1.1 Synthetic aperture radar imaging

Chapter 1

Introduction

1.1 Synthetic aperture radar imaging

Imaging sensor systems are classified as passive and active. While passive systems exploit radiations naturally emitted or reflected by the Earth surface, active systems are equipped with a transmitter, and they receive the signal backscattered from the illuminated surface [1].

Among imaging active sensors, a predominant role is played by radar systems, which operate in the microwave region of the electromagnetic spectrum. These instruments allow day and night and all-weather imaging, which constitues an important prerequisite for the continuous and global monitoring of the Earth surface. The main limitation of these sen- sors (generally referred to as real aperture radars) is the poor resolution achievable in the azimuth direction, which is proportional to the ratio between the sensor-to-surface distance and the sensor antenna dimension. To overcome this limitation, the concept of the synthetic aperture was patented by Carl Wiley in 1965, according to which a very long antenna can be synthesized by moving a small one along the flight of the radar platform. Early spaceborne missions then demonstrated that synthetic aperture radar (SAR) is able to reliably map the Earth surface and acquire information about its physical properties. Nowadays, SAR remote sensing is an established technique finding many applications to geophysical problems, either by themselves or in conjunction with data from other remote sensing instruments. Examples of such applications include land use mapping, vegetation, biomass measurements, and soil moisture mapping [1, 2].

Basically, the large bandwidth of the transmitted signal, typically a long chirp, assures a short pulse duration at the output of the receiver matched filter, enabling the high range resolution. Moreover, coherently (i.e., amplitude and phase) integrating the compressed pulses from several antenna locations, the output of the synthetic antenna is produced, with a very narrow beam width and thus guaranteeing the high azimuth resolution. So doing, the SAR imaging process provides a geometric projection of the 3-D radar reflectivity func- tion γ (x, r, z) into 2-D cylindrical coordinates (x, r), followed by a 2-D convolution with the system point-spread function (PSF) f (x, R) [3, 4]:

g (x, r) =

 _Z

γ (x, y, z)Rd θ · exp



− j 4 π λ ^r



⊗ ⊗ f (x,r) (1.1)

Chapter 1 - Introduction

where g (x, r) is the complex SAR image, x is the along-track or azimuth direction, r is the slant range, z is the vertical height, r is the slant range (the distance of the point scatterers to the SAR sensor), θ is the elevation (look) angle, and λ is the wavelength. As shown in equa- tion (1.1), due to the projection, information about the spatial structure and the location of the scatterer gets lost. For many applications, this height-dependent distortion adversely affects the interpretation of the imagery. As a consequence, the development of SAR interferometry techniques (InSAR) has enabled the measurement of the third dimension.

1.2 SAR interferometry

To solve the ambiguity in height intrinsic in a SAR image, it is necessary to introduce some kind of diversity. SAR interferometry (InSAR) introduces this diversity to provide us with information about the missing dimension, the elevation angle θ . The first application of interferometry to radar dates back to 1969 by Rogers and Ingalls to solve firstly the am- biguities arising in the radar observation of the planet Venus, then for the measurement of the Moon topography [2]. The first report of an InSAR system applied to Earth observation was by Graham in 1974 [5]. He equipped a conventional airborne SAR platform with an additional physical antenna displaced in the cross-track plane from the conventional SAR antenna, forming an imaging interferometer. In a few words, the phase difference between the received signals at the two antennas (or channels in the interferometry jargon) is related to the geometric path length to the image point, which depends on the topography . The Graham interferometer mixes the two signals, and records the amplitude variations induced by the beating patterns of the relative phase of the two signals. The resulting amplitude fringe variations track the topography contours. However, given the inherent difficulties of inverting amplitude fringes to get the scenario topography, subsequent InSAR systems were developed to record the complex amplitude and phase information at the two antennas, to allow a direct reconstruction of the relative phase of each image point [2, 3].

