΔ

w = 1, . . . , N − 1.

(11)

Finally, the function compensating the ml interferogram artifact is obtained by simply multiplying the m − l − 1 basis functions from day l to day m as follows:

(9)

Fl,m =

i=1

m

Fw .

(12)

w=l

This process is repeated for each day reported in Table I. A similar approach for additive-noise reduction can be found in [4]. The final step before retrieving any long-time differential information is to compensate for propagation differences among the master images. From a theoretical point of view, the deterministic nature of the area under study provides sufficient highcoherence pixels to apply again the aforedescribed technique. Nonetheless, it must be taken into account that differential phase is sensitive to atmospheric artifact as well as to the deformation process to be retrieved. Owing to the linearity of the deformation process [9], the contribution due to deformation is expected to be higher as the time separation between data sets increases. In order to avoid any artifact incorrect description, pixels belonging to the hot-area should be filtered out for time span higher than a fixed time-threshold. The main drawback of this solution is the reduced number of high-coherent pixels at disposal for the regression-line estimation. A way to circumvent this problem deals with the range linearity of the atmospheric artifacts under atmosphere-homogeneity hypothesis. In fact, it is possible to express the propagation term of day w in (9) as a function of day l, with w > l, as w   −j2kn1,l r S c w = [S]w e ej[2k(n1,i+1 −n1,i )r+ϕ0,i ]

(10)

i=l

where the first exponent describe the propagation condition on day l while each term within the product represents the atmospheric artifact arising from the variation of n between each pair of consecutive time-averaged images from day l to day m. The term ϕ0,i accounts for the phase offset between

IV. S INGLE -P OLARIZATION CPT Once the effects of the atmospheric artifacts are corrected, advanced differential interferometric techniques can be applied. An amplitude-based analysis of the scenario might seem consistent with the deterministic nature of the urban area under observation. Nevertheless, the reduced number of available measurements (N = 9) makes a coherence-based approach more reliable for the deformation-process estimation. For this reason, the classical CPT algorithm is here employed [1]. The first step consists of choosing the polarization channel of [S] to be analyzed and estimating the value of the differential coherence γ for each pixel of the scene in the N (N − 1)/2 possible interferograms. Then, a minimum threshold γmin is fixed, and the coherence range between one and γmin is divided into M quality layers. Afterward, the time-averaged coherence map is calculated as γ=

2 N (N − 1)

N (N −1)/2



|γi |.

(13)

i=1

The quality of each pixel is labeled according to the layer γ where it belongs. The pixels fulfilling the condition γ ≥ γmin are selected and processed in a top-down quality order. The highest quality layer is processed first. The Delaunay triangulation technique is employed to connect each selected point to its natural neighbors. In order to retrieve the linear component of the deformation process, the differential-phase increments between neighboring pixels are fitted to a linear

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 6, NO. 1, JANUARY 2009

Fig. 4. Geocoded vertical deformation-rate map of the station district of Sallent retrieved by classical CPT using (a) hh and (b) vv polarizations information. γ has been estimated with a 5 × 5 pixel window, four quality layers (thresholds: 0.9, 0.8, 0.6, 0.4) have been used for the spatial integration of the deformation velocity increments for the estimation of the subsidence linear component.

model. As explained in [1], the deformation velocity v between two points Pm and Pn connected by a triangulation arc is estimated by minimizing the quality function Γm,n equal to

