Multidimensional imaging with ERS data

Gianfranco Fornaro(1), Fabrizio Lombardini(2) , and Francesco Serafino(1)

1IREA-CNR Via Diocleziano,328 I-80124 Napoli (Italy) + 39 081 570 7999 Fax. +39 081 570 5734

{fornaro.g, serafino.f}@irea.cnr.it

2Dipartimento di Ingegneria della Informazione Università of Pisa Via G. Caruso, 14 56122 Pisa (ITALY)

+ 39 050 2217675 Fax. +39 050 2217522 e-mail: f.lombardini@iet.unipi.it

Abstract—The work aims to present results of a multidimensional imaging experiment carried out by processing long-term repeat pass ERS data. In particular we address the topic of full 3D reconstruction, and we show the capability of ERS system to separate, using multibaseline data, different scattering centres in the elevation direction, interfering in the same resolution cell. Furthermore, first result of the extension of the 3D imaging to time will be shown to demonstrate the potentialities of SAR systems to monitor slow moving interfering scattering centres.

Keywords: Multibaseline Interferometry, 3D SAR Tomography.

1. INTRODUCTION SAR archives are filled by data sets collected over the same scene and acquired with some degree of diversity in

time, observation angle, polarization, frequency, acquisition mode, etc. ERS-1 and ERS-2, both far exceeding their planned lifetime, have acquired worldwide a huge number of SAR data. Future missions planning involve the use of formations of cooperative, multi-purpose satellites (f.i., Cartwheel, Pendulum) and thus the number of images relative to the same scene is expected to exponentially grow in the future. Research in the SAR field is thus pushed towards the derivation of techniques and algorithms aimed at jointly using the multidimensional information lying in the available data cubes to produce new and/or more objective/accurate/reliable measures. Similarly to multipass Differential Interferometric SAR (DInSAR) [1] and Permanent Scatterers (PS) analysis [2], that allow accurate monitoring of ground slow moving targets, key diversity features exploited in the techniques here described of advanced multidimensional processing are observation angle (baseline) and time.

A main limitation of SAR interferometry based techniques is due to the possible penetration of the transmitted radiation inside the imaged ground objects. In fact, SAR images represent projections of the scene back-scattering characteristic onto the azimuth and slant-range plane. As a result, each azimuth-range pixel in a standard 2D SAR image may collect the response of several targets aligned along the third dimension (elevation). Consequently, retrieval of physical parameters or image interpretation can be ambiguous. In the case of ERS system, as it operates at C-Band, penetration of the radiation under the surface is generally negligible or limited to few decimeters (desert areas). Only in case of semi transparent media (sparse forest) or dry ice the penetration depth can reach the order of meters or tens of meters (for ice). However subsurface penetration is not the only mechanism that can generate target interference within azimuth range pixels and thus limit the applicability of techniques derived from standard 2D imaging, such as multipass DInSAR and standard PS (unless higher order analysis are carried out to mitigate the consequent decorrelation [3]). There are at least two other fundamental mechanisms that may occur when scattering is limited to surface: interference of response from sidelobes of strong targets and layover. The latter, due to the slant nature of the imaging geometry, may be a limiting factor in the imaging of scenes characterized by steep topography, such as mountainous regions, urban areas and complex targets (bridges, dams, etc.).

3D SAR Tomography is an advanced technique that allows overcoming such limitations [4]-[6]. In particular, by exploiting the multibaseline nature of the data, a large array (more than 1 kilometer for the ERS system) may be synthesized in the elevation direction. Focusing of the data acquired over such large array, or better profiling of the backscattering power along the elevation direction, may be achieved, with few meters of resolution, and thus also to distinguish scattering from a limited number of scattering centres.