After the first seminal experiments, the so-called across-track interferometry (XTI-SAR) is nowadays a well-assessed and operative technique for the remote sensing of the Earth surface elevation, making possible the quick and cheap production of digital elevation models (DEMs). As already mentioned, a classic XTI-SAR system estimates the surface height from the phase difference ϕ (the interferometric phase) between the two images collected by two sensors slightly separated by a cross-track baseline. So, an XTI-SAR system operates in viewing angle diversity (spatial diversity), and it can also be seen as an elevation direction of arrival (DOA) estimation technique [4]. The overall relationship between terrain height z and ϕ ^is

z = H − r cos



φ − arccos



− ϕλ 4 π ^b _⊥



(1.2)

where H is the platform altitude, φ is the baseline tilt angle (the angle between the baseline

and the ground range axis), and b _⊥ is the baseline length. The measure of the interferometric

phase ϕ is generally corrupted by the presence of the thermal noise and the so-called speckle,

which can be well modeled as a complex-valued multiplicative stochastic process. To coun-

teract the effects of the resulting phase noise, especially for natural extended targets, it is of-

ten advantageous to make use of some kind of coherent averaging over different sub-images

of the same scene. The sub-images formed during the SAR processing are usually called

looks. For a pixel at fixed range-azimuth coordinates, let g ₁ (n) and g 2 (n), n = 1, . . . , N, be

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the pixel complex amplitudes for N looks ¹ . Therefore, the maximum likelihood estimator of the interferometric phase is given by:

ϕ ˆ = arg ( N

n=1 ∑

g ₁ (n) g ^∗ ₂ (n) )

(1.3)

where symbol ^∗ denotes the conjugate operator. It is worth noting that the interferometric processing of two SAR images needs the set up of specific pre-processing procedures. First of all, each SAR image must be focused preserving the phase information, and compensat- ing the undesired platform motion instabilities, especially in the airborne case. Then, the two complex SAR images must be co-registered with sub-pixel accuracy and spatially smoothed.

Subsequently, the interferometric phase can be estimated through (1.3) and unwrapped to remove the 2 π ambiguities. Finally, the height can be computed, geocoded, and converted into a desired cartographic reference system. Each of these steps represents a specific tech- nical and research field per se. Classical two-channels XTI-SAR has also been extended to process more than one single baseline in order to reduce problems of data noise and phase ambiguity [3, 4].

More generally, in addition to measuring the topography, InSAR represents a powerful technique also for measuring changes over both short- and long-time scale, and other changes in the detailed characteristics of the monitored surface. The key idea is to change the kind of diversity among the two complex-valued SAR images [2]. When the diversity parameter is the acquisition time, the technique is called along track interferometry (ATI-SAR). This technique was advanced for the first time by Goldstein and Zebker in 1987, and experimented by the same authors by augmenting a conventional airborne SAR system with an additional aperture, separated on the fuselage of the aircraft. If the flight path and imaging geometries of all the SAR observations are identical, any interferometric phase difference is due to changes over time of the SAR system clock, variable propagation delay, or surface motion in the direction of the radar line of sight. However, for short (fraction of second) time scales clock drift and propagation delay are negligible, and ATI-SAR can be used to measure small velocities (e.g. ocean currents, moving vehicles). In the ideal case, since the two antennas are arranged along the flight track of a single platform, there is no cross-track separation of the aperture, and therefore no sensitivity to topography.

ATI-SAR can also be regarded as a particular case of repeat-pass interferometry, which can be used to generate topography and motion at the same time. If the repeat flight path result in a cross-track separation, and the surface has not changed between observations, then the repeat-track observation pair will act as an interferometer for the topography mea- surement. On the other hand, if there is no cross-track separation, there is no sensitivity to topography and radial motion can be measured directly. Since the temporal separation between observation is typically hours to days, the ability to detect small radial velocities is substantially better than a conventional ATI-SAR [4]. First investigations of repeat track interferometry for velocity mapping were carried out by Goldstein in 1993 over the Rutford ice stream in Antarctica with ERS-1 data. More commonly, the track of the sensor does not repeat itself exactly, thus the time-induced phase comprises both the topographic phase and the one originated by the surface or the radial movement. In this case, in the last two decades, specific procedures have been developed to measure surface displacements by get- ting rid of the topography. These techniques are referred to as differential SAR interferometry

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The range and azimuth coordinates have been dropped to simplify the notation.

Chapter 1 - Introduction

(D-InSAR) [2, 4]. In this approach, at least three images are required to form two interfer- ometric phase measurements: in the simplest case, one pair of the images is assumed to contain the signature of the topography only, while the other pair measures topography and change. This is generally true as the cross-track baselines of the two interferometric combi- nations are rarely the same. Nowadays, D-InSAR is a mature technique based on possibly more than three SAR acquisitions. In this context, two operative techniques are persistent scatterer interferometry (PSI) [6] and D-InSAR stacking [7]. The former operates at a high horizontal resolution scale, and focuses on point-like scatterers, while the latter operates at a low resolution scale, assuming distributed scattering. The possibility has been widely demonstrated of accurately detecting and mapping centimeter to millimeter scale deforma- tions of the ground, and monitoring buildings, glacier flows and slope instabilities with large coverage, high density of measures and low cost.

