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Differential SAR tomography extends the synthetic aperture principle into the elevation and time directions for 4-D imaging. With modern meter-resolution space-borne SAR systems like TerraSAR-X (TS-X), systematic tomographic imaging of urban infrastructure and its deformations becomes feasible. We demonstrate the potential of TS-X data for this purpose and introduce several novel concepts. Since building deformation in general is nonlinear, e.g. due to thermal dilation, we start from a tomographic system formulation that is general enough to allow for the inclusion of motion models (linear, periodic, etc.). By appropriate warping of the time axis we map the motion model function to become linear and lead to a peak in the spectral domain. For the differential tomographic inversion itself we propose a 2-D compressive sensing (CS) based approach - “SL1MMER”. We demonstrate the super-resolution power and the robustness of SL1MMER both with simulated and with real data. We also show that it provides an attractive compromise between parametric and non-parametric methods. A full reconstruction of a building complex and its seasonal deformation from a stack of TS-X spotlight data is finally presented.