A main difficulty in implementing this technique is related to the fact that acquired data are sampled in space with a non-uniform baseline distribution. This fact introduces a degree of ill conditioning in the inversion (focusing) process. Singular Value Decomposition (SVD) allows carrying out a regularized inversion [4], that comply the introduction of a priori knowledge on the extension of the scene in the elevation direction, able to achieve a good compromise between uneven pass distribution distortions, robustness to possible array miscalibration and super-resolution capability. More sophisticated algorithms, developed in the context of adaptive spectral analysis, such as Capon, can reach much higher resolution degrees compared to SVD, but requires spatial averaging (multilooking) to evaluate local statistics and exhibits more sensitivity to miscalibration problem. Additional difficulties, arising when processing multibaseline data sets acquired (as for the ERS case) with repeated passes of the satellite, are due to atmospheric variations and temporal decorrelation. As for PS, the former may be mitigated by exploiting their spatio-

temporal correlation properties, even by using simple filters; the latter, generally limited in urban regions, may irreversibly impair the 3D imaging process and could be overcome only by using a formation of cooperative satellite data which acquire simultaneously the multibaseline stack. The multitemporal data nature of repeat pass acquisitions coupled to the availability of different baselines may be, on the contrary, a key factor for implementing even more advanced techniques, able not only to discriminate different targets within the same resolution cell, but also to monitor their slow movements, even at different velocities. Such technique, recently proposed in the literature, is known as Differential SAR Tomography or 4D (3D + Time) imaging [7].

This work gives a brief overview of the key aspects of 3D and 4D imaging. This includes the description of the processing steps necessary to calibrate spaceborne long-term data prior to the application the inversion techniques that bring to the mapping of the scattering power in the elevation direction and/or in the elevation/time plane. We also present the results, some of them very preliminary, achieved by processing real multipass data acquired by the ERS 1 and ERS-2 satellites over the urban region of Napoli. Simulation results regarding multitemporal acquisitions with systems equipped with multiple antennas are also discussed to figure out the potentialities associated to the advanced imaging concept here addressed, with respect to future missions planning.

2. MULTIDIMENSIONAL SAR IMAGING We refer to the general multipass-multibaseline acquisition geometry depicted in Fig.1 where, mnS , represents

the antenna position along the elevation (axis s) and the index n, m the pass- and antenna-number position in a multipass multistatic scenario of a total of M passes and N antennas (in each pass) [7]; x, r and z are the azimuth, range and height. The received signal from the (n, m) pair, due to a collection of point target located at x and r coordinates on the ground, distributed along the elevation direction (s) that may move with mean velocity v, and is given by the following relation:

( )∫ ∫− −

−=

max

max

max

max

,4exp),(ˆ ,,

v

v

s

s

mnmn dsdvvsrjvsλπ

γγ (1)

where λ is the wavelength of the probing radiation, ),(, vsr mn is the distance between the n-th antenna at the m-th

acquisition time and the scatterer point on the ground, ),( vsγ is the unknown elevation-velocity reflectivity function whose reconstruction is the purpose of this work, smax and vmax are the admissible elevation and velocity semi dimensions that we suppose a priori known (i.e., fixed).

2.1 Three Dimensional SAR Imaging (SAR Tomography) If we assume the mean velocity v to be equal to zero and compensate the intrinsic quadratic phase variation

along the array (deramping) [4], data collected in a monostatic scenario at different antennas from fixed ground targets can be expressed as:

∫−

⊥

=

max

max

22exp )(s

s

nn dsbrsjsg

λπγ (2)

where nb⊥ is the n-th orthogonal baseline with respect to a master reference.

Equation (2) shows that the data acquired by the different antennas are the samples of the one-dimensional elevation reflectivity spectrum. In the hypothesis of uniformly distributed baselines, profiling of the scattering power along elevation direction may be simply achieved via an inverse DFT (beamforming). Unfortunately in the real case data are hardly uniformly sampled and beamforming may give poor reconstruction performances in terms of sidelobes [4]-[6].

To improve the quality of the reconstruction of ( )sγ in the presence of highly uneven baseline distribution, inversion of (2) may be carried out by applying regularized inversion well known in the context of linear inverse problem. In particular, we can exploit the Singular Value Decomposition (SVD) tool. The result of the inversion

provided by the SVD is ( ) ( )∑ =

−=L

k kkk svs0 Y

1 ,ugσγ , where g is the vector collecting the data, kσ are the singular

values of the operator in (2), kv and ku are the orthonormal basis for the subspace of the unknown objects and for the range of the operator, respectively, Y is the data space. The truncation index L must be properly chosen in order to trade off resolution and sidelobes in the regularized inversion. Alternatively, one can resort to Capon adaptive beamforming in place of the classical beamforming. It allows data-dependent sidelobe cancellation by rejecting interference coming from other elevation directions than the selected, as sensed through the information in the array spatial correlation matrix. This method does not rely on any a-priori information, yet it has to be cast in a coherent multilook framework to allow spatial correlation estimation. The result of the inversion provided by Capon is given

by ( ) ( ) ( )[ ] 11ˆ −−= sss gH aRaγ , where ( )sa is the array steering vector, and gR̂ is the correlation matrix estimate from a

multilook set of vector data ( )lg , l=1,2,..,NL, with NL the number of looks.