1.3 Multidimensional imaging: SAR Tomography and Dif- ferential SAR Tomography

A basic limitation of conventional InSAR and D-InSAR techniques is that they do not pro- vide resolving capability along the elevation dimension, i.e. they are not able to distinguish multiple different backscattering sources present in the same range azimuth cell. This corre- sponds to the well known layover condition, in which the imaged area is characterized by the presence of a steep enough surface topography, generating critical projection of the scatterers in the slant imaging geometry, or by a high spatial density of strong scatterers. This condi- tion is common also for volumetric scenarios such as forested areas, glaciers, and arid zones, especially for low frequency SARs, and it is frequent when data are acquired over complex scenarios such as urban areas or large structures and infrastructures [3, 8, 9]. In Fig. 1.1 two examples of layover geometries are shown in urban and forest scenarios, also highlighting different types of scattering mechanisms. Existing InSAR and D-InSAR algorithms can not separate the multiple scattering phenomena in the same pixel, thus degrade or can not operate in these conditions.

SAR 3-D tomography (Tomo-SAR) is a quite recent way of overcoming limitations of standard algorithms for target height determination by achieving fully focused 3-D images [9–11]. Starting from multibaseline (MB) data, it is possible to separate multiple scatter- ers at different heights in any given range-azimuth cell, and to produce a continuous radar reflectivity profile along the height direction. In fact, Tomo-SAR exploits an aperture syn- thesis also along the vertical plane, that is the height-ground range plane, to obtain full 3-D imaging through elevation beam forming (BF) [9, 12, 13]. In this framework, in addition to the phase, it is well-known that the amplitude information of the received signal is useful in order to exploit the modulation induced by the beating phenomena for the separation of the multiple signal components, and to possibly enhance statistical accuracy even for a single scatterer. Given its capabilities of imaging the distribution of the scatterers along the height direction, Tomo-SAR is a good candidate for the analysis of complex scenarios, adding more features, e.g., for biomass estimation, forest classification, tree and building height estima- tion, and other geophysical parameter extraction problems; interest is growing also for ice thickness monitoring. The Tomo-SAR concept was successfully demonstrated by means of experiments with anechoic chamber in controlled conditions [10] and live recorded airborne L-band data [9]. Other experiments have been carried out with the conventional Fourier-

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(a) Urban scenario

(b) Forest scenario

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Chapter 1 - Introduction

based tomographic processor exploiting repeat-pass satellites acquisitions over a scene con- taining a corner reflector [11]. Research efforts have concentrated so far on improving the typical unsatisfactory 3-D imaging quality of conventional Fourier-based Tomo-SAR due to the typically limited and sparse baseline distribution, see e.g. [8, 9, 12–16]. In particular, tomographic processors framed in the general context of linear inverse problems [12] or of advanced spatial spectral estimation [8, 13] have been proposed to overcome the mentioned limitations.

Nevertheless, the observed scenes are generally non-stationary, as deformation motions and temporal decorrelation generally occur during the repeat-pass MB acquisitions. This can cause height misplacement or defocusing effects in the Tomo-SAR imaging process [17].

Moreover, although Tomo-SAR can separate multiple scatterers, it has no measuring sensi- tivity to their deformation motion. First efforts to extend D-InSAR to the multiple scatterer case has been recently proposed in [18] and [19]. In particular, the very recent general framework of differential SAR tomography (Diff-Tomo, sometimes also referred to as “4-D”

Diff-Tomo), a technique firstly originated at the Department of Information Engineering of the University of Pisa, exploits MB-repeat pass (or, equivalently, multitemporal) data, and deeply integrates Tomo-SAR and D-InSAR in an unified framework. A joint resolution and estimation is then allowed of the heights and the radial velocities of the multiple scatterers in the same cell through a 2-D space-time “beam” forming in the height-velocity plane [19].

For this reason, Diff-Tomo-based techniques are powerful candidates for the analysis of lay- over urban scenarios, e.g. subjected to subsidence. The concept has been demonstrated with spaceborne data over an urban area with layover elevation-concentrated scatterers [20, 21].

