Very high resolution tomographic SAR inversion for urban infrastructure monitoring — a sparse and nonlinear tour

Abstract

Synthetic aperture radar (SAR) is the only way to assess deformation of the Earth’s surface from space on the order of centimeters and millimeters due to its coherent nature and short wavelengths (typically 3-25 cm). In particular, with the launches of new SAR sensors, such as the German TerraSAR-X/TanDEM-X and the Italian COSMO-Skymed satellites, SAR remote sensing from space has made a big leap forward. These satellites deliver SAR data with a very high spatial resolution of up to 1 m, and hence open up for the first time opportunities to use SAR for 2-D, 3-D, 4-D (space-time) or even higher dimensional imaging of urban structures and individual buildings from space. That means the 3-D shape and deformation or subsidence of the individual buildings can be retrieved. A single SAR image can only provide cartographic information in the two native coordinates "azimuth" and "range". In order to retrieve the 3-D position, i.e. including the "elevation" coordinate, as well as motion information of the scattering objects, advanced interferometric SAR techniques are required that exploit stacks of complex-valued SAR images with diversity in space and time. Among them, tomographic SAR inversion, including SAR tomography and differential SAR tomography, provides the most advanced means for 4-D SAR imaging to date. It is a relatively new technique and is not yet exploited with very high resolution SAR data over urban areas. The intention of this thesis is to further develop this technique, and hence, to explore the potential of very high resolution SAR data for urban infrastructure mapping. The work presented in this thesis contributes to the field by addressing the following four new aspects: Very high resolution tomographic SAR inversion is demonstrated using TerraSAR-X spotlight data to provide 3-D and 4-D maps of an entire high rise city area including layover separation. For individual buildings, a high proportion of double scatterers — up to 20% — is detected by using a modified version of the conventional singular value decomposition inversion method followed by model order selection. Due to the tight orbital tube of modern SAR sensors the elevation aperture is small, i.e.the inherent resolution in elevation is about 50 times worse than in azimuth or range. This extreme anisotropy calls for super-resolution algorithms in the elevation direction while maintaining the meter azimuth-range resolution. On the other hand, the high anisotropy of the 3-D tomographic resolution element renders the signals sparse in the elevation direction; only a few point-like reflections are expected per azimuth-range cell. A compressive sensing based algorithm tailored to very high resolution SAR data is developed for tomographic SAR inversion by exploiting the sparsity of the signal in elevation. It is named "Scale-down by L1 norm Minimization, Model selection, and Estimation Reconstruction" (SL1MMER, pronounced "slimmer"). SL1MMER combines the advantage of compressive sensing sparse reconstruction (e.g. super-resolution properties and high point localization accuracy) and amplitude and phase estimation accuracy of linear estimation, and hence gives reliable estimation of the number of scatterers, elevation, motion parameters, amplitude and phase of each scatterer. Furthermore, a practical demonstration of the super-resolution of SL1MMER for SAR tomographic reconstruction is provided with a tremendously increased proportion of detected double scatterers of up to 38%. A systematic performance assessment of the proposed SL1MMER algorithm is performed regarding the elevation estimation accuracy, super-resolution power and robustness. Compared to the Cramér-Rao lower bound, both numeric results and an analytic approximation of the elevation estimation accuracy are provided. It is shown that SL1MMER is an efficient estimator. The super-resolution factors are found by extensive simulations. These establish fundamental bounds for super-resolution of spectral estimators. The achievable super-resolution factors of SL1MMER in the typical parameter range of tomographic SAR are found to be promising and are on the order 1.525. The minimal number of acquisitions required for a robust estimation is derived and given by explicit formulas. Conventional tomographic inversion allows only for the retrieval of linear motion, although motion or deformation of buildings is often nonlinear (periodic, accelerating, stepwise, etc.). A generalized time warp method is developed which enables tomographic SAR to estimate multi-component nonlinear motion by a nonlinear warping of the time axis. All developed methods are validated with both simulated and extensive processing of large volumes of real data from TerraSAR-X. I hope the work presented in this thesis constitutes a substantial contribution to the vision of "a dynamic city model showing the shape and the deformation of each building".