Potential of SAR for monitoring transportation infrastructures: an analysis with the multi-dimensional imaging technique

Infrastructures provide services to citizens which are of paramount importance in modern society. Aspects related to increasing the safety of infrastructures are therefore fundamental. The interruption of services also has a major effect in terms of social impact and economic losses. Therefore, engineers working in this field are continuously facing the problem of developing systems which monitor the structural health and the safety conditions of infrastructures in general.

Concerning transportation, maintenance teams are currently responsible for monitoring the health of infrastructures. Scheduled and periodic inspections on most infrastructures are performed by costly and time-consuming manual and visual operations. Specific technologies which allow for measuring more accurate parameters, such as stiffness and damping, related to the 'state' of bridges, have recently been proposed. A current trend is towards so-called smart infrastructures, which integrate sensors and sensor networks (in some cases remotely controlled) that are capable of acquiring multi-parametric and multi-scale measurements. Distributed monitoring via fibre optics is an example of a powerful technology that meets some of those requirements (Chang and Mehta 2010).

Limitations in terms of accessibility, spatial extension of the measurements, costs of integration and remote operability, etc, generally apply to this class of in situ monitoring technique.

Remote sensing of infrastructures from satellites can provide a cost effective alternative to these traditional methods. Among the remote sensing systems, synthetic aperture radar (SAR) is a system that operates at microwave frequencies and allows all-time operability, i.e. it acquires information day and night and in almost any weather conditions.

A technique known as differential SAR interferometry (DInSAR) measures the deformation to within centimetre/millimetre accuracy from distances of several hundreds of kilometres. By exploiting a synoptic view of satellite sensors, DInSAR monitors large areas of several tens of kilometres and provides the main advances in the application of surface deformation monitoring for natural risk assessments. Satellites operating for several years, for instance ERS and ENVISAT of the European Space Agency (ESA), have regularly acquired data related to the Earth's surface. Modern DInSAR algorithms, such as coherent and persistent scatterer interferometry (CSI/PSI) (Berardino et al 2002, Ferretti et al 2000), analyse data collection over the same scene, acquired during different passes of the sensor.

Examples of applications for the monitoring of seismological or active volcanic areas, landslides, areas subject to underground excavation and water withdrawal etc, can be found in several papers from the past 15 years.

Due to these advantages, major international space agencies have pushed the development and launch of satellites equipped with SAR sensors. In recent years, technological improvements have concerned the development of new SAR sensors characterized by better performances in terms of both the spatial resolution, nowadays reaching the metre scale, and the reduction of the revisiting time to the order of a few days. This new generation of sensors is mostly based on radar sensors operating in the X-band, as in the case of the Italian Cosmo-Skymed four-satellite constellation and of the German TerraSAR-X/Tandem-X (TSX/TDX) mission. The enhanced imaging capabilities of these new SAR sensors result in an impressive increase in the density of monitored targets, both in urban and rural areas (Gernhardt et al 2010, Reale et al 2011b).

Parallel to the development of space technology from the point of view of sensor performance, research has been pushed toward the set-up of techniques that allow, as much as possible, for the reliable extraction of information from the data.

Multi-dimensional SAR imaging (MDI-SAR), also referred to as SAR tomography, is an example along these lines which was specifically developed with the aim of imaging and monitoring single structures, such as buildings, bridges, etc.

3D (space) (Fornaro et al 2005) and 4D (space/velocity) (Lombardini 2005, Fornaro et al 2009b, Zhu and Bamler 2010) imaging approaches, in fact, reconstruct the distribution of backscattering from the observed scene, by processing the whole (amplitude and phase) received data. It improves the monitoring quality in terms of better accuracy in the 3D target localization and monitoring and, by properly investigating the response of each pixel, it allows for a separation of contributions from different persistent scatterers, thus leading to an increase in the density of the monitored ground targets, with respect to classical interferometric processing.

The imaging capabilities of MDI-SAR are emphasized in the new generation of high resolution SAR products: in Reale et al (2011a) and Zhu and Bamler (2011a) it was shown that the impressive density of the points monitored allows a full 3D reconstruction of even single buildings and structures.