It is worth noting that Diff-Tomo has a rich output, consisting in a power distribution in the heigth-velocity plane, allowing a wider range of applications [22]. It has been shown that Diff-Tomo potentially enables a volumetric differential interferometry, in which the continu- ous profiling could be possible of the velocity versus the height, jointly with a reconstruction of non-blurred tomo profile, for moving layered volumetric scatterers (e.g. a moving glacier) and deformation velocity estimation of buried scatterers (e.g. sub-canopy). From a more general point of view, Diff-Tomo has potentials of identifying scattering components inten- sity distributions in the joint domain of spatial (height) and temporal frequency (phase rate of change) of harmonics in which a signal from a scattering component can be decomposed, avoiding their misinterpretation [22, 23].

Tomo-SAR and Diff-Tomo have been recently unified in a framework named multidi- mensional SAR imaging [24], given their capability to perform fully 3-D analyses in space and space plus the temporal dimension, respectively. It is worth remarking that multidimen- sional imaging can be more generally included among the experimental techniques based on the coherent combination of SAR images at the complex (amplitude and phase) data level, which have gained increasing attention from the SAR community in the last decade. They allow the extraction of a more rich and/or accurate information on the observed scene w.r.t.

the phase-only InSAR techniques. Coherent techniques have then been conceived exploit- ing also the polarimetric information. As an example, in the analysis of forest scenario, Tomo-SAR super-resolution methods may not achieve a sufficiently fine height resolution to separate different scattering mechanisms, which could also be present at the same height, especially in forest scenarios. A first effort to overcome these difficulties is represented by polarimetric interferometry (Pol-InSAR), which retrieves the forest parameters through a model-based inversion starting from multipolarimetric data [25]. Pol-InSAR has then been extended to polarimetric Tomo-SAR (PolTomo-SAR) [26–28], which starting from MB-

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multipolarimetric data improves the accuracy of the estimation of the vertical position of the imaged scatterers, and estimates a set of normalized complex coefficients characterizing the corresponding polarimetric scattering mechanism. More recently, also a (possibly non model-based) algebraic decomposition of MB-multipolarimetric data has been proposed for mechanism separation [29]. It is also worth observing that the development of this kind of coherent techniques goes in parallel to the growth of the number of SAR images relative to a same scene. Archives associated to SAR spaceborne sensors are getting filled by data collected with time and observation angle diversity (MB-multipass data), and with the new high resolution systems also with polarization diversity. Moreover, current system planning trends in the SAR field involve clusters of cooperative formation-flying satellites with capa- bility of multiple simultaneous acquisitions, airborne systems with multibaseline acquisition capability in a single pass are also experimented, and unmanned air vehicles with capability of differential monitoring of rapid phenomena are incoming.

1.4 Contributions and outline of the thesis

This thesis is focused on the development and the experimentation on simulated and real radar data of tomographic SAR techniques for the analysis of complex scenarios, in which multiple scattering contribution are interfering from different heights in the same SAR cell.

In this context, the contributions of this thesis are the following:

• the development of Cram´er-Rao lower bound (hybrid and not) formulations for the characterization of the achievable precision limits in height and height/deformation velocity estimation through 3-D SAR Tomography and Differential Tomography, re- spectively;

• the extensive experimentation on real urban and forest data of a radiometrically non- linear, high contrast and adaptive 3-D imaging technique based on the Capon spatial spectral estimator;

• the proposal and the experimentation of a pre-processing technique for the 3-D imag- ing with low radar bandwith data aimed at the reduction of the bandwidth-induced detrimental perspective effects along the vertical direction. The proposed solution is based on the common band pre-filtering of the data, a well known principle in InSAR.

The importance of this issue is motivated by the requirements on the signal bandwidth of P-band radars, whose emitted radiation could interfere with existing emitting ground systems;

• the development and experimentation of a knowledge-based imaging technique based on data interpolation for a high contrast linear tomography; this technique makes use of an a priori information about the height sector containing the scatterers in a given SAR cell, and can also deal with single look multibaseline data corrupted by miscalibration residuals;

• the development and experimentation with real urban data of an algorithm for the iden- tification (i.e. detection and height or height/deformation velocity estimation) of mul- tiple layover scatterers in the same SAR cell for the monitoring of ground structures.