2



N (N −1)/2



2 jΔϕi (Pn ,Pm ) j2k0 vΔTi

Γm,n (v) = e − e



N (N − 1) i=1

(14) where Δϕi is the differential-phase increment between the two arc nodes in the ith interferogram and ΔTi is the temporal span between the corresponding SLC images. A relation between two pixels providing a value of Γ higher than a minimum threshold Γmin survives in the triangulation scheme; otherwise, it is deleted. The final map of the absolute deformation velocity is obtained by spatially integrating the increments v. At least one reference point of known deformation, called seed, is required to tie the floating solution. Once the integration step is finished, the next layer is analyzed, and the information retrieved at the higher level is fixed and considered as seed for the next layers. The process is repeated until the pixels belonging to the lowest quality layer have been processed. The polarimetric study of the urban area carried out in [10] revealed that trihedral- and dihedral-like reflection mechanisms dominate the scene, whereas the cross-polar backscattering contribution is much lower. For this reason, the classical CPT has been applied just to the copolar channels of [S] separately. The result in terms of radial deformation-rate map has been converted into equivalent vertical displacement according to the acquisition geometry and, finally, shown in Fig. 4. It is worth noting that a maximum vertical movement close to 5 cm/year has been estimated. This value, which indicates that the deformation process is speeding up with respect to the results published in [9], has been confirmed by IGC ground-truth measurements. Concerning the shape of the deformation retrieved from the GBSAR data sets and the map of Fig. 3, a good agreement can be observed. Slight differences, as the location of bowl center, are supposed to be partially related to shadowing effect affecting GBSAR acquisitions but also to possible modifications induced by the process acceleration. Finally, it is worth noting the isolated pixels characterized by a high deformation-rate are due to the temporal instability of urban targets highlighted in [10] that affects the polarization channels in a different way. Although these pixels fulfill the conditions imposed on γ and Γ parameters, the variation of their scattering behavior along the time axis leads to a different esti-

mation of v, depending on the chosen polarization. As a matter of fact, the position of red spots shown in Fig. 4(a) and (b) is not the same. V. P OLARIMETRIC CPT Under the hypothesis of temporal stationarity of the targets’ polarimetric response, the zero-baseline interferometric phase is independent of the polarization of the incident wave. In other words, if the scattering mechanism characterizing two linked pixels Pm and Pn remains constant in the two acquisitions generating the ith interferogram, the differential-phase increment between them may be expressed as Δϕi (Pm , Pn ) = ϕρi 1(Pm )−ϕρi 2(Pn ),

i= 1, . . . , N (N−1)/2 (15)

where the terms ρ1 , ρ2 are two generic polarizations employed for the estimation of the differential phase ϕi . Note that, in the classical CPT, it is always the case ρ1 = ρ2 . In this letter, the set of possible polarization states is reduced to the [S] channels, i.e., to hh, hv, and vv. Since perfect zero-baseline PolSAR data are collected by the GBSAR sensor, decorrelation effects are caused only by changes of the polarimetric scattering mechanism within the area used for the coherence estimation. It is worth recalling that a rigid displacement of the target does not contribute to decorrelate two SAR images. Not even atmospheric-phase artifacts affect the coherence parameter, as far as the medium can be assumed homogeneous. Therefore, the differential phase obtained from the ith pair of acquisitions is given by 4π Δri + ϕPOL arg(γi,l ) = i,l λ i = 1, . . . , N (N − 1)/2, l ∈ {hh, hv, vv} (16) where Δri indicates the rigid displacement and ϕl,POL is related to polarimetric changes due to target modifications. A high value of coherence in a specific channel of [S] guarantees that the polarimetric response of the target has remained stable in that polarization. Based on this idea, the selection at pixel level of the polarimetric channel providing the highest γ is expected to reduce ϕl,POL and to improve the quality of the retrieved radialdeformation information. In other words, it is possible to state that 4π Δri , γ M = max(γ hh , γ hv , γ vv ) ⇒ arg(γM,i )  λ i = 1, . . . , N (N − 1)/2. (17)

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TABLE II NUMBER OF RELIABLE PIXELS SELECTED IN THE SINGLE-POLARIZATION AND P OLARIMETRIC A PPROACHES . T HE T ERMS ∩ AND ∪ D ENOTE THE SET OPERATIONS OF INTERSECTION AND UNION, RESPECTIVELY

Fig. 5. Map of selected pixels and triangulation arc in the case of single-pol and polarimetric selections.

pixels’ differential phase improves. In fact, the information of pixels selected in both channels (hh ∩ vv) is often nonredundant because it gives the opportunity to discard a wrong estimation of the deformation process [red spots as shown in Fig. 5(a) and (b)] and to achieve a global improvement of the retrieved information quality. VI. C ONCLUSION

Fig. 6. Geocoded vertical deformation-rate map retrieved by the new polarimetric CPT.

