Tomographic SAR Inversion by L1 Norm Regularization – The Compressive Sensing Approach

Abstract

SAR tomography (TomoSAR) extends the synthetic aperture principle into the elevation direction for 3-D imaging. The resolution in the elevation direction depends on the size of the elevation aperture, i.e. on the spread of orbit tracks. Since the orbits of modern meter-resolution space-borne SAR systems, like TerraSAR-X, are tightly controlled, the tomographic elevation resolution is at least an order of magnitude lower than in range and azimuth. Hence, super-resolution reconstruction algorithms are desired. The high anisotropy of the 3D tomographic resolution element renders the signals sparse in the elevation direction; only a few point-like reflections are expected per azimuth-range cell. This property suggests using compressive sensing (CS) methods for tomographic reconstruction. The paper presents the theory of 4-D (differential, i.e. space-time) CS TomoSAR and compares it with parametric (nonlinear least-squares) and non-parametric (singular value decomposition) reconstruction 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.