The presented technique is based on the tomographic/differential tomographic adap-

tive analysis of the cell under test, followed by a model-based fitting in the complex

Chapter 1 - Introduction

data domain. A proper thresholding system has been designed in order to counteract the possible data non-idealities;

• the proposal and the experimentation of Tomo-SAR based techniques for the anal- ysis of volumetric scatterers in forest scenarios. In particular, model-based and not techniques have been taken into account for the extraction of the digital terrain model under the canopy. Moreover, an original solution based on multiband filters has been proposed to obtain a multibaseline coherent (i.e. amplitude and phase) dataset with only the signal components of interest, e.g. the components related to the ground or the canopy scatterer only, which could be useful for further interferometric analyses;

• the proposal of algorithms exploiting the Differential Tomography framework for the 3-D analysis of non-stationary volumetric scatterers, as forested areas subjected to temporal decorrelation. In particular, solutions are proposed for the tomographic pro- filing robust to the blurring effects due to the temporal decorrelation, and first results are shown of the accuracy obtained in the estimation of the forest canopy height with real data.

The remainder of this thesis is structured as follows.

In Chapter 2, the Tomo-SAR concept is briefly presented, and its interpretation as a spectral estimation problem along the height dimension is shown on a theoretical basis. Af- terwards, Cram´er-Rao lower bounds on the height estimation with Tomo-SAR are derived.

Then, 3-D imaging methods are experimented with simulated and real urban and forest multi- baseline data. In particular, in order to obtain an high contrast tomographic imaging (i.e. with low sidelobes) two solutions are the taken into account. The first one is non-linear, and it is based on the data-adaptive Capon spectral estimator. The second one is linear, and it is based on the data interpolation along the interferometric array exploiting an a priori infor- mation about the height sector containing the scatterers to be imaged. Differently from the non-linear option, it does not possess height super-resolution capabilities, although it can re- duce the sidelobe amplitude also by operating with single look data. Finally, the well-known interferometric concept of common band pre-filtering of the data is applied for mitigating the detrimental perspective effects in height arising in the tomographic profiling with low bandwidth radar signals.

In Chapter 3 the problem of the identification of multiple scatterers in layover in the same cell is afforded. Since the detection step can be rather complicated (even in its basic form), here it has been tackled by resorting to a sub-optimal hybrid detection technique which combines the adaptive tomography and a complex data domain model fitting, properly robustified against data non-idealities. The results obtained with real multibaseline data over the city of Rome have also been pre-validated through the geocoding of the 3-D coordinates (range, azimuth, height) of the identified scatterers.

Chapter 4 shows experimentally how Tomo-SAR can be used for the analysis of volu- metric forest scenarios. Here we show how the 3-D separation of ground and canopy can be exploited e.g. to obtain the ground height depurated from the height bias originated by the presence of the volume, contrarily to a non 3-D technique (e.g. classical InSAR). Further- more, a multiband matrix filter is proposed to isolate the ground and canopy contributions in two different coherent multibaseline datasets. In this case, a preliminary Tomo-SAR analysis is required for determinating the filter settings. The datasets available after filtering can be used for the application of interferometric techniques originally conceived to work with data containing a single scattering layer in height.

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In Chapter 5 the Tomo-SAR concept is extended to the Diff-Tomo concept in order to handle non-stationary scenarios, in which the layover scatterers are affected by deformation movements (e.g. those caused by subsidence) and/or temporal decorrelation. Analogously to Chapter 2, it will be shown that the Diff-Tomo imaging problem can be seen as a 2- D spectral estimation problem in the height-deformation velocity plane. Afterwards, the Cram´er-Rao bounds of Chapter 2 are extended in the Diff-Tomo framework. As a study case, their use is shown for the performance prediction in the DEM estimation with multistatic acquisitions affected by temporal decorrelation and a collective phase shift from pass to pass of the distributed interferometer. Afterwards, an extension is presented of the scatterer identification technique of Chapter 3 to the Diff-Tomo framework, and the results obtained in scatterers height and deformation velocity estimation with a spaceborne dataset over the city of Naples are discussed. Finally, the Diff-Tomo processing is used also for the analysis of forested scenarios affected by temporal decorrelation. In this case, two issues are addressed.

Firstly, we show how Diff-Tomo can furnish a non-blurred Tomo-SAR profile in presence of temporal decorrelation, restoring the possibility of resolution of the ground and the canopy scatterers. Secondly, we show that a Diff-Tomo processor can lead to an enhanced parameter estimation accuracy w.r.t. a Tomo-SAR processor with temporal decorrelated data. Both aspects have been investigated by means of super-resolution model based techniques, whose employment is crucial for scenarios in which the resolution is a critical factor.

Finally, Chapter 6 draws some conclusions of the entire work, discussing open issues and

further perspectives for the tomographic imaging.

Chapter 1 - Introduction

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