Super-resolution for 4-D SAR Tomography via Compressive Sensing

SAR tomography (TomoSAR) extends the synthetic aperture principle into the elevation direction for 3-D imaging. Since the orbits of modern space-borne SAR systems, like TerraSAR-X, are tightly controlled, the elevation resolution (depends on the elevation aperture size) is at least an order of magnitude lower than in range and azimuth. Hence, super-resolution algorithms are desired. The high anisotropic 3D resolution element renders the signals sparse in elevation. This property suggests using compressive sensing (CS) methods. The paper presents the theory of 4-D (differential, i.e. space-time) CS TomoSAR and compares it with classical tomographic methods. Super-resolution properties and point localization accuracies are demonstrated using simulations and real data. A CS reconstruction of a building complex from TerraSAR-X spotlight date is presented.