Assuming that the hypothesis in (15) is correct, the selection criterion in (17) leads to a significant increase of the number of pixel candidates for the linear-fitting test. Besides, the number of spatial relations also increases. This is shown in Fig. 5, where an example of triangulation obtained in the single-pol case is compared with the result of the new polarimetric approach. For the sake of simplicity, just the copolar channels have been considered in the sketch. It is worth pointing out that, according to (17), the time behavior of each pixel is still described by the same polarization. This assures that the location of the scattering phase center within each resolution cell does not change. The main difference with respect to the classical CPT is that the differential-phase information of two linked pixels might come now from two different polarizations (green segments as shown in Fig. 5). The unique requirement is that no phase offset is present among the elements, and it can be achieved through an accurate polarimetric calibration of data sets. Once the multilayer polarimetric selection and the triangulation are performed, linked pixels are fitted to a linear model as described in the classical CPT approach. The process ends up with the integration of spatial increments. The deformation-rate map obtained in the polarimetric approach with the same parameters used for the singlepolarization study [Fig. 4(a) and (b)] is shown in Fig. 6. It can be noticed that the anomalous points detectable in the hh and vv maps have now disappeared. The polarimetric selection has allowed us to replace them with a more reliable estimation of the subsidence velocity. Moreover, the reconstruction of the critical zone and of the surrounding area has improved. In Table II, a quantitative comparison between the classical and the modified technique concerning the hot-area demonstrates the benefits of merging the copolar information. On the one hand, the number of reliable pixels increases, as shown by the hh ∪ vv column. On the other hand, the quality of

In this letter, the results of the one-year subsidence monitoring activity carried out by the RSLab of UPC in Sallent using an X-Band GBSAR system has been presented. The polarimetric capability of the sensor has allowed us to perform a comparison between single-pol and polarimetric approaches for advanced DInSAR applications. The results here presented constitute a first demonstration of the potentials of polarimetry for differential applications. It has been shown that the use of one polarimetric channel leads to a good description of the subsidence phenomenon, but the quality of the results is limited by the changes in the polarimetric scattering response of urban targets at X-band. Contrarily, a remarkable improvement has been obtained in terms of total number of reliable pixels selected within the scenario and quality of the retrieved deformation process when the whole polarimetric information is employed. R EFERENCES [1] P. Sanchez-Blanco, J. J. Mallorquí, S. Duque, and D. Monells, “The coherent pixels technique (CPT): An advanced DInSAR technique for nonlinear deformation monitoring,” Pure Appl. Geophys., vol. 165, no. 6, pp. 1167–1193, Jun. 2008. [2] A. Ferretti, C. Prati, and F. Rocca, “Permanent scatterers in SAR interferometry,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 1, pp. 8–20, Jan. 2001. [3] A. Aguasca, A. Broquetas, J. J. Mallorquí, and X. Fàbregas, “A solid state L to X-band flexible ground-based sar system for continuous monitoring applications,” in Proc. IGARSS, 2004, vol. 2, pp. 757–760. [4] L. Noferini, T. Takayama, M. Pieraccini, D. Mecatti, G. Macaluso, G. Luzi, and C. Atzeni, “Analysis of ground-based SAR data with diverse temporal baselines,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 6, pp. 1614–1623, Jun. 2008. [5] L. Pipia, X. Fabregas, A. Aguasca, and C. López-Martínez, “Atmospheric artifact compensation in ground-based DInSAR applications,” IEEE Geosci. Remote Sens. Lett., vol. 5, no. 1, pp. 88–92, Jan. 2008. [6] F. T. Ulaby and C. Elachi, Radar Polarimetry for Geoscience Applications. Norwood, MA: Artech House, 1990. [7] M. P. M. Hall, Effect of the Troposphere on Radio Communication. Exeter, U.K.: A. Wheaton & Co, Ltd., 1979. [8] K. Sarabandi, F. T. Ulaby, and M. A. Tassoudji, “Calibration of polarimetric radar systems with good polarization isolation,” IEEE Trans. Geosci. Remote Sens., vol. 28, no. 1, pp. 70–75, Jan. 1990. [9] J. Marturià, O. Mora, D. Xifre, P. Martinez, and A. Roca, “DInSAR techniques versus high topographic leveling surveys: The subsidence phenomena in Sallent,” in Proc. ECONGEO, 2006, pp. 53–57. [10] L. Pipia, X. Fabregas, A. Aguasca, C. López-Martínez, J. J. Mallorqui, and O. Moraline, “Polarimetric temporal information for urban deformation map retrieval,” in Proc. IGARSS, 2007, pp. 192–195.