Besides the improved spatial resolution, the data acquired by the new X-band SAR sensors carries the information to be exploited further. In fact, the X-band wavelength (about 3.1 cm) is more sensitive to small displacements, such as those caused by the thermal dilation of ground targets. In this sense, the seasonal behaviour of man-made structures can be monitored. This phenomenon was already observed with C-band data acquired by the former satellites' generation (ERS and ENVISAT) (Perissin and Rocca 2006), but it is much more evident from X-band data due to the increase of the sensitivity associated with wavelength reduction. As a matter of fact, in Gernhardt et al (2010) and Monserrat et al (2011) the standard PSI approach has been extended to account for the thermal dilation, and results from experiments on real TerraSAR-X data have already been presented. The interpretation of the estimated thermal dilation map, with reference to the nature and materials of the targets, confirms the effectiveness of the results.

Along these lines, MDI-SAR processing has recently been extended to comply with such a higher sensitivity, thus providing an accurate measurement of thermal dilation (Reale et al 2012). In this work we focus in particular on the use of the extended MDI processing for monitoring transportation infrastructures to show the perspective of the application of the new X-band's very high resolution SAR systems in this framework. We therefore present an overview of the MDI processing technique and the results of an analysis carried out on data acquired by the TerraSAR-X system at 1 m of spatial resolution over the city of Las Vegas, USA.

The paper is organized as follows: in section 2 the basic concepts of SAR imaging and the use of interferometry for 3D image generation and monitoring of deformations are given. In section 3 the multi-dimensional SAR imaging and its extension to the robust detection of thermally dilating scatterers is briefly summarized. Then, a description of the real data set's characteristics is given in section 4. Finally, in section 5, the experimental results of the application of tomographic techniques are presented.

Imaging radars are systems that are used to reconstruct the scene from the backscattering property, that is, the ability of ground targets to scatter back the radiation transmitted by the radar. By using large bandwidths, reaching the order of hundreds of megahertz, modern sensors distinguish targets in range (distance) with a resolution degree that reaches the metre/sub-metre scale. In addition to this high range resolution, a high azimuth resolution capability of the final 2D images is achieved by synthesizing antennas in the order of kilometres through the exploitation of the intrinsic motion of the platform along its orbit.

As in any electromagnetic coherent system, the phase information is related to the travelled path, which is the distance of the scene from the sensor in the imaging radar system. The phase can therefore measure distances with an extremely high accuracy, i.e. on the order of a fraction of a wavelength. SAR interferometry (InSAR) is a technique that, by exploiting at least two SAR images, retrieves the topography of the observed scene, thus providing the measurements of the 3D distribution of ground scatterers. The key principle of SAR interferometry is the use, as in classical stereometric systems, of a parallax in the viewing geometry: access to the phase provides an extremely high sensitivity of the system in sensing distance variations. For 3D reconstruction the two images are typically acquired simultaneously or almost simultaneously; see for instance the Shuttle Radar Topography Mission (SRTM) and Tandem-X missions. In the case of DInSAR, by exploiting the phase difference of images acquired over successive (repeated) passes and by removing the topographic contribution via an external digital elevation model (DEM), it is possible to measure the displacements occurring at each acquisition epoch along the radar's line-of-sight (LOS). Since the accuracy of radar in estimating distance is in the order of a fraction of wavelength, DInSAR can estimate movements with sub-centimetre accuracy using C- or even X-band radars.

Classical DInSAR has been extensively applied to detect displacements related to many deformation phenomena, mainly of a volcanic and seismic nature. However, in order to fully exploit the potential of the SAR technology in measuring deformation with centimetre/millimetre accuracy, two or a few images are typically not sufficient: this is because of the presence of additional disturbing contributions to the formation of the measured phase.

The measured phase difference Δφ between two acquisitions of a differential interferometric system operating at a wavelength λ is, according to the following equation, composed of several factors:

$$\begin{equation} \Delta \varphi = \frac{{4\pi }}{\lambda }\delta r = \frac{{4\pi }}{\lambda }\delta r_d + \varphi _z + \varphi _a + \varphi _o + \varphi _n , \end{equation} \tag{ 1 }$$

