Very High Resolution Sar Tomography via Compressive Sensing

By using multi-pass SAR acquisitions, 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 (depending on the elevation aperture size) is at least an order of magnitude lower than in range and azimuth. Hence, superresolution 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 4D (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 data is presented. In addition, the model based time warp method for differential tomographic non-linear motion monitoring is proposed and validated by reconstructing seasonal motion (caused by thermal expansion) of a building complex.