Realistic Lower Bound on Elevation Estimation for Tomographic SAR

The noise in a tomographic synthetic aperture radar (Tomo-SAR) model is normally assumed to be independent and identically distributed (i.i.d.) Gaussian. In this paper, the correlated Tomo-SAR model is introduced by studying the effect of random residual phase and correlated additive Gaussian noise, and a realistic and general hybrid Cramér-Rao bound (HCRB) on elevation estimation is derived for such a model. Then, a simplified calculation of the HCRB is proposed when the bound of elevation is the main focus. Computer simulations are performed to analyze the proposed HCRB for elevation estimation. The results obtained from estimators based on compressive sensing and distributed compressive sensing show that the proposed HCRB can provide a more realistic bound than the CRB derived with the white additive noise and perfect phase compensation assumption. This is also validated through processing results on real data acquired by TerraSAR-X/Tandem-X sensors

Non-Local Compressive Sensing Based SAR Tomography

Tomographic SAR (TomoSAR) inversion of urban areas is an inherently sparse reconstruction problem and, hence, can be solved using compressive sensing (CS) algorithms. This paper proposes solutions for two notorious problems in this field: 1) TomoSAR requires a high number of data sets, which makes the technique expensive. However, it can be shown that the number of acquisitions and the signal-to-noise ratio (SNR) can be traded off against each other, because it is asymptotically only the product of the number of acquisitions and SNR that determines the reconstruction quality. We propose to increase SNR by integrating non-local estimation into the inversion and show that a reasonable reconstruction of buildings from only seven interferograms is feasible. 2) CS-based inversion is computationally expensive and therefore barely suitable for large-scale applications. We introduce a new fast and accurate algorithm for solving the non-local L1-L2-minimization problem, central to CS-based reconstruction algorithms. The applicability of the algorithm is demonstrated using simulated data and TerraSAR-X high-resolution spotlight images over an area in Munich, Germany.Comment: 10 page

Advances and Experiments of Tomographic SAR Imaging for the Analysis of Complex Scenarios

It is expected that the number of synthetic aperture radar (SAR) images available for a same scene will increase exponentially in the future, thanks to the technical developments in this area. In order to fully exploit the information lying in data acquired in looking angle (multibaseline, MB), time, and polarization diversity, developments are underway of processing techniques which constitute an evolution of the mature phase-only SAR interferometry for producing new and/or more accurate measures. In particular, by combining coherently (i.e. amplitude and phase) the SAR data, new opportunities are arising for an improved imaging and information extraction of the observed scene. Among these techniques, a very promising advance is constituted by SAR Tomography, a MB interferometric mode allowing a full 3-D imaging in the range-azimuth-height space, thus separating multiple scatterers in layover at different heights in the same SAR cell in complex scenarios. Recently, a new interferometric mode called Differential SAR Tomography has been conceived at the University of Pisa from the synergic fusion of SAR Tomography and the conventional Differential Interferometry, allowing the estimation of also the possible relative deformations between multiple layover scatterers. In this thesis, theoretical advances and experimental results are presented in the analysis of complex scenarios. In particular, the tomographic imaging problem is addressed by exploring different algorithmic options able to enhance the image contrast and possibly also increase the scatterer resolution in height. Moreover, in order to automate the estimation of the height or height/deformation velocity, a scatterer detection algorithm has been developed, which constitutes also a preliminary step for the extensive validation of the information extracted. With regards to volumetric scatterers (e.g. the scatterer in forest scenarios), tomography-based coherent data combination techniques have been proposed and investigated, in particular for the extraction of the sub-canopy digital terrain model and for deriving in a non-model based fashion a coherent MB dataset with only the signal from the scattering layer of interest. Finally, the differential tomographic framework has been exploited for the robust tomographic analysis of temporal decorrelating volumetric scatterers. For each investigated topic, extensive experiments have been carried out with MB urban and forest SAR data