where δr_d is the distance (range) variation induced by the deformation signal, φ_z is a residual phase corresponding to the difference in the actual localization of the scatterer with respect to the external DEM, φ_a is associated with propagation delays through the atmosphere, φ_o is associated with orbital inaccuracies and finally φ_n is associated with the noise. The availability of on-board GPS systems significantly mitigates the effects of orbital errors. The atmospheric component typically has a variation over the scene of the order of a few (1–4) centimetres with a spatial correlation over a few hundreds of metres. In the cases where interest is on a low scale (coarse resolution) analysis and the deformation signal is predominant, such as for instance in the observation of deformation related to earthquakes and volcanic activities, it suffices to use DEM available for free on the web (for instance the DEM derived by the SRTM, referred to as the SRTM DEM) to obtain measurements which are valuable from a geophysical point of view. Nevertheless, to measure subtle (up to a millimetre per year) displacements and to handle the problem of monitoring ground scatterers at full resolution, techniques have been developed which are based on the use of several images acquired over the same scene. In fact, by exploiting multiple acquisitions with a diversity of spatial baselines and times, the 'phase firms' of the different components can be deterministically or stochastically characterized and estimated directly from the received data. Besides achieving a high accuracy with respect to the classical two- or few-pass interferometry, modern multipass differential SAR interferometric techniques, based on processing a large set of multitemporal data, have the advantage of generating very accurate deformation time series and therefore, achieving a regular monitoring of the deformation of the observed scene. These techniques, known as advanced DInSAR (A-DInSAR) techniques, also overcome most of the limitations of the standard single-interferogram approaches, such as temporal and geometric decorrelation and the presence of phase patterns associated with the atmospheric propagation delay, and thus increase the measurement accuracy from a centimetre up to a millimetre.

Depending on the processing methodology, A-DInSAR can be divided into two classes: (temporal) PSI and (spatial) CSI, as defined above. The first class encompasses all the approaches that operate at full resolution and identify scatterers by measuring the multitemporal coherence degree. Monitored pixels correspond to scatterers whose size is lower than the system resolution and typically correspond to objects on man-made structures, such as buildings, bridges, dams, water-pipelines and antennas, as well as to stable natural reflectors (e.g. exposed rocks) (Ferretti et al 2000). CSI is, on the other hand, the direct extension of the classical two-pass DInSAR technique. In this case coherent scatterers are identified by analysing stacks of interferograms, which are properly multilooked (i.e. spatially averaged) to extract the coherent parameters describing the spatial degree of the coherence of scatterers, and also improve the quality of the phase signal. CSI techniques are typically used to monitor deformation over large areas, using a small scale (i.e. coarse resolution) (Berardino et al 2002).

The approach followed in this work is specifically designed to monitor the deformation of surface scatterers at full resolution and is based on a two-step approach, schematically reported in figure 1. The first stage consists of the application of a CSI approach to the received data. In our case we used a specific upgrade (Fornaro et al 2009a) of the approach known as the small baseline algorithm (Berardino et al 2002) which is applied to estimate the background deformation signal occurring on a small scale and the atmospheric phase contribution: both components are used to phase calibrate the full resolution data for subsequent processing. In particular, the approach in Fornaro et al (2009a) exploits a model for the phase differences between adjacent pixels to support the phase unwrapping step, which is the most critical part of the processing stage. A similar approach is also adopted in Mora et al (2003).

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The second step consists of an approach based on a tomographic analysis, which uses the amplitude and the phase of the received signal, to identify, localize and monitor scatterers at full resolution: more details on this technique, which specifically monitors infrastructures, are provided in the following section.

MDI is founded on the principles of tomography: acquiring images with angular diversity. Multipass interferometric datasets are characterized by coherent properties: 3D imaging exploits the characteristics of such a dataset which is acquired from different positions along the slant height (elevation) direction, orthogonal to the radar's LOS. In particular, similarly to the azimuth focusing, it synthesizes an antenna also along the elevation direction, carried out during the azimuth focusing. This provides images which are characterized by a high resolution also along the third direction, the elevation, which is not accessible in a standard 2D image, corresponding to a single SAR acquisition. Scatterers showing a good degree of temporal coherence can be identified in such 3D images by analysing the peaks of the elevation focused backscattering profile (Fornaro et al 2005) in each azimuth and range pixel. Therefore, such scatterers can also be monitored during the time it takes to detect the presence of a slow deformation. Space/velocity (4D) imaging techniques, which are an extension of 3D imaging, can also in fact be applied to measure the deformation parameters (velocity spectrum) of any temporal coherent (persistent) scatterer in the focused 3D space (Lombardini 2005).

MDI imaging has been shown to outperform the classical persistent scatterer's interferometric approach which is aimed at monitoring the deformation of scatterers at full resolution. Specifically, in De Maio et al (2009) theoretical and experimental results on both simulated and real data have shown that the use of an imaging approach that exploits (as in the tomographic case) the phase as well as the amplitude information performs better in the detection of persistent scatters and in the estimation of their localization and deformation parameters, with respect to techniques based only on the use of the phase signal, such as PSI (Ferretti et al 2000).