Fig. 1. Multipass multistatic acquisition geometry.

2.2 Four-Dimensional SAR Imaging If we relax the hypothesis of the absence of ground target movements, the received signal, again after proper

compensation of quadratic terms, is given by:

∫ ∫− −

⊥

+=

max

max

max

max

222exp ),( m,

v

v

s

s

nmn dvdstvbrsjvsg

λλπγ (3)

where, with respect to (2), the mt term represents the acquisition time and vmax the semi dimension of the searched velocity interval. Parallel to (2), (3) shows that the signal acquired by the different antennas at different times represents samples of the two-dimensional elevation-velocity reflectivity function spectrum. The problem in (3) may be still seen as the inversion of a linear operator. Also in this case the use of (two-dimensional) SVD tool allows to invert the operator and to reconstruct the unknown (two-dimensional) function ),( vsγ .

3. DATA CALIBRATION The expressions (2) and (3) represent the received signal from the n-th antenna at the m-th pass in an ideal case.

Real data require proper pre-processing for correct implementation of the 3D and 4D techniques, which can be critical for data acquired over large temporal and spatial intervals. First of all precise co-registration of the data stack is required to multidimensional processing of the data relative to the same ground pixels. Accurate registration is a challenging issue due to large temporal and spatial baseline spans. In our case the technique is based on the use of orbital information and an external reference DEM [8] and refinements based on the use of the response of Isolated Point Scatterers (IPS) that are characterized by a high level of signal to clutter (SCR) ratio and thus a high coherence even at large baselines.

Fig. 3. Left: spatial baseline vs. the temporal baseline (in years) and the tree obtained by using the MST algorithm related to the used real data

set. Right: amplitude image (a) and interferograms associated to the compensation steps, before (b) and after (c) deramping, after residual topography and deformation compensation (d) and after atmospheric correction (e) for a selected image pair.

After registration, the data stack is phase compensated. In particular the first phase compensation step eliminates the quadratic phase distortion in all images: in our case it steers also the multibaseline array with respect to a local topography. This procedure is carried out again by exploiting the external DEM and orbital information. As a

(a) (b) (c) (d) (e)

consequence, the final elevation (height) distribution of the tomographic reconstruction is referred to the local topography of the external DEM unless this signal is reinserted after elevation focusing.

The second step is the compensation of the terms related to possible inaccuracies of the external DEM and, in case of multipass acquisition as for the ERS system, associated to the presence of ground deformation. Both terms can be directly estimated from the data stack via standard multipass interferometry [1] or PS [2]. The last phase compensation step regards the accommodation of atmospheric variation in the different acquisitions. If not available, this signal can be estimated from interferograms working stepwise with image pairs according to a Minimum Spanning Tree (MST) strategy, as proposed in [9]. In other words we chose pairs in the baseline time plane in such a way to minimize temporal and baseline separation and thus limit temporal and baseline decorrelation effects. Figure 3 left shows the tree (nodes represent the acquisitions and branches their interferences) obtained by considering the real data set where experiments have been carried out. It is possible to change the structure of the tree by modifying some temporal and/or spatial parameters of the system to trade off between the temporal and the spatial separation. Figure 3 right shows, together with the amplitude image (a), the images resulting from the three phase compensation steps. The interferogram (b) after deramping (c) and residual topography and deformation compensation (d) does not more exhibit any deformation pattern, but rather phase variations caused by the atmosphere. Also this contribution can be eliminated form the final interferogram (e).

Fig. 4. Amplitude and phase behavior and reconstruction of a double scatterer: dot lines are the ideal response of two targets located at -12m and

4m.

4. EXPERIMENTAL RESULTS Multidimensional imaging has been applied to a real data set of 63 images acquired over the city of Napoli (Italy)

by the ERS 1 and ERS-2 sensors between 1992 and 2004 on descending passes; track 36, frame 2781. The temporal span is of 12 years whereas the baseline span is about 1700m, with a mean baseline separation almost 28m. The first experiment regards the profiling of the scattering in the elevation direction. The Raileigh resolution ([4]-[6]) in elevation is about 14m in elevation (5.5m in height) whereas the unambiguous elevation span (2smax)is of 830m (335m in height).