Approches tomographiques structurelles pour l'analyse du milieu urbain par tomographie SAR THR : TomoSAR

SAR tomography consists in exploiting multiple images from the same area acquired from a slightly different angle to retrieve the 3-D distribution of the complex reflectivity on the ground. As the transmitted waves are coherent, the desired spatial information (along with the vertical axis) is coded in the phase of the pixels. Many methods have been proposed to retrieve this information in the past years. However, the natural redundancies of the scene are generally not exploited to improve the tomographic estimation step. This Ph.D. presents new approaches to regularize the estimated reflectivity density obtained through SAR tomography by exploiting the urban geometrical structures.La tomographie SAR exploite plusieurs acquisitions d'une même zone acquises d'un point de vue légerement différent pour reconstruire la densité complexe de réflectivité au sol. Cette technique d'imagerie s'appuyant sur l'émission et la réception d'ondes électromagnétiques cohérentes, les données analysées sont complexes et l'information spatiale manquante (selon la verticale) est codée dans la phase. De nombreuse méthodes ont pu être proposées pour retrouver cette information. L'utilisation des redondances naturelles à certains milieux n'est toutefois généralement pas exploitée pour améliorer l'estimation tomographique. Cette thèse propose d'utiliser l'information structurelle propre aux structures urbaines pour régulariser les densités de réflecteurs obtenues par cette technique

Autofocus and Back-Projection in Synthetic Aperture Radar Imaging.

Spotlight-mode Synthetic Aperture Radar (SAR) imaging has received considerable attention due to its ability to produce high-resolution images of scene reflectivity. One of the main challenges in successful image recovery is the problem of defocusing, which occurs due to inaccuracies in the estimated round-trip delays of the transmitted radar pulses. The problem is most widely studied for far-field imaging scenarios with a small range of look angles since the problem formulation can be significantly simplified under the assumptions of planar wavefronts and one-dimensional defocusing. In practice, however, these assumptions are frequently violated. MultiChannel Autofocus (MCA) is a subspace-based approach to the defocusing problem that was originally proposed for far-field imaging, with a small range of look angles. A key motivation behind MCA is the observation that there exists a low-return region within the recovered image, due to the weak illumination near the edges of the antenna footprint. The strength of the MCA formulation is that it can be easily extended to more realistic scenarios with polar-format data, spherical wavefronts, and arbitrary terrain, due to its flexible linear-algebraic framework. The main aim of this thesis is to devise a more broadly effective autofocus approach by adopting MCA to the aforementioned scenarios. By forming the solution space in a domain where the defocusing effect is truly one-dimensional, we show that drastically improved restorations can be obtained for applications with small to fairly wide ranges of look angles. When the terrain topography is known, we utilize the versatile backprojection-based imaging methods in the model formulations for MCA to accurately account for the underlying geometry. The proposed extended MCA shows reductions in RMSE of up to 50% when the underlying terrain is highly elevated. We also analyze the effects of the filtering step, the amount of wave curvature, the shape of the terrain, and the flight path of the radar, on the reconstructed image via backprojection. Finally, we discuss the selection of low-return constraints and the importance of using terrain elevation within MCA formulation.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135868/1/zzon_1.pd

Region-enhanced passive radar imaging

The authors adapt and apply a recently-developed region-enhanced synthetic aperture radar (SAR) image reconstruction technique to the problem of passive radar imaging. One goal in passive radar imaging is to form images of aircraft using signals transmitted by commercial radio and television stations that are reflected from the objects of interest. This involves reconstructing an image from sparse samples of its Fourier transform. Owing to the sparse nature of the aperture, a conventional image formation approach based on direct Fourier transformation results in quite dramatic artefacts in the image, as compared with the case of active SAR imaging. The regionenhanced image formation method considered is based on an explicit mathematical model of the observation process; hence, information about the nature of the aperture is explicitly taken into account in image formation. Furthermore, this framework allows the incorporation of prior information or constraints about the scene being imaged, which makes it possible to compensate for the limitations of the sparse apertures involved in passive radar imaging. As a result, conventional imaging artefacts, such as sidelobes, can be alleviated. Experimental results using data based on electromagnetic simulations demonstrate that this is a promising strategy for passive radar imaging, exhibiting significant suppression of artefacts, preservation of imaged object features, and robustness to measurement noise