In addition to this, complex scenarios, such as urban areas and infrastructures, are typically characterized by the presence of a high density of vertical structures which generate interference, between the response of scatterers among different structures (a phenomenon known as layover). Scatterers located at different heights in layover areas may share the same distance from the sensor and contribute to the signal measured in a pixel; see figure 2. This phenomenon is extremely evident in data characterized by very high spatial resolutions, such as those acquired by the recently launched X-band systems (TerraSAR-X and COSMO/Skymed), because of their increased sensitivity to scatterers distributed on the surface of ground structures such as building façades, roads, bridges, etc.

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Classic interferometry is not able to manage this interference due to a lack of proper models; however, tomography can efficiently separate the interfering targets by distinguishing the different peaks in the 3D (or 4D) focused amplitude.

Recent progress in tomographic-based SAR processing has concerned the ability to measure whether thermal dilation affects ground structures. The reduced wavelength makes, in fact, the new X-band SAR sensor more sensitive, and hence able to appreciate small movements, such as the deformation caused by thermal dilation. In this sense, by extending the deformation model, typically made of the linear temporal term with a new one which is linearly related to the temperature of the area at the instant of acquisition, tomography is extended to a 5D imaging given by the 4D reconstruction plus a thermal dilation coefficient, measured in cm K^–1 (Reale et al 2012, Zhu and Bamler 2011b).

An overview of the key features of tomographic processing are summarized here: more details can be found in Fornaro et al (2005, 2009b), Lombardini (2005) and Zhu and Bamler (2010). For the tomographic processing of multipass data we use the following model for the data g_n which represents the measured signal in a fixed pixel, collected at time t_n during different passes of the sensor:

$$\begin{equation} g_n = \int {\gamma _s ( s )\,{\rm e}^{{\rm j}2\pi \xi _n s}\, {\rm e}^{{\rm j}\frac{{4\pi }}{\lambda }( {d_n + kT_n } )} \,{\rm d}s,} \end{equation} \tag{ 2 }$$

where T_n indicates the temperature distribution, k is the thermal dilation coefficient, d_n are the deformations depurated from the thermal component, s is the elevation and γ_s(s) is the function that describes the backscattering distribution along the elevation; ξ_n = 2b_n/(λr₀) is a parameter related to the spatial separation of the nth acquisition which determins the angular diversity, where b_n, λ and r₀ are the baseline of the nth acquisition with respect to a reference acquisition, the working wavelength and the scene centre's distance from the sensor, respectively.

The deformation term in (2) can be expanded in Fourier harmonics depending on the velocity v and the thermal dilation coefficient k, ${\rm e}^{{\rm j}2\pi \eta _n v}$ and ${\rm e}^{{\rm j}2\pi \zeta _n k}$ with η_n = 2t_n/λ and ζ_n = 2T_n/λ, t_n and T_n being the temporal and temperature distributions, respectively. Accordingly, from (2) we have

$$\begin{equation} g_n = \int\limits_{}^{} {\gamma ( {s,v,k})K( {\xi _n ,\eta _n ,\zeta _n } )}\, {\rm d}s\,{\rm d}v\,{\rm d}k \end{equation} \tag{ 3 }$$

thus providing an integral relation involving a function γ(s, v, k) which measures the backscattering distribution along the elevation velocity and thermal dilation space through a kernel K associated with the elevation velocity and thermal dilation Fourier basis.

Deformation of targets which also exhibit possible thermal dilations can be carried out by inverting (3): the detection of persistent (i.e. monitorable) scatterers is achieved by analysing the peaks of the amplitude of the estimated multi-dimensional backscattering function γ(s, v, k).

The real dataset exploited in this work is composed of 25 images acquired over the city of Las Vegas, USA, by the TerraSAR-X sensor during ascending orbits of the satellite. The sensor parameters are summarized in table 1. The images are acquired in the high resolution spotlight image mode of the TerraSAR-X sensor, which reaches spatial resolution at a ground level of 1.1 m in azimuth (along-track) and 0.77 m in ground range (cross-track) directions, respectively. The spaceborne platform flies at about 619 km from the scene's centre with a velocity of about 7000 m s^–1. The counterpart of such an impressive resolution is a limited extension of the imaged area of about 5 × 10 km².

