PhD Alumni

Tebaldini Stefano

Present position: Temporary Researcher

Thesis title:  Multi-Baseline SAR Imaging: Models and Algorithms
Advisor:  Andrea Monti Guarnieri
Research area:  Signals
Thesis abstract:  
This research focuses on the joint processing of multiple airborne or spaceborne Synthetic Aperture Radar (SAR) images for the remote sensing of the Earth’s surface. From a theoretical point of view, there are two possible ways to face this subject. One is to start from the concepts developed in the analysis of a single image pair, namely from conventional SAR Interferometry, and note that the inclusion in the analysis of further images results in the possibility to improve the accuracy of the results, or even to enlarge the set of the unknowns to be inferred from the data. This perspective is, in a sense, historical, as it reflects the time-line of the developments presented in the literature of the last years. A different point of view is instead that to consider a multi-image SAR system as a complete 3D imaging tool for the portion of the Earth’s surface into which the transmitted wave penetrates. This point of view is in a sense similar to what is commonly done in the field of Seismic Processing, by exploiting the concept of Diffraction Tomography. In other words, if an infinite number of images were available, then the 3D structure of the upper layer of the Earth could be completely reconstructed from SAR data without the need of any a-priori information. This perspective is clearly ideal, as the sparsity and the low number of the acquisitions available in real cases would result in a significant degradation of the SAR 3D imaging capabilities. Moreover, a further degradation has to be accounted for in the case where the SAR acquisitions are taken at different times, as a result of the changes undergone by the imaged scene. Such degradations, however, can be recovered, or at least mitigated, by including some a priori information about the imaged scene or, in other words, by representing the scene through models, in such a way as to pass from the problem of 3D reconstruction to that of model inversion. Clearly, the choice of the model in practical applications is subjected to the characteristics of the imaged scene and the acquisition system. A strongly structured model is mandatory in the case of a small data-set, but it can also be the only reasonable choice for the analysis of large data-sets if the SAR sensor operates at shorter wavelengths, due to the poor penetration of the wave into the Earth’s surface. This is the framework in which this dissertation will take place. Accordingly, this thesis has been thought in such a way as to gradually move from a totally unstructured model, where the scene is merely represented as an ensemble of scatterers, to a strongly structured model, where scattering from a single target is assumed. The first case gives rise to the basic formulation of SAR Tomography (T-SAR), while the latter corresponds to the general assumption within SAR Interferometry (InSAR).

The least structured model to be considered in this work is the one corresponding to the sole hypothesis of temporal stability. By virtue of its simplicity, this approach will be shown to provide many useful insights about the nature of the reconstruction problem. In particular, it will be shown that:
• In distributed target environments the vertical resolution is determined not only by baseline aperture, but also by pulse bandwidth, as a consequence of the fact that T-SAR resolution capabilities are limited to sensing target projections along the cross range direction.
• In presence of Propagation Disturbances, the scene reconstruction is affected by a convolutive distortion. The impact of such phenomenon has been shown to be more severe in the case where the scene under analysis is characterized by a complex vertical structure, therefore leading to the conclusion that T-SAR analyses require the employment of more accurate phase calibration techniques with respect to InSAR analyses.

The dissertation will then focus on the problem of T-SAR of forested areas, assuming a two layered scenario constituted by ground and tree canopies. The challenge with such kind of analysis is that the vertical separation between the ground and the tree canopies is often well below the vertical resolution that is determined by baseline aperture and pulse bandwidth. Hence, the ideal tomographic processor has to be capable of super-resolving the targets while properly accounting for the statistics of each. Accordingly, a statistical model will be formulated to explicitly account for the presence of multiple distributed targets. On the basis of this model, a ML based technique will be proposed to yield a quantitative characterization of forested sites in terms of ground and canopy elevation, identification of bald and forested areas, and assessment of the contributions to the total backscatter power associated to the ground and to the canopy. Furthermore, it will be shown that such technique is suited to the treatment of both single and multi-polarimetric channel data, resulting in the possibility to separate the polarimetric signatures associated to ground and canopy scattering. As a case study, an extensive polarimetric-tomographic analysis of the forest site of Remningstorp, Sweden, will be shown, basing on a data-set of 9 P-Band, fully polarimetric SAR images acquired by the DLR's airborne system E-SAR in the framework of the ESA experiment BioSAR.

InSAR applications will be treated in the final part of the dissertation, under the basic hypothesis that a single target, either point-like or distributed, is present within the system resolution cell. A model of the data will be formulated that takes into account both target statistics and the presence of propagation disturbances, through which a discussion will be provided about the lower bounds of the accuracy achievable by InSAR. It will be shown that this approach leads to a viable evaluation of InSAR performance as a function of system configuration, target decorrelation, and extent of the propagation disturbances. A novel framework for conducting InSAR analyses over scene dominated by decorrelating scatterers will be proposed. The basic idea is to split the estimation process into two steps. The first step employs a maximum likelihood (ML) estimator jointly process all the available acquisitions in order to yield the best estimates of the interferometric phases. Then, the second step is required to separate the contributions to the interferometric phases due to the scene topography and deformation field from those due to decorrelation noise and atmospheric disturbances. It will be shown that the estimates yielded through this two-step approach are asymptotically unbiased and minimum variance. Experimental evidence supporting the validity of these concepts will be shown by reporting the results relative to the interferometric analysis of a desert area near Las Vegas, USA, basing on a data-set of 18 SAR images acquired by the ASAR sensor aboard ENVISAT.