Geodetic monitoring of complex shaped infrastructures using Ground-Based InSAR

In the context of climate change, alternatives to fossil energies need to be used as much as possible to produce electricity. Hydroelectric power generation through the utilisation of dams stands out as an exemplar of highly effective methodologies in this endeavour. Various monitoring sensors can be installed with different characteristics w.r.t. spatial resolution, temporal resolution and accuracy to assess their safe usage. Among the array of techniques available, it is noteworthy that ground-based synthetic aperture radar (GB-SAR) has not yet been widely adopted for this purpose. Despite its remarkable equilibrium between the aforementioned attributes, its sensitivity to atmospheric disruptions, specific acquisition geometry, and the requisite for phase unwrapping collectively contribute to constraining its usage. Several processing strategies are developed in this thesis to capitalise on all the opportunities of GB-SAR systems, such as continuous, flexible and autonomous observation combined with high resolutions and accuracy. The first challenge that needs to be solved is to accurately localise and estimate the azimuth of the GB-SAR to improve the geocoding of the image in the subsequent step. A ray tracing algorithm and tomographic techniques are used to recover these external parameters of the sensors. The introduction of corner reflectors for validation purposes confirms a significant error reduction. However, for the subsequent geocoding, challenges persist in scenarios involving vertical structures due to foreshortening and layover, which notably compromise the geocoding quality of the observed points. These issues arise when multiple points at varying elevations are encapsulated within a singular resolution cell, posing difficulties in pinpointing the precise location of the scattering point responsible for signal return. To surmount these hurdles, a Bayesian approach grounded in intensity models is formulated, offering a tool to enhance the accuracy of the geocoding process. The validation is assessed on a dam in the black forest in Germany, characterised by a very specific structure. The second part of this thesis is focused on the feasibility of using GB-SAR systems for long-term geodetic monitoring of large structures. A first assessment is made by testing large temporal baselines between acquisitions for epoch-wise monitoring. Due to large displacements, the phase unwrapping can not recover all the information. An improvement is made by adapting the geometry of the signal processing with the principal component analysis. The main case study consists of several campaigns from different stations at Enguri Dam in Georgia. The consistency of the estimated displacement map is assessed by comparing it to a numerical model calibrated on the plumblines data. It exhibits a strong agreement between the two results and comforts the usage of GB-SAR for epoch-wise monitoring, as it can measure several thousand points on the dam. It also exhibits the possibility of detecting local anomalies in the numerical model. Finally, the instrument has been installed for continuous monitoring for over two years at Enguri Dam. An adequate flowchart is developed to eliminate the drift happening with classical interferometric algorithms to achieve the accuracy required for geodetic monitoring. The analysis of the obtained time series confirms a very plausible result with classical parametric models of dam deformations. Moreover, the results of this processing strategy are also confronted with the numerical model and demonstrate a high consistency. The final comforting result is the comparison of the GB-SAR time series with the output from four GNSS stations installed on the dam crest. The developed algorithms and methods increase the capabilities of the GB-SAR for dam monitoring in different configurations. It can be a valuable and precious supplement to other classical sensors for long-term geodetic observation purposes as well as short-term monitoring in cases of particular dam operations