The acquisitions cover a time interval spanning about 13 months, from February 2008 to April 2009. Almost all the images are acquired with the minimum repeat cycle (11 days) of the TerraSAR-X mission, i.e. the minimum time interval between two consecutive acquisitions over the same area with identical acquisition characteristics for interferometric purposes.

The spatial separation, described by the perpendicular baseline which plays a key role in accuracy estimation, is limited within an orbital tube whose diameter is about 200 m. Table 2 provides the parameters describing the dataset characteristics.

The dataset was first investigated by a 4D tomographic process, covering most of the area imaged by the sensor and corresponding to the centre of Las Vegas. The result of this processing is reported in figure 3, and shows the estimated residual topography (with respect to the subtraction of the external DEM, in this case the SRTM); colours are associated with the estimated topography, and allow for easy recognition of the shape of the main hotels and buildings, and generally of ground structures such as roads, bridges, etc. The black area in the bottom left part of the image has been subject to a massive rebuild during the acquisition interval: this explains the lack of measurement points.

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A deeper investigation with the 5D imaging technique, which is characterized by higher computational complexity with respect to 4D imaging, is concerned with the area highlighted in the white box. This area is relevant to a part of the Las Vegas monorail: a 6.3 km elevated monorail train system connecting many hotels and casinos along the famous Las Vegas Strip. In its higher part, the elevation is about 18 m. In figure 4 a picture taken from Google Earth of the processed area and the corresponding SAR amplitude image, after temporal multilook of all 25 images, are shown.

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The results of the 5D imaging are shown in figure 5, corresponding to the estimated residual topography, deformation mean velocity and finally, the thermal dilation coefficient due to thermal deformations. It has to be noted that measured deformations are the component of the vector deformation along the radar's LOS. Furthermore, interferometric and tomographic processing of data, acquired along only ascending or descending passes of the sensor, does not allow for the measurement of possible horizontal deformation components along the sensor's trajectory (approximately south–north). The vertical and east–west deformation components can be estimated by combining the components carried out by processing both the ascending and descending datasets.

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The first point of interest is the very high density of monitored pixels both on the monorail and surrounding structures. Concerning the estimated topography (left image in figure 5), the monorail shares approximately the height of the left structure, which is higher than that of the surrounding areas (see the top and bottom part of the image which are in cyan, while the monorail is green).

From a deformation point of view, the whole area does not exhibit any linear subsidence, as shown in the middle image in figure 5, while the monorail is affected by a substantial thermal dilation. Particularly, it is interesting to note the different behaviour of the estimated thermal dilation affecting the upper and lower curves of the monorail track. More specifically, in the first case there is a component indicating a reduction of the range distance from the sensor, which is looking from the left side, thus indicating an expansion toward the left, whereas for the lower curve the behaviour is opposite, i.e. the track is dilating toward the right. This is consistent with the fact that MDI–SAR measures only the deformation along the LOS.

After geocoding, this last result has been imported into Google Earth: in figure 6 a picture representing the 3D view of the detected targets, coloured according to their estimated thermal dilation coefficient, is shown. Note again the very high density of measurement points collected along the monorail path.

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Interferometric SAR processing can monitor accurately the deformation components of targets along the radar's LOS. The new generation of X-band SAR sensors provides a technological advance which is fully exploited in the context of multipass SAR interferometry by tomographic processing, first of all by the improved resolution which allows for the precise monitoring of even single structures. These data are particularly important in that they enable applications which were clearly not possible with the medium resolution data of the former satellite generation. Moreover, the lower wavelength makes these sensors more sensitive to small deformations, even those caused by thermal dilations. Processing techniques must therefore be developed in order to treat and extract this additional information.

In this work we present the results of the application of extended tomographic processing, which accounts for the presence of deformations associated with thermal dilation, to a real 1 m resolution TerraSAR-X dataset. The results allow for an appreciation of the noticeable amount of information that can be retrieved for infrastructure monitoring. We have investigated an application to the reconstruction and monitoring of the Las Vegas monorail, highlighting also different behaviour along the same structure related to different projections of the thermal dilation vector along the radar's LOS.

This work has been partially funded by the project 'Integrated System for Transport Infrastructures Surveillance and Monitoring by Electromagnetic Sensing' (ISTIMES), 7FP. We are grateful to Professor Bamler and Dr X X Zhu for providing us with the 1 m resolution TerraSAR-X data.