Many single and multiple scattering centres where located in the image. Figure 4 shows a result obtained on a selected pixel, where the presence of two scattering centres with almost equal power is clearly demonstrated by the oscillating behavior of amplitude plot vs. the orthogonal baseline (Fig. 4a). Further confirmation of such effect is given by the appearance of regular 180° phase jumps between oscillating lobes (Fig. 4b). Superimposed to the real amplitude and phase measures, the ideal amplitude and phase measure obtained with two scatterers at -12m and 4m is also show in dot line. Finally Fig. 4c shows how well the real elevation scattering profile (continuous line) fits the ideal response of the two scatterers (dot line).

In the next figure we consider 3D imaging of extended areas; in particular the analyzed structure is the S. Paolo stadium. The tomographic reconstruction of the stadium is shown in 6 azimuth-height sections at different range: the overall structure is well distinguishable with high scattering points located in the flank of the stadium: also the shape of the metallic coverage built in 1990 for the soccer world-championship is clearly visible. The second experiment regards the verification of 4D imaging capabilities of ERS system, that is to distinguish and monitor different targets in the same azimuth resolution cell. This time we consider the subsiding area of Vomero in the city of Napoli: the multilook image relative to the selected area carried out by averaging the 63 SLC images at full resolution is shown in the top of Fig. 6.

a)

b)

c)

Fig. 5. Six tomografic section (azimuth-elevation) of the San Paolo stadium at the different ranges shown in the multibaseline average image at

rightmost column. First, second and third column are the results obtained with SVD, 5 azimuth look SVD, and 5 azimuth look Capon.

Fig. 6. Top: multibaseline average image obtained by averaging the 63 images over an area including Vomero. Bottom: distribution of the scattering along the elevation (vertical) and velocity (horizontal) directions.

We inverted the operator in (3) and we selected three points whose location is shown in the top of Fig. 6. The first point is outside the subsidence area whereas points 2 and 3 are both moving at a rate of approximately 6 mm/yr with the last one showing two scattering centres. It should be pointed out that, due to the very sparse nature of the data in the baseline time domain, the singular values are, differently from the 3D reconstruction experiment, almost constant. Accordingly performances of the SVD reconstruction are very similar to a classical beamforming.

-80m

0

80m

-1.4cm/yr 1.4cm/yr0 -1.4cm/yr 1.4cm/yr0 -1.4cm/yr 1.4cm/yr 0

321

In order to figure out the potentialities offered by systems with simultaneous acquisition we have carried out a very simple experiment. In particular, with reference to the real ERS passes and we simulated data acquired from multistatic systems. The investigated scene velocity semi-extension maxv is fixed to 6cm/yr. In Fig. 7 we shown the spatial and temporal baseline distribution for three different simulation cases, in particular Fig. 7a is related to the case of existing satellite where one antenna is available for each pass; Fig. 7b refers to an ideal case in which we assumed to have 63 antennas that simultaneously acquire data with 63 different passes (a very unpractical case here used only as reference limit); Fig. 7c considers the case of 3 antennas and 63 passes centered around the real acquisition of the ERS system; this case is associated to a realistic future system with a master satellite and only two receive micro-satellite that simultaneously acquire data at two different baselines.

Impulse response with an additive noise of 15dB in the elevation velocity plane of these three configurations are shown in Fig. 8: here we realize how critical can be sidelobes in the case of multiple passes of single antenna system (left) and how even only two different baselines allows having a response (right) well approximating the ideal but impractical limit (middle). Note that in the latter case, singular values exhibit a degree of variation thus allowing SVD to perform better than beamforming.

Fig. 7. Acqusition for the three simulation cases. Left: 63 non uniform passes of a single antenna (real passes of ERS). Middle: ideal limit case of

63 passes and 63 antennas. Right: 63 non uniform passes of a formation of 3 satellite centered aroun the locations of the left distribution.

Fig. 8. Reconstructions of the simulated data for the three different acquisition grid of Fig.. 8

5. ACKNOWLEDGMENT The work is part of the project of the Regional Center of Competence, “Analysis and Monitoring of the

Environmental Risk” supported by the European Community on Provision 3.16.

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a b