ARRAY PROCESSING TECHNIQUES FOR ESTIMATION AND TRACKING OF AN ICE-SHEET BOTTOM

Ice bottom topography layers are an important boundary condition required to model the flow dynamics of an ice sheet. In this work, using low frequency multichannel radar data, we locate the ice bottom using two types of automatic trackers. First, we use the multiple signal classification (MUSIC) beamformer to determine the pseudo-spectrum of the targets at each range-bin. The result is passed into a sequential tree-reweighted message passing belief-propagation algorithm to track the bottom of the ice in the 3D image. This technique is successfully applied to process data collected over the Canadian Arctic Archipelago ice caps in 2014, and produce digital elevation models (DEMs) for 102 data frames. We perform crossover analysis to self-assess the generated DEMs, where flight paths cross over each other and two measurements are made at the same location. Also, the tracked results are compared before and after manual corrections. We found that there is a good match between the overlapping DEMs, where the mean error of the crossover DEMs is 38±7 m, which is small relative to the average ice-thickness, while the average absolute mean error of the automatically tracked ice-bottom, relative to the manually corrected ice-bottom, is 10 range-bins. Second, a direction of arrival (DOA)-based tracker is used to estimate the DOA of the backscatter signals sequentially from range bin to range bin using two methods: a sequential maximum a posterior probability (S-MAP) estimator and one based on the particle filter (PF). A dynamic flat earth transition model is used to model the flow of information between range bins. A simulation study is performed to evaluate the performance of these two DOA trackers. The results show that the PF-based tracker can handle low-quality data better than S-MAP, but, unlike S-MAP, it saturates quickly with increasing numbers of snapshots. Also, S-MAP is successfully applied to track the ice-bottom of several data frames collected from over Russell glacier in 2011, and the results are compared against those generated by the beamformer-based tracker. The results of the DOA-based techniques are the final tracked surfaces, so there is no need for an additional tracking stage as there is with the beamformer technique

The European Space Agency BIOMASS mission: Measuring forest above-ground biomass from space

The primary objective of the European Space Agency's 7th Earth Explorer mission, BIOMASS, is to determine the worldwide distribution of forest above-ground biomass (AGB) in order to reduce the major uncertainties in calculations of carbon stocks and fluxes associated with the terrestrial biosphere, including carbon fluxes associated with Land Use Change, forest degradation and forest regrowth. To meet this objective it will carry, for the first time in space, a fully polarimetric P-band synthetic aperture radar (SAR). Three main products will be provided: global maps of both AGB and forest height, with a spatial resolution of 200 m, and maps of severe forest disturbance at 50 m resolution (where “global” is to be understood as subject to Space Object tracking radar restrictions). After launch in 2022, there will be a 3-month commissioning phase, followed by a 14-month phase during which there will be global coverage by SAR tomography. In the succeeding interferometric phase, global polarimetric interferometry Pol-InSAR coverage will be achieved every 7 months up to the end of the 5-year mission. Both Pol-InSAR and TomoSAR will be used to eliminate scattering from the ground (both direct and double bounce backscatter) in forests. In dense tropical forests AGB can then be estimated from the remaining volume scattering using non-linear inversion of a backscattering model. Airborne campaigns in the tropics also indicate that AGB is highly correlated with the backscatter from around 30 m above the ground, as measured by tomography. In contrast, double bounce scattering appears to carry important information about the AGB of boreal forests, so ground cancellation may not be appropriate and the best approach for such forests remains to be finalized. Several methods to exploit these new data in carbon cycle calculations have already been demonstrated. In addition, major mutual gains will be made by combining BIOMASS data with data from other missions that will measure forest biomass, structure, height and change, including the NASA Global Ecosystem Dynamics Investigation lidar deployed on the International Space Station after its launch in December 2018, and the NASA-ISRO NISAR L- and S-band SAR, due for launch in 2022. More generally, space-based measurements of biomass are a core component of a carbon cycle observation and modelling strategy developed by the Group on Earth Observations. Secondary objectives of the mission include imaging of sub-surface geological structures in arid environments, generation of a true Digital Terrain Model without biases caused by forest cover, and measurement of glacier and icesheet velocities. In addition, the operations needed for ionospheric correction of the data will allow very sensitive estimates of ionospheric Total Electron Content and its changes along the dawn-dusk orbit of the mission